64.81/34.08	MAYBE
64.81/34.09	proof of /export/starexec/sandbox2/benchmark/theBenchmark.hs
64.81/34.09	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
64.81/34.09	
64.81/34.09	
64.81/34.09	H-Termination with start terms of the given HASKELL could not be shown:
64.81/34.09	
64.81/34.09	(0) HASKELL
64.81/34.09	(1) IFR [EQUIVALENT, 0 ms]
64.81/34.09	(2) HASKELL
64.81/34.09	(3) BR [EQUIVALENT, 0 ms]
64.81/34.09	(4) HASKELL
64.81/34.09	(5) COR [EQUIVALENT, 18 ms]
64.81/34.09	(6) HASKELL
64.81/34.09	(7) LetRed [EQUIVALENT, 0 ms]
64.81/34.09	(8) HASKELL
64.81/34.09	(9) NumRed [SOUND, 0 ms]
64.81/34.09	(10) HASKELL
64.81/34.09	(11) Narrow [SOUND, 0 ms]
64.81/34.09	(12) AND
64.81/34.09	    (13) QDP
64.81/34.09	        (14) TransformationProof [EQUIVALENT, 0 ms]
64.81/34.09	        (15) QDP
64.81/34.09	        (16) QDPSizeChangeProof [EQUIVALENT, 0 ms]
64.81/34.09	        (17) YES
64.81/34.09	    (18) QDP
64.81/34.09	        (19) MNOCProof [EQUIVALENT, 0 ms]
64.81/34.09	        (20) QDP
64.81/34.09	        (21) NonTerminationLoopProof [COMPLETE, 0 ms]
64.81/34.09	        (22) NO
64.81/34.09	    (23) QDP
64.81/34.09	        (24) TransformationProof [EQUIVALENT, 0 ms]
64.81/34.09	        (25) QDP
64.81/34.09	        (26) QDPSizeChangeProof [EQUIVALENT, 0 ms]
64.81/34.09	        (27) YES
64.81/34.09	    (28) QDP
64.81/34.09	        (29) DependencyGraphProof [EQUIVALENT, 0 ms]
64.81/34.09	        (30) AND
64.81/34.09	            (31) QDP
64.81/34.09	                (32) MRRProof [EQUIVALENT, 1 ms]
64.81/34.09	                (33) QDP
64.81/34.09	                (34) PisEmptyProof [EQUIVALENT, 0 ms]
64.81/34.09	                (35) YES
64.81/34.09	            (36) QDP
64.81/34.09	                (37) QDPSizeChangeProof [EQUIVALENT, 0 ms]
64.81/34.09	                (38) YES
64.81/34.09	    (39) QDP
64.81/34.09	        (40) QDPSizeChangeProof [EQUIVALENT, 0 ms]
64.81/34.09	        (41) YES
64.81/34.09	    (42) QDP
64.81/34.09	        (43) QDPSizeChangeProof [EQUIVALENT, 0 ms]
64.81/34.09	        (44) YES
64.81/34.09	    (45) QDP
64.81/34.09	        (46) MNOCProof [EQUIVALENT, 0 ms]
64.81/34.09	        (47) QDP
64.81/34.09	        (48) InductionCalculusProof [EQUIVALENT, 0 ms]
64.81/34.09	        (49) QDP
64.81/34.09	        (50) TransformationProof [EQUIVALENT, 0 ms]
64.81/34.09	        (51) QDP
64.81/34.09	            (52) TransformationProof [EQUIVALENT, 0 ms]
64.81/34.09	            (53) QDP
64.81/34.09	            (54) DependencyGraphProof [EQUIVALENT, 0 ms]
64.81/34.09	            (55) QDP
64.81/34.09	            (56) TransformationProof [EQUIVALENT, 0 ms]
64.81/34.09	            (57) QDP
64.81/34.09	            (58) DependencyGraphProof [EQUIVALENT, 0 ms]
64.81/34.09	            (59) QDP
64.81/34.09	            (60) TransformationProof [EQUIVALENT, 0 ms]
64.81/34.09	            (61) QDP
64.81/34.09	            (62) DependencyGraphProof [EQUIVALENT, 0 ms]
64.81/34.09	            (63) QDP
64.81/34.09	            (64) TransformationProof [EQUIVALENT, 0 ms]
64.81/34.09	            (65) QDP
64.81/34.09	            (66) DependencyGraphProof [EQUIVALENT, 0 ms]
64.81/34.09	            (67) QDP
64.81/34.09	            (68) TransformationProof [EQUIVALENT, 0 ms]
64.81/34.09	            (69) QDP
64.81/34.09	            (70) DependencyGraphProof [EQUIVALENT, 0 ms]
64.81/34.09	            (71) QDP
64.81/34.09	            (72) TransformationProof [EQUIVALENT, 0 ms]
64.81/34.09	            (73) QDP
64.81/34.09	            (74) TransformationProof [EQUIVALENT, 0 ms]
64.81/34.09	            (75) QDP
64.81/34.09	            (76) TransformationProof [EQUIVALENT, 0 ms]
64.81/34.09	            (77) QDP
64.81/34.09	            (78) TransformationProof [EQUIVALENT, 0 ms]
64.81/34.09	            (79) QDP
64.81/34.09	            (80) TransformationProof [EQUIVALENT, 0 ms]
64.81/34.09	            (81) QDP
64.81/34.09	            (82) DependencyGraphProof [EQUIVALENT, 0 ms]
64.81/34.09	            (83) QDP
64.81/34.09	            (84) TransformationProof [EQUIVALENT, 0 ms]
64.81/34.09	            (85) QDP
64.81/34.09	            (86) DependencyGraphProof [EQUIVALENT, 0 ms]
64.81/34.09	            (87) QDP
64.81/34.09	            (88) TransformationProof [EQUIVALENT, 0 ms]
64.81/34.09	            (89) QDP
64.81/34.09	            (90) TransformationProof [EQUIVALENT, 0 ms]
64.81/34.09	            (91) QDP
64.81/34.09	            (92) TransformationProof [EQUIVALENT, 0 ms]
64.81/34.09	            (93) QDP
64.81/34.09	            (94) TransformationProof [EQUIVALENT, 0 ms]
64.81/34.09	            (95) QDP
64.81/34.09	            (96) TransformationProof [EQUIVALENT, 0 ms]
64.81/34.09	            (97) QDP
64.81/34.09	            (98) DependencyGraphProof [EQUIVALENT, 0 ms]
64.81/34.09	            (99) QDP
64.81/34.09	            (100) TransformationProof [EQUIVALENT, 0 ms]
64.81/34.09	            (101) QDP
64.81/34.09	            (102) DependencyGraphProof [EQUIVALENT, 0 ms]
64.81/34.09	            (103) QDP
64.81/34.09	            (104) TransformationProof [EQUIVALENT, 0 ms]
64.81/34.09	            (105) QDP
64.81/34.09	            (106) TransformationProof [EQUIVALENT, 0 ms]
64.81/34.09	            (107) QDP
64.81/34.09	            (108) TransformationProof [EQUIVALENT, 0 ms]
64.81/34.09	            (109) QDP
64.81/34.09	            (110) TransformationProof [EQUIVALENT, 0 ms]
64.81/34.09	            (111) QDP
64.81/34.09	            (112) TransformationProof [EQUIVALENT, 0 ms]
64.81/34.09	            (113) QDP
64.81/34.09	            (114) DependencyGraphProof [EQUIVALENT, 0 ms]
64.81/34.09	            (115) QDP
64.81/34.09	            (116) TransformationProof [EQUIVALENT, 0 ms]
64.81/34.09	            (117) QDP
64.81/34.09	            (118) DependencyGraphProof [EQUIVALENT, 0 ms]
64.81/34.09	            (119) QDP
64.81/34.09	            (120) TransformationProof [EQUIVALENT, 0 ms]
64.81/34.09	            (121) QDP
64.81/34.09	            (122) TransformationProof [EQUIVALENT, 0 ms]
64.81/34.09	            (123) QDP
64.81/34.09	            (124) TransformationProof [EQUIVALENT, 0 ms]
64.81/34.09	            (125) QDP
64.81/34.09	            (126) TransformationProof [EQUIVALENT, 0 ms]
64.81/34.09	            (127) QDP
64.81/34.09	            (128) TransformationProof [EQUIVALENT, 0 ms]
64.81/34.09	            (129) QDP
64.81/34.09	            (130) DependencyGraphProof [EQUIVALENT, 0 ms]
64.81/34.09	            (131) QDP
64.81/34.09	            (132) TransformationProof [EQUIVALENT, 0 ms]
64.81/34.09	            (133) QDP
64.81/34.09	            (134) TransformationProof [EQUIVALENT, 0 ms]
64.81/34.09	            (135) QDP
64.81/34.09	            (136) TransformationProof [EQUIVALENT, 0 ms]
64.81/34.09	            (137) QDP
64.81/34.09	            (138) TransformationProof [EQUIVALENT, 0 ms]
64.81/34.09	            (139) QDP
64.81/34.09	            (140) TransformationProof [EQUIVALENT, 0 ms]
64.81/34.09	            (141) QDP
64.81/34.09	            (142) TransformationProof [EQUIVALENT, 0 ms]
64.81/34.09	            (143) QDP
64.81/34.09	            (144) TransformationProof [EQUIVALENT, 0 ms]
64.81/34.09	            (145) QDP
64.81/34.09	            (146) TransformationProof [EQUIVALENT, 0 ms]
64.81/34.09	            (147) QDP
64.81/34.09	            (148) TransformationProof [EQUIVALENT, 0 ms]
64.81/34.09	            (149) QDP
64.81/34.09	            (150) TransformationProof [EQUIVALENT, 0 ms]
64.81/34.09	            (151) QDP
64.81/34.09	            (152) DependencyGraphProof [EQUIVALENT, 0 ms]
64.81/34.09	            (153) QDP
64.81/34.09	            (154) TransformationProof [EQUIVALENT, 0 ms]
64.81/34.09	            (155) QDP
64.81/34.09	            (156) TransformationProof [EQUIVALENT, 0 ms]
64.81/34.09	            (157) QDP
64.81/34.09	            (158) TransformationProof [EQUIVALENT, 0 ms]
64.81/34.09	            (159) QDP
64.81/34.09	            (160) TransformationProof [EQUIVALENT, 0 ms]
64.81/34.09	            (161) QDP
64.81/34.09	            (162) DependencyGraphProof [EQUIVALENT, 0 ms]
64.81/34.09	            (163) QDP
64.81/34.09	            (164) TransformationProof [EQUIVALENT, 0 ms]
64.81/34.09	            (165) QDP
64.81/34.09	            (166) TransformationProof [EQUIVALENT, 0 ms]
64.81/34.09	            (167) QDP
64.81/34.09	            (168) TransformationProof [EQUIVALENT, 0 ms]
64.81/34.09	            (169) QDP
64.81/34.09	            (170) TransformationProof [EQUIVALENT, 0 ms]
64.81/34.09	            (171) QDP
64.81/34.09	            (172) TransformationProof [EQUIVALENT, 0 ms]
64.81/34.09	            (173) QDP
64.81/34.09	            (174) TransformationProof [EQUIVALENT, 0 ms]
64.81/34.09	            (175) QDP
64.81/34.09	            (176) TransformationProof [EQUIVALENT, 0 ms]
64.81/34.09	            (177) QDP
64.81/34.09	            (178) TransformationProof [EQUIVALENT, 0 ms]
64.81/34.09	            (179) QDP
64.81/34.09	            (180) TransformationProof [EQUIVALENT, 0 ms]
64.81/34.09	            (181) QDP
64.81/34.09	            (182) TransformationProof [EQUIVALENT, 0 ms]
64.81/34.09	            (183) QDP
64.81/34.09	            (184) DependencyGraphProof [EQUIVALENT, 0 ms]
64.81/34.09	            (185) QDP
64.81/34.09	            (186) TransformationProof [EQUIVALENT, 0 ms]
64.81/34.09	            (187) QDP
64.81/34.09	            (188) TransformationProof [EQUIVALENT, 0 ms]
64.81/34.09	            (189) QDP
64.81/34.09	            (190) TransformationProof [EQUIVALENT, 0 ms]
64.81/34.09	            (191) QDP
64.81/34.09	            (192) TransformationProof [EQUIVALENT, 0 ms]
64.81/34.09	            (193) QDP
64.81/34.09	            (194) DependencyGraphProof [EQUIVALENT, 0 ms]
64.81/34.09	            (195) QDP
64.81/34.09	            (196) TransformationProof [EQUIVALENT, 0 ms]
64.81/34.09	            (197) QDP
64.81/34.09	            (198) TransformationProof [EQUIVALENT, 0 ms]
64.81/34.09	            (199) QDP
64.81/34.09	            (200) TransformationProof [EQUIVALENT, 0 ms]
64.81/34.09	            (201) QDP
64.81/34.09	            (202) TransformationProof [EQUIVALENT, 0 ms]
64.81/34.09	            (203) QDP
64.81/34.09	            (204) TransformationProof [EQUIVALENT, 0 ms]
64.81/34.09	            (205) QDP
64.81/34.09	            (206) TransformationProof [EQUIVALENT, 0 ms]
64.81/34.09	            (207) QDP
64.81/34.09	            (208) TransformationProof [EQUIVALENT, 0 ms]
64.81/34.09	            (209) QDP
64.81/34.09	            (210) TransformationProof [EQUIVALENT, 0 ms]
64.81/34.09	            (211) QDP
64.81/34.09	            (212) TransformationProof [EQUIVALENT, 0 ms]
64.81/34.09	            (213) QDP
64.81/34.09	            (214) TransformationProof [EQUIVALENT, 0 ms]
64.81/34.09	            (215) QDP
64.81/34.09	            (216) DependencyGraphProof [EQUIVALENT, 0 ms]
64.81/34.09	            (217) QDP
64.81/34.09	            (218) TransformationProof [EQUIVALENT, 0 ms]
67.32/34.78	            (219) QDP
67.32/34.78	            (220) TransformationProof [EQUIVALENT, 0 ms]
67.32/34.78	            (221) QDP
67.32/34.78	            (222) TransformationProof [EQUIVALENT, 0 ms]
67.32/34.78	            (223) QDP
67.32/34.78	            (224) TransformationProof [EQUIVALENT, 0 ms]
67.32/34.78	            (225) QDP
67.32/34.78	            (226) DependencyGraphProof [EQUIVALENT, 0 ms]
67.32/34.78	            (227) QDP
67.32/34.78	            (228) TransformationProof [EQUIVALENT, 0 ms]
67.32/34.78	            (229) QDP
67.32/34.78	            (230) TransformationProof [EQUIVALENT, 0 ms]
67.32/34.78	            (231) QDP
67.32/34.78	            (232) TransformationProof [EQUIVALENT, 0 ms]
67.32/34.78	            (233) QDP
67.32/34.78	            (234) TransformationProof [EQUIVALENT, 0 ms]
67.32/34.78	            (235) QDP
67.32/34.78	            (236) TransformationProof [EQUIVALENT, 0 ms]
67.32/34.78	            (237) QDP
67.32/34.78	            (238) TransformationProof [EQUIVALENT, 0 ms]
67.32/34.78	            (239) QDP
67.32/34.78	            (240) TransformationProof [EQUIVALENT, 0 ms]
67.32/34.78	            (241) QDP
67.32/34.78	            (242) TransformationProof [EQUIVALENT, 0 ms]
67.32/34.78	            (243) QDP
67.32/34.78	            (244) TransformationProof [EQUIVALENT, 0 ms]
67.32/34.78	            (245) QDP
67.32/34.78	            (246) TransformationProof [EQUIVALENT, 0 ms]
67.32/34.78	            (247) QDP
67.32/34.78	            (248) DependencyGraphProof [EQUIVALENT, 0 ms]
67.32/34.78	            (249) QDP
67.32/34.78	            (250) TransformationProof [EQUIVALENT, 0 ms]
67.32/34.78	            (251) QDP
67.32/34.78	            (252) TransformationProof [EQUIVALENT, 0 ms]
67.32/34.78	            (253) QDP
67.32/34.78	            (254) TransformationProof [EQUIVALENT, 0 ms]
67.32/34.78	            (255) QDP
67.32/34.78	            (256) TransformationProof [EQUIVALENT, 0 ms]
67.32/34.78	            (257) QDP
67.32/34.78	            (258) DependencyGraphProof [EQUIVALENT, 0 ms]
67.32/34.78	            (259) QDP
67.32/34.78	            (260) TransformationProof [EQUIVALENT, 0 ms]
67.32/34.78	            (261) QDP
67.32/34.78	            (262) TransformationProof [EQUIVALENT, 0 ms]
67.32/34.78	            (263) QDP
67.32/34.78	            (264) TransformationProof [EQUIVALENT, 0 ms]
67.32/34.78	            (265) QDP
67.32/34.78	            (266) TransformationProof [EQUIVALENT, 0 ms]
67.32/34.78	            (267) QDP
67.32/34.78	            (268) TransformationProof [EQUIVALENT, 0 ms]
67.32/34.78	            (269) QDP
67.32/34.78	            (270) TransformationProof [EQUIVALENT, 0 ms]
67.32/34.78	            (271) QDP
67.32/34.78	            (272) TransformationProof [EQUIVALENT, 0 ms]
67.32/34.78	            (273) QDP
67.32/34.78	            (274) TransformationProof [EQUIVALENT, 0 ms]
67.32/34.78	            (275) QDP
67.32/34.78	            (276) TransformationProof [EQUIVALENT, 0 ms]
67.32/34.78	            (277) QDP
67.32/34.78	            (278) TransformationProof [EQUIVALENT, 0 ms]
67.32/34.78	            (279) QDP
67.32/34.78	            (280) TransformationProof [EQUIVALENT, 0 ms]
67.32/34.78	            (281) QDP
67.32/34.78	            (282) TransformationProof [EQUIVALENT, 0 ms]
67.32/34.78	            (283) QDP
67.32/34.78	            (284) DependencyGraphProof [EQUIVALENT, 0 ms]
67.32/34.78	            (285) QDP
67.32/34.78	            (286) TransformationProof [EQUIVALENT, 0 ms]
67.32/34.78	            (287) QDP
67.32/34.78	            (288) TransformationProof [EQUIVALENT, 0 ms]
67.32/34.78	            (289) QDP
67.32/34.78	            (290) TransformationProof [EQUIVALENT, 0 ms]
67.32/34.78	            (291) QDP
67.32/34.78	            (292) TransformationProof [EQUIVALENT, 1 ms]
67.32/34.78	            (293) QDP
67.32/34.78	            (294) TransformationProof [EQUIVALENT, 0 ms]
67.32/34.78	            (295) QDP
67.32/34.78	            (296) TransformationProof [EQUIVALENT, 0 ms]
67.32/34.78	            (297) QDP
67.32/34.78	            (298) TransformationProof [EQUIVALENT, 0 ms]
67.32/34.78	            (299) QDP
67.32/34.78	            (300) DependencyGraphProof [EQUIVALENT, 0 ms]
67.32/34.78	            (301) QDP
67.32/34.78	            (302) TransformationProof [EQUIVALENT, 0 ms]
67.32/34.78	            (303) QDP
67.32/34.78	            (304) TransformationProof [EQUIVALENT, 0 ms]
67.32/34.78	            (305) QDP
67.32/34.78	            (306) TransformationProof [EQUIVALENT, 0 ms]
67.32/34.78	            (307) QDP
67.32/34.78	            (308) TransformationProof [EQUIVALENT, 0 ms]
67.32/34.78	            (309) QDP
67.32/34.78	            (310) TransformationProof [EQUIVALENT, 0 ms]
67.32/34.78	            (311) QDP
67.32/34.78	            (312) TransformationProof [EQUIVALENT, 0 ms]
67.32/34.78	            (313) QDP
67.32/34.78	            (314) TransformationProof [EQUIVALENT, 0 ms]
67.32/34.78	            (315) QDP
67.32/34.78	            (316) TransformationProof [EQUIVALENT, 0 ms]
67.32/34.78	            (317) QDP
67.32/34.78	            (318) TransformationProof [EQUIVALENT, 0 ms]
67.32/34.78	            (319) QDP
67.32/34.78	            (320) TransformationProof [EQUIVALENT, 0 ms]
67.32/34.78	            (321) QDP
67.32/34.78	            (322) TransformationProof [EQUIVALENT, 0 ms]
67.32/34.78	            (323) QDP
67.32/34.78	            (324) TransformationProof [EQUIVALENT, 0 ms]
67.32/34.78	            (325) QDP
67.32/34.78	            (326) DependencyGraphProof [EQUIVALENT, 0 ms]
67.32/34.78	            (327) QDP
67.32/34.78	            (328) TransformationProof [EQUIVALENT, 0 ms]
67.32/34.78	            (329) QDP
67.32/34.78	            (330) TransformationProof [EQUIVALENT, 0 ms]
67.32/34.78	            (331) QDP
67.32/34.78	            (332) TransformationProof [EQUIVALENT, 0 ms]
67.32/34.78	            (333) QDP
67.32/34.78	            (334) TransformationProof [EQUIVALENT, 0 ms]
67.32/34.78	            (335) QDP
67.32/34.78	            (336) TransformationProof [EQUIVALENT, 0 ms]
67.32/34.78	            (337) QDP
67.32/34.78	            (338) TransformationProof [EQUIVALENT, 0 ms]
67.32/34.78	            (339) QDP
67.32/34.78	            (340) TransformationProof [EQUIVALENT, 0 ms]
67.32/34.78	            (341) QDP
67.32/34.78	            (342) DependencyGraphProof [EQUIVALENT, 0 ms]
67.32/34.78	            (343) QDP
67.32/34.78	            (344) TransformationProof [EQUIVALENT, 0 ms]
67.32/34.78	            (345) QDP
67.32/34.78	            (346) TransformationProof [EQUIVALENT, 0 ms]
67.32/34.78	            (347) QDP
67.32/34.78	            (348) TransformationProof [EQUIVALENT, 0 ms]
67.32/34.78	            (349) QDP
67.32/34.78	            (350) TransformationProof [EQUIVALENT, 0 ms]
67.32/34.78	            (351) QDP
67.32/34.78	            (352) TransformationProof [EQUIVALENT, 0 ms]
67.32/34.78	            (353) QDP
67.32/34.78	            (354) TransformationProof [EQUIVALENT, 0 ms]
67.32/34.78	            (355) QDP
67.32/34.78	            (356) TransformationProof [EQUIVALENT, 0 ms]
67.32/34.78	            (357) QDP
67.32/34.78	            (358) TransformationProof [EQUIVALENT, 0 ms]
67.32/34.78	            (359) QDP
67.32/34.78	            (360) TransformationProof [EQUIVALENT, 0 ms]
67.32/34.78	            (361) QDP
67.32/34.78	            (362) TransformationProof [EQUIVALENT, 0 ms]
67.32/34.78	            (363) QDP
67.32/34.78	            (364) TransformationProof [EQUIVALENT, 0 ms]
67.32/34.78	            (365) QDP
67.32/34.78	            (366) TransformationProof [EQUIVALENT, 0 ms]
67.32/34.78	            (367) QDP
67.32/34.78	            (368) DependencyGraphProof [EQUIVALENT, 0 ms]
67.32/34.78	            (369) QDP
67.32/34.78	            (370) TransformationProof [EQUIVALENT, 0 ms]
67.32/34.78	            (371) QDP
67.32/34.78	            (372) TransformationProof [EQUIVALENT, 0 ms]
67.32/34.78	            (373) QDP
67.32/34.78	            (374) TransformationProof [EQUIVALENT, 0 ms]
67.32/34.78	            (375) QDP
67.32/34.78	            (376) TransformationProof [EQUIVALENT, 0 ms]
67.32/34.78	            (377) QDP
67.32/34.78	            (378) TransformationProof [EQUIVALENT, 0 ms]
67.32/34.78	            (379) QDP
67.32/34.78	            (380) TransformationProof [EQUIVALENT, 0 ms]
67.32/34.78	            (381) QDP
67.32/34.78	            (382) TransformationProof [EQUIVALENT, 0 ms]
67.32/34.78	            (383) QDP
67.32/34.78	            (384) DependencyGraphProof [EQUIVALENT, 0 ms]
67.32/34.78	            (385) QDP
67.32/34.78	            (386) TransformationProof [EQUIVALENT, 0 ms]
67.32/34.78	            (387) QDP
67.32/34.78	            (388) TransformationProof [EQUIVALENT, 0 ms]
67.32/34.78	            (389) QDP
67.32/34.78	            (390) TransformationProof [EQUIVALENT, 0 ms]
67.32/34.78	            (391) QDP
67.32/34.78	            (392) TransformationProof [EQUIVALENT, 0 ms]
67.32/34.78	            (393) QDP
67.32/34.78	            (394) TransformationProof [EQUIVALENT, 0 ms]
67.32/34.78	            (395) QDP
67.32/34.78	            (396) TransformationProof [EQUIVALENT, 0 ms]
67.32/34.78	            (397) QDP
67.32/34.78	            (398) TransformationProof [EQUIVALENT, 0 ms]
67.32/34.78	            (399) QDP
67.32/34.78	            (400) TransformationProof [EQUIVALENT, 0 ms]
67.32/34.78	            (401) QDP
67.32/34.78	            (402) TransformationProof [EQUIVALENT, 0 ms]
67.32/34.78	            (403) QDP
67.32/34.78	            (404) TransformationProof [EQUIVALENT, 0 ms]
67.32/34.78	            (405) QDP
67.32/34.78	            (406) TransformationProof [EQUIVALENT, 0 ms]
67.32/34.78	            (407) QDP
67.32/34.78	            (408) TransformationProof [EQUIVALENT, 0 ms]
67.32/34.78	            (409) QDP
67.32/34.78	            (410) DependencyGraphProof [EQUIVALENT, 0 ms]
67.32/34.78	            (411) QDP
67.32/34.78	            (412) TransformationProof [EQUIVALENT, 0 ms]
67.32/34.78	            (413) QDP
67.32/34.78	            (414) TransformationProof [EQUIVALENT, 0 ms]
67.32/34.78	            (415) QDP
67.32/34.78	            (416) TransformationProof [EQUIVALENT, 0 ms]
67.32/34.78	            (417) QDP
67.32/34.78	            (418) TransformationProof [EQUIVALENT, 0 ms]
67.32/34.78	            (419) QDP
67.32/34.78	            (420) TransformationProof [EQUIVALENT, 0 ms]
67.32/34.78	            (421) QDP
67.32/34.78	            (422) TransformationProof [EQUIVALENT, 0 ms]
67.32/34.78	            (423) QDP
67.32/34.78	            (424) TransformationProof [EQUIVALENT, 0 ms]
67.32/34.78	            (425) QDP
67.32/34.78	            (426) DependencyGraphProof [EQUIVALENT, 0 ms]
67.32/34.78	            (427) QDP
67.32/34.78	            (428) QDPOrderProof [EQUIVALENT, 88 ms]
67.32/34.78	            (429) QDP
67.32/34.78	            (430) MNOCProof [EQUIVALENT, 0 ms]
67.32/34.78	            (431) QDP
67.32/34.78	            (432) InductionCalculusProof [EQUIVALENT, 0 ms]
67.32/34.78	            (433) QDP
67.32/34.78	    (434) QDP
67.32/34.78	        (435) TransformationProof [EQUIVALENT, 0 ms]
67.32/34.78	        (436) QDP
67.32/34.78	        (437) QDPSizeChangeProof [EQUIVALENT, 0 ms]
67.32/34.78	        (438) YES
67.32/34.78	    (439) QDP
67.32/34.78	        (440) QDPSizeChangeProof [EQUIVALENT, 0 ms]
67.32/34.78	        (441) YES
67.32/34.78	    (442) QDP
67.32/34.78	        (443) TransformationProof [EQUIVALENT, 0 ms]
67.32/34.78	        (444) QDP
67.32/34.78	        (445) QDPSizeChangeProof [EQUIVALENT, 0 ms]
67.32/34.78	        (446) YES
67.32/34.78	    (447) QDP
67.32/34.78	        (448) DependencyGraphProof [EQUIVALENT, 0 ms]
67.32/34.78	        (449) AND
67.32/34.78	            (450) QDP
67.32/34.78	                (451) QDPOrderProof [EQUIVALENT, 0 ms]
67.32/34.78	                (452) QDP
67.32/34.78	                (453) DependencyGraphProof [EQUIVALENT, 0 ms]
67.32/34.78	                (454) QDP
67.32/34.78	                (455) QDPSizeChangeProof [EQUIVALENT, 0 ms]
67.32/34.78	                (456) YES
67.32/34.78	            (457) QDP
67.32/34.78	                (458) MRRProof [EQUIVALENT, 0 ms]
67.32/34.78	                (459) QDP
67.32/34.78	                (460) PisEmptyProof [EQUIVALENT, 0 ms]
67.32/34.78	                (461) YES
67.32/34.78	    (462) QDP
67.32/34.78	        (463) TransformationProof [EQUIVALENT, 0 ms]
67.32/34.78	        (464) QDP
67.32/34.78	        (465) QDPSizeChangeProof [EQUIVALENT, 0 ms]
67.32/34.78	        (466) YES
67.32/34.78	    (467) QDP
67.32/34.78	        (468) TransformationProof [EQUIVALENT, 0 ms]
67.32/34.78	        (469) QDP
67.32/34.78	        (470) QDPSizeChangeProof [EQUIVALENT, 0 ms]
67.32/34.78	        (471) YES
67.32/34.78	    (472) QDP
67.32/34.78	        (473) TransformationProof [EQUIVALENT, 0 ms]
67.32/34.78	        (474) QDP
67.32/34.78	        (475) QDPSizeChangeProof [EQUIVALENT, 0 ms]
67.32/34.78	        (476) YES
67.32/34.78	    (477) QDP
67.32/34.78	        (478) TransformationProof [EQUIVALENT, 0 ms]
67.32/34.78	        (479) QDP
67.32/34.78	        (480) QDPSizeChangeProof [EQUIVALENT, 0 ms]
67.32/34.78	        (481) YES
67.32/34.78	    (482) QDP
67.32/34.78	        (483) QDPSizeChangeProof [EQUIVALENT, 0 ms]
67.32/34.78	        (484) YES
67.32/34.78	    (485) QDP
67.32/34.78	        (486) QDPSizeChangeProof [EQUIVALENT, 0 ms]
67.32/34.78	        (487) YES
67.32/34.78	(488) Narrow [COMPLETE, 0 ms]
67.32/34.78	(489) TRUE
67.32/34.78	
67.32/34.78	
67.32/34.78	----------------------------------------
67.32/34.78	
67.32/34.78	(0)
67.32/34.78	Obligation:
67.32/34.78	mainModule Main 
67.32/34.78	module Main where {
67.32/34.78	import qualified Prelude;
67.32/34.78	}
67.32/34.78	
67.32/34.78	----------------------------------------
67.32/34.78	
67.32/34.78	(1) IFR (EQUIVALENT)
67.32/34.78	If Reductions:
67.32/34.78	The following If expression
67.32/34.78	"if primGEqNatS x y then Succ (primDivNatS (primMinusNatS x y) (Succ y)) else Zero"
67.32/34.78	is transformed to
67.32/34.78	"primDivNatS0 x y True = Succ (primDivNatS (primMinusNatS x y) (Succ y));
67.32/34.78	primDivNatS0 x y False = Zero;
67.32/34.78	"
67.32/34.78	The following If expression
67.32/34.78	"if primGEqNatS x y then primModNatS (primMinusNatS x y) (Succ y) else Succ x"
67.32/34.78	is transformed to
67.32/34.78	"primModNatS0 x y True = primModNatS (primMinusNatS x y) (Succ y);
67.32/34.78	primModNatS0 x y False = Succ x;
67.32/34.78	"
67.32/34.78	
67.32/34.78	----------------------------------------
67.32/34.78	
67.32/34.78	(2)
67.32/34.78	Obligation:
67.32/34.78	mainModule Main 
67.32/34.78	module Main where {
67.32/34.78	import qualified Prelude;
67.32/34.78	}
67.32/34.78	
67.32/34.78	----------------------------------------
67.32/34.78	
67.32/34.78	(3) BR (EQUIVALENT)
67.32/34.78	Replaced joker patterns by fresh variables and removed binding patterns.
67.32/34.78	----------------------------------------
67.32/34.78	
67.32/34.78	(4)
67.32/34.78	Obligation:
67.32/34.78	mainModule Main 
67.32/34.78	module Main where {
67.32/34.78	import qualified Prelude;
67.32/34.78	}
67.32/34.78	
67.32/34.78	----------------------------------------
67.32/34.78	
67.32/34.78	(5) COR (EQUIVALENT)
67.32/34.78	Cond Reductions:
67.32/34.78	The following Function with conditions
67.32/34.78	"absReal x|x >= 0x|otherwise`negate` x;
67.32/34.78	"
67.32/34.78	is transformed to
67.32/34.78	"absReal x = absReal2 x;
67.32/34.78	"
67.32/34.78	"absReal1 x True = x;
67.32/34.78	absReal1 x False = absReal0 x otherwise;
67.32/34.78	"
67.32/34.78	"absReal0 x True = `negate` x;
67.32/34.78	"
67.32/34.78	"absReal2 x = absReal1 x (x >= 0);
67.32/34.78	"
67.32/34.78	The following Function with conditions
67.32/34.78	"gcd' x 0 = x;
67.32/34.78	gcd' x y = gcd' y (x `rem` y);
67.32/34.78	"
67.32/34.78	is transformed to
67.32/34.78	"gcd' x xz = gcd'2 x xz;
67.32/34.78	gcd' x y = gcd'0 x y;
67.32/34.78	"
67.32/34.78	"gcd'0 x y = gcd' y (x `rem` y);
67.32/34.78	"
67.32/34.78	"gcd'1 True x xz = x;
67.32/34.78	gcd'1 yu yv yw = gcd'0 yv yw;
67.32/34.78	"
67.32/34.78	"gcd'2 x xz = gcd'1 (xz == 0) x xz;
67.32/34.78	gcd'2 yx yy = gcd'0 yx yy;
67.32/34.78	"
67.32/34.78	The following Function with conditions
67.32/34.78	"gcd 0 0 = error [];
67.32/34.78	gcd x y = gcd' (abs x) (abs y) where {
67.32/34.78	gcd' x 0 = x;
67.32/34.78	gcd' x y = gcd' y (x `rem` y);
67.32/34.78	} 
67.32/34.78	;
67.32/34.78	"
67.32/34.78	is transformed to
67.32/34.78	"gcd yz zu = gcd3 yz zu;
67.32/34.78	gcd x y = gcd0 x y;
67.32/34.78	"
67.32/34.78	"gcd0 x y = gcd' (abs x) (abs y) where {
67.32/34.78	gcd' x xz = gcd'2 x xz;
67.32/34.78	gcd' x y = gcd'0 x y;
67.32/34.78	;
67.32/34.78	gcd'0 x y = gcd' y (x `rem` y);
67.32/34.78	;
67.32/34.78	gcd'1 True x xz = x;
67.32/34.78	gcd'1 yu yv yw = gcd'0 yv yw;
67.32/34.78	;
67.32/34.78	gcd'2 x xz = gcd'1 (xz == 0) x xz;
67.32/34.78	gcd'2 yx yy = gcd'0 yx yy;
67.32/34.78	} 
67.32/34.78	;
67.32/34.78	"
67.32/34.78	"gcd1 True yz zu = error [];
67.32/34.78	gcd1 zv zw zx = gcd0 zw zx;
67.32/34.78	"
67.32/34.78	"gcd2 True yz zu = gcd1 (zu == 0) yz zu;
67.32/34.78	gcd2 zy zz vuu = gcd0 zz vuu;
67.32/34.78	"
67.32/34.78	"gcd3 yz zu = gcd2 (yz == 0) yz zu;
67.32/34.78	gcd3 vuv vuw = gcd0 vuv vuw;
67.32/34.78	"
67.32/34.78	The following Function with conditions
67.32/34.78	"undefined |Falseundefined;
67.32/34.78	"
67.32/34.78	is transformed to
67.32/34.78	"undefined  = undefined1;
67.32/34.78	"
67.32/34.78	"undefined0 True = undefined;
67.32/34.78	"
67.32/34.78	"undefined1  = undefined0 False;
67.32/34.78	"
67.32/34.78	The following Function with conditions
67.32/34.78	"reduce x y|y == 0error []|otherwisex `quot` d :% (y `quot` d) where {
67.32/34.78	d  = gcd x y;
67.32/34.78	} 
67.32/34.78	;
67.32/34.78	"
67.32/34.78	is transformed to
67.32/34.78	"reduce x y = reduce2 x y;
67.32/34.78	"
67.32/34.78	"reduce2 x y = reduce1 x y (y == 0) where {
67.32/34.78	d  = gcd x y;
67.32/34.78	;
67.32/34.78	reduce0 x y True = x `quot` d :% (y `quot` d);
67.32/34.78	;
67.32/34.78	reduce1 x y True = error [];
67.32/34.78	reduce1 x y False = reduce0 x y otherwise;
67.32/34.78	} 
67.32/34.78	;
67.32/34.78	"
67.32/34.78	
67.32/34.78	----------------------------------------
67.32/34.78	
67.32/34.78	(6)
67.32/34.78	Obligation:
67.32/34.78	mainModule Main 
67.32/34.78	module Main where {
67.32/34.78	import qualified Prelude;
67.32/34.78	}
67.32/34.78	
67.32/34.78	----------------------------------------
67.32/34.78	
67.32/34.78	(7) LetRed (EQUIVALENT)
67.32/34.78	Let/Where Reductions:
67.32/34.78	The bindings of the following Let/Where expression
67.32/34.78	"gcd' (abs x) (abs y) where {
67.32/34.78	gcd' x xz = gcd'2 x xz;
67.32/34.78	gcd' x y = gcd'0 x y;
67.32/34.78	;
67.32/34.78	gcd'0 x y = gcd' y (x `rem` y);
67.32/34.78	;
67.32/34.78	gcd'1 True x xz = x;
67.32/34.78	gcd'1 yu yv yw = gcd'0 yv yw;
67.32/34.78	;
67.32/34.78	gcd'2 x xz = gcd'1 (xz == 0) x xz;
67.32/34.78	gcd'2 yx yy = gcd'0 yx yy;
67.32/34.78	} 
67.32/34.78	"
67.32/34.78	are unpacked to the following functions on top level
67.32/34.78	"gcd0Gcd'2 x xz = gcd0Gcd'1 (xz == 0) x xz;
67.32/34.78	gcd0Gcd'2 yx yy = gcd0Gcd'0 yx yy;
67.32/34.78	"
67.32/34.78	"gcd0Gcd'1 True x xz = x;
67.32/34.78	gcd0Gcd'1 yu yv yw = gcd0Gcd'0 yv yw;
67.32/34.78	"
67.32/34.78	"gcd0Gcd'0 x y = gcd0Gcd' y (x `rem` y);
67.32/34.78	"
67.32/34.78	"gcd0Gcd' x xz = gcd0Gcd'2 x xz;
67.32/34.78	gcd0Gcd' x y = gcd0Gcd'0 x y;
67.32/34.78	"
67.32/34.78	The bindings of the following Let/Where expression
67.32/34.78	"reduce1 x y (y == 0) where {
67.32/34.78	d  = gcd x y;
67.32/34.78	;
67.32/34.78	reduce0 x y True = x `quot` d :% (y `quot` d);
67.32/34.78	;
67.32/34.78	reduce1 x y True = error [];
67.32/34.78	reduce1 x y False = reduce0 x y otherwise;
67.32/34.78	} 
67.32/34.78	"
67.32/34.78	are unpacked to the following functions on top level
67.32/34.78	"reduce2Reduce1 vux vuy x y True = error [];
67.32/34.78	reduce2Reduce1 vux vuy x y False = reduce2Reduce0 vux vuy x y otherwise;
67.32/34.78	"
67.32/34.78	"reduce2Reduce0 vux vuy x y True = x `quot` reduce2D vux vuy :% (y `quot` reduce2D vux vuy);
67.32/34.78	"
67.32/34.78	"reduce2D vux vuy = gcd vux vuy;
67.32/34.78	"
67.32/34.78	
67.32/34.78	----------------------------------------
67.32/34.78	
67.32/34.78	(8)
67.32/34.78	Obligation:
67.32/34.78	mainModule Main 
67.32/34.78	module Main where {
67.32/34.78	import qualified Prelude;
67.32/34.78	}
67.32/34.78	
67.32/34.78	----------------------------------------
67.32/34.78	
67.32/34.78	(9) NumRed (SOUND)
67.32/34.78	Num Reduction:All numbers are transformed to their corresponding representation with Succ, Pred and Zero.
67.32/34.78	----------------------------------------
67.32/34.78	
67.32/34.78	(10)
67.32/34.78	Obligation:
67.32/34.78	mainModule Main 
67.32/34.78	module Main where {
67.32/34.78	import qualified Prelude;
67.32/34.78	}
67.32/34.78	
67.32/34.78	----------------------------------------
67.32/34.78	
67.32/34.78	(11) Narrow (SOUND)
67.32/34.78	Haskell To QDPs
67.32/34.78	
67.32/34.78	digraph dp_graph {
67.32/34.78	node [outthreshold=100, inthreshold=100];1[label="enumFromThen",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
67.32/34.78	3[label="enumFromThen vuz3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
67.32/34.78	4[label="enumFromThen vuz3 vuz4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
67.32/34.78	5[label="numericEnumFromThen vuz3 vuz4",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
67.32/34.78	6[label="iterate (vuz4 - vuz3 +) vuz3",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3];
67.32/34.78	7[label="vuz3 : iterate (vuz4 - vuz3 +) (vuz4 - vuz3 + vuz3)",fontsize=16,color="green",shape="box"];7 -> 8[label="",style="dashed", color="green", weight=3];
67.32/34.78	8 -> 13[label="",style="dashed", color="red", weight=0];
67.32/34.78	8[label="iterate (vuz4 - vuz3 +) (vuz4 - vuz3 + vuz3)",fontsize=16,color="magenta"];8 -> 14[label="",style="dashed", color="magenta", weight=3];
67.32/34.78	14[label="vuz3",fontsize=16,color="green",shape="box"];13[label="iterate (vuz4 - vuz3 +) (vuz4 - vuz3 + vuz5)",fontsize=16,color="black",shape="triangle"];13 -> 16[label="",style="solid", color="black", weight=3];
67.32/34.78	16[label="vuz4 - vuz3 + vuz5 : iterate (vuz4 - vuz3 +) (vuz4 - vuz3 + (vuz4 - vuz3 + vuz5))",fontsize=16,color="green",shape="box"];16 -> 17[label="",style="dashed", color="green", weight=3];
67.32/34.78	16 -> 18[label="",style="dashed", color="green", weight=3];
67.32/34.78	17[label="vuz4 - vuz3 + vuz5",fontsize=16,color="black",shape="box"];17 -> 5645[label="",style="solid", color="black", weight=3];
67.32/34.78	18 -> 13[label="",style="dashed", color="red", weight=0];
67.32/34.78	18[label="iterate (vuz4 - vuz3 +) (vuz4 - vuz3 + (vuz4 - vuz3 + vuz5))",fontsize=16,color="magenta"];18 -> 20[label="",style="dashed", color="magenta", weight=3];
67.32/34.78	5645 -> 5329[label="",style="dashed", color="red", weight=0];
67.32/34.78	5645[label="vuz4 + (negate vuz3) + vuz5",fontsize=16,color="magenta"];5645 -> 6517[label="",style="dashed", color="magenta", weight=3];
67.32/34.78	5645 -> 6518[label="",style="dashed", color="magenta", weight=3];
67.32/34.78	20[label="vuz4 - vuz3 + vuz5",fontsize=16,color="black",shape="box"];20 -> 5425[label="",style="solid", color="black", weight=3];
67.32/34.78	6517[label="vuz5",fontsize=16,color="green",shape="box"];6518 -> 5329[label="",style="dashed", color="red", weight=0];
67.32/34.78	6518[label="vuz4 + (negate vuz3)",fontsize=16,color="magenta"];6518 -> 7106[label="",style="dashed", color="magenta", weight=3];
67.32/34.78	6518 -> 7107[label="",style="dashed", color="magenta", weight=3];
67.32/34.78	5329[label="vuz306 + vuz307",fontsize=16,color="burlywood",shape="triangle"];10820[label="vuz306/vuz3060 :% vuz3061",fontsize=10,color="white",style="solid",shape="box"];5329 -> 10820[label="",style="solid", color="burlywood", weight=9];
67.32/34.78	10820 -> 5964[label="",style="solid", color="burlywood", weight=3];
67.32/34.78	5425 -> 5329[label="",style="dashed", color="red", weight=0];
67.32/34.78	5425[label="vuz4 + (negate vuz3) + vuz5",fontsize=16,color="magenta"];5425 -> 6125[label="",style="dashed", color="magenta", weight=3];
67.32/34.78	5425 -> 6126[label="",style="dashed", color="magenta", weight=3];
67.32/34.78	7106[label="negate vuz3",fontsize=16,color="burlywood",shape="triangle"];10821[label="vuz3/vuz30 :% vuz31",fontsize=10,color="white",style="solid",shape="box"];7106 -> 10821[label="",style="solid", color="burlywood", weight=9];
67.32/34.78	10821 -> 7111[label="",style="solid", color="burlywood", weight=3];
67.32/34.78	7107[label="vuz4",fontsize=16,color="green",shape="box"];5964[label="vuz3060 :% vuz3061 + vuz307",fontsize=16,color="burlywood",shape="box"];10822[label="vuz307/vuz3070 :% vuz3071",fontsize=10,color="white",style="solid",shape="box"];5964 -> 10822[label="",style="solid", color="burlywood", weight=9];
67.32/34.78	10822 -> 7081[label="",style="solid", color="burlywood", weight=3];
67.32/34.78	6125[label="vuz5",fontsize=16,color="green",shape="box"];6126 -> 5329[label="",style="dashed", color="red", weight=0];
67.32/34.78	6126[label="vuz4 + (negate vuz3)",fontsize=16,color="magenta"];6126 -> 7108[label="",style="dashed", color="magenta", weight=3];
67.32/34.78	6126 -> 7109[label="",style="dashed", color="magenta", weight=3];
67.32/34.78	7111[label="negate vuz30 :% vuz31",fontsize=16,color="black",shape="box"];7111 -> 7113[label="",style="solid", color="black", weight=3];
67.32/34.78	7081[label="vuz3060 :% vuz3061 + vuz3070 :% vuz3071",fontsize=16,color="black",shape="box"];7081 -> 7110[label="",style="solid", color="black", weight=3];
67.32/34.78	7108 -> 7106[label="",style="dashed", color="red", weight=0];
67.32/34.79	7108[label="negate vuz3",fontsize=16,color="magenta"];7109[label="vuz4",fontsize=16,color="green",shape="box"];7113[label="(negate vuz30) :% vuz31",fontsize=16,color="green",shape="box"];7113 -> 7115[label="",style="dashed", color="green", weight=3];
67.32/34.79	7110[label="reduce (vuz3060 * vuz3071 + vuz3070 * vuz3061) (vuz3061 * vuz3071)",fontsize=16,color="black",shape="box"];7110 -> 7112[label="",style="solid", color="black", weight=3];
67.32/34.79	7115[label="negate vuz30",fontsize=16,color="black",shape="triangle"];7115 -> 7122[label="",style="solid", color="black", weight=3];
67.32/34.79	7112[label="reduce2 (vuz3060 * vuz3071 + vuz3070 * vuz3061) (vuz3061 * vuz3071)",fontsize=16,color="black",shape="box"];7112 -> 7114[label="",style="solid", color="black", weight=3];
67.32/34.79	7122[label="primNegInt vuz30",fontsize=16,color="burlywood",shape="box"];10823[label="vuz30/Pos vuz300",fontsize=10,color="white",style="solid",shape="box"];7122 -> 10823[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10823 -> 7127[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	10824[label="vuz30/Neg vuz300",fontsize=10,color="white",style="solid",shape="box"];7122 -> 10824[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10824 -> 7128[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	7114 -> 7116[label="",style="dashed", color="red", weight=0];
67.32/34.79	7114[label="reduce2Reduce1 (vuz3060 * vuz3071 + vuz3070 * vuz3061) (vuz3061 * vuz3071) (vuz3060 * vuz3071 + vuz3070 * vuz3061) (vuz3061 * vuz3071) (vuz3061 * vuz3071 == fromInt (Pos Zero))",fontsize=16,color="magenta"];7114 -> 7117[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7114 -> 7118[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7114 -> 7119[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7114 -> 7120[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7114 -> 7121[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7127[label="primNegInt (Pos vuz300)",fontsize=16,color="black",shape="box"];7127 -> 7133[label="",style="solid", color="black", weight=3];
67.32/34.79	7128[label="primNegInt (Neg vuz300)",fontsize=16,color="black",shape="box"];7128 -> 7134[label="",style="solid", color="black", weight=3];
67.32/34.79	7117[label="vuz3061 * vuz3071 == fromInt (Pos Zero)",fontsize=16,color="blue",shape="box"];10825[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];7117 -> 10825[label="",style="solid", color="blue", weight=9];
67.32/34.79	10825 -> 7123[label="",style="solid", color="blue", weight=3];
67.32/34.79	10826[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];7117 -> 10826[label="",style="solid", color="blue", weight=9];
67.32/34.79	10826 -> 7124[label="",style="solid", color="blue", weight=3];
67.32/34.79	7118[label="vuz3060",fontsize=16,color="green",shape="box"];7119[label="vuz3071",fontsize=16,color="green",shape="box"];7120[label="vuz3061",fontsize=16,color="green",shape="box"];7121[label="vuz3070",fontsize=16,color="green",shape="box"];7116[label="reduce2Reduce1 (vuz316 * vuz317 + vuz318 * vuz319) (vuz319 * vuz317) (vuz316 * vuz317 + vuz318 * vuz319) (vuz319 * vuz317) vuz320",fontsize=16,color="burlywood",shape="triangle"];10827[label="vuz320/False",fontsize=10,color="white",style="solid",shape="box"];7116 -> 10827[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10827 -> 7125[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	10828[label="vuz320/True",fontsize=10,color="white",style="solid",shape="box"];7116 -> 10828[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10828 -> 7126[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	7133[label="Neg vuz300",fontsize=16,color="green",shape="box"];7134[label="Pos vuz300",fontsize=16,color="green",shape="box"];7123 -> 9987[label="",style="dashed", color="red", weight=0];
67.32/34.79	7123[label="vuz3061 * vuz3071 == fromInt (Pos Zero)",fontsize=16,color="magenta"];7123 -> 9988[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7124[label="vuz3061 * vuz3071 == fromInt (Pos Zero)",fontsize=16,color="black",shape="box"];7124 -> 7130[label="",style="solid", color="black", weight=3];
67.32/34.79	7125[label="reduce2Reduce1 (vuz316 * vuz317 + vuz318 * vuz319) (vuz319 * vuz317) (vuz316 * vuz317 + vuz318 * vuz319) (vuz319 * vuz317) False",fontsize=16,color="black",shape="box"];7125 -> 7131[label="",style="solid", color="black", weight=3];
67.32/34.79	7126[label="reduce2Reduce1 (vuz316 * vuz317 + vuz318 * vuz319) (vuz319 * vuz317) (vuz316 * vuz317 + vuz318 * vuz319) (vuz319 * vuz317) True",fontsize=16,color="black",shape="box"];7126 -> 7132[label="",style="solid", color="black", weight=3];
67.32/34.79	9988[label="vuz3061 * vuz3071",fontsize=16,color="black",shape="triangle"];9988 -> 10015[label="",style="solid", color="black", weight=3];
67.32/34.79	9987[label="vuz551 == fromInt (Pos Zero)",fontsize=16,color="black",shape="triangle"];9987 -> 10016[label="",style="solid", color="black", weight=3];
67.32/34.79	7130[label="error []",fontsize=16,color="red",shape="box"];7131[label="reduce2Reduce0 (vuz316 * vuz317 + vuz318 * vuz319) (vuz319 * vuz317) (vuz316 * vuz317 + vuz318 * vuz319) (vuz319 * vuz317) otherwise",fontsize=16,color="black",shape="box"];7131 -> 7136[label="",style="solid", color="black", weight=3];
67.32/34.79	7132[label="error []",fontsize=16,color="black",shape="box"];7132 -> 7137[label="",style="solid", color="black", weight=3];
67.32/34.79	10015[label="primMulInt vuz3061 vuz3071",fontsize=16,color="burlywood",shape="box"];10829[label="vuz3061/Pos vuz30610",fontsize=10,color="white",style="solid",shape="box"];10015 -> 10829[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10829 -> 10168[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	10830[label="vuz3061/Neg vuz30610",fontsize=10,color="white",style="solid",shape="box"];10015 -> 10830[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10830 -> 10169[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	10016[label="primEqInt vuz551 (fromInt (Pos Zero))",fontsize=16,color="burlywood",shape="box"];10831[label="vuz551/Pos vuz5510",fontsize=10,color="white",style="solid",shape="box"];10016 -> 10831[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10831 -> 10170[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	10832[label="vuz551/Neg vuz5510",fontsize=10,color="white",style="solid",shape="box"];10016 -> 10832[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10832 -> 10171[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	7136[label="reduce2Reduce0 (vuz316 * vuz317 + vuz318 * vuz319) (vuz319 * vuz317) (vuz316 * vuz317 + vuz318 * vuz319) (vuz319 * vuz317) True",fontsize=16,color="black",shape="box"];7136 -> 7140[label="",style="solid", color="black", weight=3];
67.32/34.79	7137[label="error []",fontsize=16,color="red",shape="box"];10168[label="primMulInt (Pos vuz30610) vuz3071",fontsize=16,color="burlywood",shape="box"];10833[label="vuz3071/Pos vuz30710",fontsize=10,color="white",style="solid",shape="box"];10168 -> 10833[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10833 -> 10194[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	10834[label="vuz3071/Neg vuz30710",fontsize=10,color="white",style="solid",shape="box"];10168 -> 10834[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10834 -> 10195[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	10169[label="primMulInt (Neg vuz30610) vuz3071",fontsize=16,color="burlywood",shape="box"];10835[label="vuz3071/Pos vuz30710",fontsize=10,color="white",style="solid",shape="box"];10169 -> 10835[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10835 -> 10196[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	10836[label="vuz3071/Neg vuz30710",fontsize=10,color="white",style="solid",shape="box"];10169 -> 10836[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10836 -> 10197[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	10170[label="primEqInt (Pos vuz5510) (fromInt (Pos Zero))",fontsize=16,color="burlywood",shape="box"];10837[label="vuz5510/Succ vuz55100",fontsize=10,color="white",style="solid",shape="box"];10170 -> 10837[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10837 -> 10198[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	10838[label="vuz5510/Zero",fontsize=10,color="white",style="solid",shape="box"];10170 -> 10838[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10838 -> 10199[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	10171[label="primEqInt (Neg vuz5510) (fromInt (Pos Zero))",fontsize=16,color="burlywood",shape="box"];10839[label="vuz5510/Succ vuz55100",fontsize=10,color="white",style="solid",shape="box"];10171 -> 10839[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10839 -> 10200[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	10840[label="vuz5510/Zero",fontsize=10,color="white",style="solid",shape="box"];10171 -> 10840[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10840 -> 10201[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	7140[label="(vuz316 * vuz317 + vuz318 * vuz319) `quot` reduce2D (vuz316 * vuz317 + vuz318 * vuz319) (vuz319 * vuz317) :% (vuz319 * vuz317 `quot` reduce2D (vuz316 * vuz317 + vuz318 * vuz319) (vuz319 * vuz317))",fontsize=16,color="green",shape="box"];7140 -> 7145[label="",style="dashed", color="green", weight=3];
67.32/34.79	7140 -> 7146[label="",style="dashed", color="green", weight=3];
67.32/34.79	10194[label="primMulInt (Pos vuz30610) (Pos vuz30710)",fontsize=16,color="black",shape="box"];10194 -> 10238[label="",style="solid", color="black", weight=3];
67.32/34.79	10195[label="primMulInt (Pos vuz30610) (Neg vuz30710)",fontsize=16,color="black",shape="box"];10195 -> 10239[label="",style="solid", color="black", weight=3];
67.32/34.79	10196[label="primMulInt (Neg vuz30610) (Pos vuz30710)",fontsize=16,color="black",shape="box"];10196 -> 10240[label="",style="solid", color="black", weight=3];
67.32/34.79	10197[label="primMulInt (Neg vuz30610) (Neg vuz30710)",fontsize=16,color="black",shape="box"];10197 -> 10241[label="",style="solid", color="black", weight=3];
67.32/34.79	10198[label="primEqInt (Pos (Succ vuz55100)) (fromInt (Pos Zero))",fontsize=16,color="black",shape="box"];10198 -> 10242[label="",style="solid", color="black", weight=3];
67.32/34.79	10199[label="primEqInt (Pos Zero) (fromInt (Pos Zero))",fontsize=16,color="black",shape="box"];10199 -> 10243[label="",style="solid", color="black", weight=3];
67.32/34.79	10200[label="primEqInt (Neg (Succ vuz55100)) (fromInt (Pos Zero))",fontsize=16,color="black",shape="box"];10200 -> 10244[label="",style="solid", color="black", weight=3];
67.32/34.79	10201[label="primEqInt (Neg Zero) (fromInt (Pos Zero))",fontsize=16,color="black",shape="box"];10201 -> 10245[label="",style="solid", color="black", weight=3];
67.32/34.79	7145[label="(vuz316 * vuz317 + vuz318 * vuz319) `quot` reduce2D (vuz316 * vuz317 + vuz318 * vuz319) (vuz319 * vuz317)",fontsize=16,color="blue",shape="box"];10841[label="`quot` :: Integer -> Integer -> Integer",fontsize=10,color="white",style="solid",shape="box"];7145 -> 10841[label="",style="solid", color="blue", weight=9];
67.32/34.79	10841 -> 7151[label="",style="solid", color="blue", weight=3];
67.32/34.79	10842[label="`quot` :: Int -> Int -> Int",fontsize=10,color="white",style="solid",shape="box"];7145 -> 10842[label="",style="solid", color="blue", weight=9];
67.32/34.79	10842 -> 7152[label="",style="solid", color="blue", weight=3];
67.32/34.79	7146[label="vuz319 * vuz317 `quot` reduce2D (vuz316 * vuz317 + vuz318 * vuz319) (vuz319 * vuz317)",fontsize=16,color="blue",shape="box"];10843[label="`quot` :: Integer -> Integer -> Integer",fontsize=10,color="white",style="solid",shape="box"];7146 -> 10843[label="",style="solid", color="blue", weight=9];
67.32/34.79	10843 -> 7153[label="",style="solid", color="blue", weight=3];
67.32/34.79	10844[label="`quot` :: Int -> Int -> Int",fontsize=10,color="white",style="solid",shape="box"];7146 -> 10844[label="",style="solid", color="blue", weight=9];
67.32/34.79	10844 -> 7154[label="",style="solid", color="blue", weight=3];
67.32/34.79	10238[label="Pos (primMulNat vuz30610 vuz30710)",fontsize=16,color="green",shape="box"];10238 -> 10260[label="",style="dashed", color="green", weight=3];
67.32/34.79	10239[label="Neg (primMulNat vuz30610 vuz30710)",fontsize=16,color="green",shape="box"];10239 -> 10261[label="",style="dashed", color="green", weight=3];
67.32/34.79	10240[label="Neg (primMulNat vuz30610 vuz30710)",fontsize=16,color="green",shape="box"];10240 -> 10262[label="",style="dashed", color="green", weight=3];
67.32/34.79	10241[label="Pos (primMulNat vuz30610 vuz30710)",fontsize=16,color="green",shape="box"];10241 -> 10263[label="",style="dashed", color="green", weight=3];
67.32/34.79	10242 -> 7519[label="",style="dashed", color="red", weight=0];
67.32/34.79	10242[label="primEqInt (Pos (Succ vuz55100)) (Pos Zero)",fontsize=16,color="magenta"];10242 -> 10264[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	10243 -> 7520[label="",style="dashed", color="red", weight=0];
67.32/34.79	10243[label="primEqInt (Pos Zero) (Pos Zero)",fontsize=16,color="magenta"];10244 -> 7526[label="",style="dashed", color="red", weight=0];
67.32/34.79	10244[label="primEqInt (Neg (Succ vuz55100)) (Pos Zero)",fontsize=16,color="magenta"];10244 -> 10265[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	10245 -> 7527[label="",style="dashed", color="red", weight=0];
67.32/34.79	10245[label="primEqInt (Neg Zero) (Pos Zero)",fontsize=16,color="magenta"];7151[label="(vuz316 * vuz317 + vuz318 * vuz319) `quot` reduce2D (vuz316 * vuz317 + vuz318 * vuz319) (vuz319 * vuz317)",fontsize=16,color="black",shape="box"];7151 -> 7163[label="",style="solid", color="black", weight=3];
67.32/34.79	7152[label="(vuz316 * vuz317 + vuz318 * vuz319) `quot` reduce2D (vuz316 * vuz317 + vuz318 * vuz319) (vuz319 * vuz317)",fontsize=16,color="black",shape="box"];7152 -> 7164[label="",style="solid", color="black", weight=3];
67.32/34.79	7153[label="vuz319 * vuz317 `quot` reduce2D (vuz316 * vuz317 + vuz318 * vuz319) (vuz319 * vuz317)",fontsize=16,color="black",shape="box"];7153 -> 7165[label="",style="solid", color="black", weight=3];
67.32/34.79	7154[label="vuz319 * vuz317 `quot` reduce2D (vuz316 * vuz317 + vuz318 * vuz319) (vuz319 * vuz317)",fontsize=16,color="black",shape="box"];7154 -> 7166[label="",style="solid", color="black", weight=3];
67.32/34.79	10260 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	10260[label="primMulNat vuz30610 vuz30710",fontsize=16,color="magenta"];10261 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	10261[label="primMulNat vuz30610 vuz30710",fontsize=16,color="magenta"];10261 -> 10279[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	10262 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	10262[label="primMulNat vuz30610 vuz30710",fontsize=16,color="magenta"];10262 -> 10280[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	10263 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	10263[label="primMulNat vuz30610 vuz30710",fontsize=16,color="magenta"];10263 -> 10281[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	10263 -> 10282[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	10264[label="vuz55100",fontsize=16,color="green",shape="box"];7519[label="primEqInt (Pos (Succ vuz3250)) (Pos Zero)",fontsize=16,color="black",shape="triangle"];7519 -> 7532[label="",style="solid", color="black", weight=3];
67.32/34.79	7520[label="primEqInt (Pos Zero) (Pos Zero)",fontsize=16,color="black",shape="triangle"];7520 -> 7533[label="",style="solid", color="black", weight=3];
67.32/34.79	10265[label="vuz55100",fontsize=16,color="green",shape="box"];7526[label="primEqInt (Neg (Succ vuz3260)) (Pos Zero)",fontsize=16,color="black",shape="triangle"];7526 -> 7547[label="",style="solid", color="black", weight=3];
67.32/34.79	7527[label="primEqInt (Neg Zero) (Pos Zero)",fontsize=16,color="black",shape="triangle"];7527 -> 7548[label="",style="solid", color="black", weight=3];
67.32/34.79	7163[label="error []",fontsize=16,color="red",shape="box"];7164[label="primQuotInt (vuz316 * vuz317 + vuz318 * vuz319) (reduce2D (vuz316 * vuz317 + vuz318 * vuz319) (vuz319 * vuz317))",fontsize=16,color="black",shape="box"];7164 -> 7175[label="",style="solid", color="black", weight=3];
67.32/34.79	7165[label="error []",fontsize=16,color="red",shape="box"];7166[label="primQuotInt (vuz319 * vuz317) (reduce2D (vuz316 * vuz317 + vuz318 * vuz319) (vuz319 * vuz317))",fontsize=16,color="black",shape="box"];7166 -> 7176[label="",style="solid", color="black", weight=3];
67.32/34.79	7480[label="primMulNat vuz30610 vuz30710",fontsize=16,color="burlywood",shape="triangle"];10845[label="vuz30610/Succ vuz306100",fontsize=10,color="white",style="solid",shape="box"];7480 -> 10845[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10845 -> 7492[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	10846[label="vuz30610/Zero",fontsize=10,color="white",style="solid",shape="box"];7480 -> 10846[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10846 -> 7493[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	10279[label="vuz30710",fontsize=16,color="green",shape="box"];10280[label="vuz30610",fontsize=16,color="green",shape="box"];10281[label="vuz30610",fontsize=16,color="green",shape="box"];10282[label="vuz30710",fontsize=16,color="green",shape="box"];7532[label="False",fontsize=16,color="green",shape="box"];7533[label="True",fontsize=16,color="green",shape="box"];7547[label="False",fontsize=16,color="green",shape="box"];7548[label="True",fontsize=16,color="green",shape="box"];7175[label="primQuotInt (primPlusInt (vuz316 * vuz317) (vuz318 * vuz319)) (reduce2D (primPlusInt (vuz316 * vuz317) (vuz318 * vuz319)) (vuz319 * vuz317))",fontsize=16,color="black",shape="box"];7175 -> 7185[label="",style="solid", color="black", weight=3];
67.32/34.79	7176[label="primQuotInt (primMulInt vuz319 vuz317) (reduce2D (vuz316 * vuz317 + vuz318 * vuz319) (primMulInt vuz319 vuz317))",fontsize=16,color="burlywood",shape="box"];10847[label="vuz319/Pos vuz3190",fontsize=10,color="white",style="solid",shape="box"];7176 -> 10847[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10847 -> 7186[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	10848[label="vuz319/Neg vuz3190",fontsize=10,color="white",style="solid",shape="box"];7176 -> 10848[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10848 -> 7187[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	7492[label="primMulNat (Succ vuz306100) vuz30710",fontsize=16,color="burlywood",shape="box"];10849[label="vuz30710/Succ vuz307100",fontsize=10,color="white",style="solid",shape="box"];7492 -> 10849[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10849 -> 7515[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	10850[label="vuz30710/Zero",fontsize=10,color="white",style="solid",shape="box"];7492 -> 10850[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10850 -> 7516[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	7493[label="primMulNat Zero vuz30710",fontsize=16,color="burlywood",shape="box"];10851[label="vuz30710/Succ vuz307100",fontsize=10,color="white",style="solid",shape="box"];7493 -> 10851[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10851 -> 7517[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	10852[label="vuz30710/Zero",fontsize=10,color="white",style="solid",shape="box"];7493 -> 10852[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10852 -> 7518[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	7185[label="primQuotInt (primPlusInt (primMulInt vuz316 vuz317) (vuz318 * vuz319)) (reduce2D (primPlusInt (primMulInt vuz316 vuz317) (vuz318 * vuz319)) (vuz319 * vuz317))",fontsize=16,color="burlywood",shape="box"];10853[label="vuz316/Pos vuz3160",fontsize=10,color="white",style="solid",shape="box"];7185 -> 10853[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10853 -> 7194[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	10854[label="vuz316/Neg vuz3160",fontsize=10,color="white",style="solid",shape="box"];7185 -> 10854[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10854 -> 7195[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	7186[label="primQuotInt (primMulInt (Pos vuz3190) vuz317) (reduce2D (vuz316 * vuz317 + vuz318 * Pos vuz3190) (primMulInt (Pos vuz3190) vuz317))",fontsize=16,color="burlywood",shape="box"];10855[label="vuz317/Pos vuz3170",fontsize=10,color="white",style="solid",shape="box"];7186 -> 10855[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10855 -> 7196[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	10856[label="vuz317/Neg vuz3170",fontsize=10,color="white",style="solid",shape="box"];7186 -> 10856[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10856 -> 7197[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	7187[label="primQuotInt (primMulInt (Neg vuz3190) vuz317) (reduce2D (vuz316 * vuz317 + vuz318 * Neg vuz3190) (primMulInt (Neg vuz3190) vuz317))",fontsize=16,color="burlywood",shape="box"];10857[label="vuz317/Pos vuz3170",fontsize=10,color="white",style="solid",shape="box"];7187 -> 10857[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10857 -> 7198[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	10858[label="vuz317/Neg vuz3170",fontsize=10,color="white",style="solid",shape="box"];7187 -> 10858[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10858 -> 7199[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	7515[label="primMulNat (Succ vuz306100) (Succ vuz307100)",fontsize=16,color="black",shape="box"];7515 -> 7528[label="",style="solid", color="black", weight=3];
67.32/34.79	7516[label="primMulNat (Succ vuz306100) Zero",fontsize=16,color="black",shape="box"];7516 -> 7529[label="",style="solid", color="black", weight=3];
67.32/34.79	7517[label="primMulNat Zero (Succ vuz307100)",fontsize=16,color="black",shape="box"];7517 -> 7530[label="",style="solid", color="black", weight=3];
67.32/34.79	7518[label="primMulNat Zero Zero",fontsize=16,color="black",shape="box"];7518 -> 7531[label="",style="solid", color="black", weight=3];
67.32/34.79	7194[label="primQuotInt (primPlusInt (primMulInt (Pos vuz3160) vuz317) (vuz318 * vuz319)) (reduce2D (primPlusInt (primMulInt (Pos vuz3160) vuz317) (vuz318 * vuz319)) (vuz319 * vuz317))",fontsize=16,color="burlywood",shape="box"];10859[label="vuz317/Pos vuz3170",fontsize=10,color="white",style="solid",shape="box"];7194 -> 10859[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10859 -> 7206[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	10860[label="vuz317/Neg vuz3170",fontsize=10,color="white",style="solid",shape="box"];7194 -> 10860[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10860 -> 7207[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	7195[label="primQuotInt (primPlusInt (primMulInt (Neg vuz3160) vuz317) (vuz318 * vuz319)) (reduce2D (primPlusInt (primMulInt (Neg vuz3160) vuz317) (vuz318 * vuz319)) (vuz319 * vuz317))",fontsize=16,color="burlywood",shape="box"];10861[label="vuz317/Pos vuz3170",fontsize=10,color="white",style="solid",shape="box"];7195 -> 10861[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10861 -> 7208[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	10862[label="vuz317/Neg vuz3170",fontsize=10,color="white",style="solid",shape="box"];7195 -> 10862[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10862 -> 7209[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	7196[label="primQuotInt (primMulInt (Pos vuz3190) (Pos vuz3170)) (reduce2D (vuz316 * Pos vuz3170 + vuz318 * Pos vuz3190) (primMulInt (Pos vuz3190) (Pos vuz3170)))",fontsize=16,color="black",shape="box"];7196 -> 7210[label="",style="solid", color="black", weight=3];
67.32/34.79	7197[label="primQuotInt (primMulInt (Pos vuz3190) (Neg vuz3170)) (reduce2D (vuz316 * Neg vuz3170 + vuz318 * Pos vuz3190) (primMulInt (Pos vuz3190) (Neg vuz3170)))",fontsize=16,color="black",shape="box"];7197 -> 7211[label="",style="solid", color="black", weight=3];
67.32/34.79	7198[label="primQuotInt (primMulInt (Neg vuz3190) (Pos vuz3170)) (reduce2D (vuz316 * Pos vuz3170 + vuz318 * Neg vuz3190) (primMulInt (Neg vuz3190) (Pos vuz3170)))",fontsize=16,color="black",shape="box"];7198 -> 7212[label="",style="solid", color="black", weight=3];
67.32/34.79	7199[label="primQuotInt (primMulInt (Neg vuz3190) (Neg vuz3170)) (reduce2D (vuz316 * Neg vuz3170 + vuz318 * Neg vuz3190) (primMulInt (Neg vuz3190) (Neg vuz3170)))",fontsize=16,color="black",shape="box"];7199 -> 7213[label="",style="solid", color="black", weight=3];
67.32/34.79	7528 -> 7549[label="",style="dashed", color="red", weight=0];
67.32/34.79	7528[label="primPlusNat (primMulNat vuz306100 (Succ vuz307100)) (Succ vuz307100)",fontsize=16,color="magenta"];7528 -> 7550[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7529[label="Zero",fontsize=16,color="green",shape="box"];7530[label="Zero",fontsize=16,color="green",shape="box"];7531[label="Zero",fontsize=16,color="green",shape="box"];7206[label="primQuotInt (primPlusInt (primMulInt (Pos vuz3160) (Pos vuz3170)) (vuz318 * vuz319)) (reduce2D (primPlusInt (primMulInt (Pos vuz3160) (Pos vuz3170)) (vuz318 * vuz319)) (vuz319 * Pos vuz3170))",fontsize=16,color="black",shape="box"];7206 -> 7220[label="",style="solid", color="black", weight=3];
67.32/34.79	7207[label="primQuotInt (primPlusInt (primMulInt (Pos vuz3160) (Neg vuz3170)) (vuz318 * vuz319)) (reduce2D (primPlusInt (primMulInt (Pos vuz3160) (Neg vuz3170)) (vuz318 * vuz319)) (vuz319 * Neg vuz3170))",fontsize=16,color="black",shape="box"];7207 -> 7221[label="",style="solid", color="black", weight=3];
67.32/34.79	7208[label="primQuotInt (primPlusInt (primMulInt (Neg vuz3160) (Pos vuz3170)) (vuz318 * vuz319)) (reduce2D (primPlusInt (primMulInt (Neg vuz3160) (Pos vuz3170)) (vuz318 * vuz319)) (vuz319 * Pos vuz3170))",fontsize=16,color="black",shape="box"];7208 -> 7222[label="",style="solid", color="black", weight=3];
67.32/34.79	7209[label="primQuotInt (primPlusInt (primMulInt (Neg vuz3160) (Neg vuz3170)) (vuz318 * vuz319)) (reduce2D (primPlusInt (primMulInt (Neg vuz3160) (Neg vuz3170)) (vuz318 * vuz319)) (vuz319 * Neg vuz3170))",fontsize=16,color="black",shape="box"];7209 -> 7223[label="",style="solid", color="black", weight=3];
67.32/34.79	7210[label="primQuotInt (Pos (primMulNat vuz3190 vuz3170)) (reduce2D (vuz316 * Pos vuz3170 + vuz318 * Pos vuz3190) (Pos (primMulNat vuz3190 vuz3170)))",fontsize=16,color="black",shape="box"];7210 -> 7224[label="",style="solid", color="black", weight=3];
67.32/34.79	7211[label="primQuotInt (Neg (primMulNat vuz3190 vuz3170)) (reduce2D (vuz316 * Neg vuz3170 + vuz318 * Pos vuz3190) (Neg (primMulNat vuz3190 vuz3170)))",fontsize=16,color="black",shape="box"];7211 -> 7225[label="",style="solid", color="black", weight=3];
67.32/34.79	7212[label="primQuotInt (Neg (primMulNat vuz3190 vuz3170)) (reduce2D (vuz316 * Pos vuz3170 + vuz318 * Neg vuz3190) (Neg (primMulNat vuz3190 vuz3170)))",fontsize=16,color="black",shape="box"];7212 -> 7226[label="",style="solid", color="black", weight=3];
67.32/34.79	7213[label="primQuotInt (Pos (primMulNat vuz3190 vuz3170)) (reduce2D (vuz316 * Neg vuz3170 + vuz318 * Neg vuz3190) (Pos (primMulNat vuz3190 vuz3170)))",fontsize=16,color="black",shape="box"];7213 -> 7227[label="",style="solid", color="black", weight=3];
67.32/34.79	7550 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7550[label="primMulNat vuz306100 (Succ vuz307100)",fontsize=16,color="magenta"];7550 -> 7551[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7550 -> 7552[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7549[label="primPlusNat vuz335 (Succ vuz307100)",fontsize=16,color="burlywood",shape="triangle"];10863[label="vuz335/Succ vuz3350",fontsize=10,color="white",style="solid",shape="box"];7549 -> 10863[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10863 -> 7553[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	10864[label="vuz335/Zero",fontsize=10,color="white",style="solid",shape="box"];7549 -> 10864[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10864 -> 7554[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	7220[label="primQuotInt (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (vuz318 * vuz319)) (reduce2D (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (vuz318 * vuz319)) (vuz319 * Pos vuz3170))",fontsize=16,color="black",shape="box"];7220 -> 7234[label="",style="solid", color="black", weight=3];
67.32/34.79	7221[label="primQuotInt (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (vuz318 * vuz319)) (reduce2D (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (vuz318 * vuz319)) (vuz319 * Neg vuz3170))",fontsize=16,color="black",shape="box"];7221 -> 7235[label="",style="solid", color="black", weight=3];
67.32/34.79	7222[label="primQuotInt (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (vuz318 * vuz319)) (reduce2D (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (vuz318 * vuz319)) (vuz319 * Pos vuz3170))",fontsize=16,color="black",shape="box"];7222 -> 7236[label="",style="solid", color="black", weight=3];
67.32/34.79	7223[label="primQuotInt (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (vuz318 * vuz319)) (reduce2D (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (vuz318 * vuz319)) (vuz319 * Neg vuz3170))",fontsize=16,color="black",shape="box"];7223 -> 7237[label="",style="solid", color="black", weight=3];
67.32/34.79	7224[label="primQuotInt (Pos (primMulNat vuz3190 vuz3170)) (gcd (vuz316 * Pos vuz3170 + vuz318 * Pos vuz3190) (Pos (primMulNat vuz3190 vuz3170)))",fontsize=16,color="black",shape="box"];7224 -> 7238[label="",style="solid", color="black", weight=3];
67.32/34.79	7225[label="primQuotInt (Neg (primMulNat vuz3190 vuz3170)) (gcd (vuz316 * Neg vuz3170 + vuz318 * Pos vuz3190) (Neg (primMulNat vuz3190 vuz3170)))",fontsize=16,color="black",shape="box"];7225 -> 7239[label="",style="solid", color="black", weight=3];
67.32/34.79	7226[label="primQuotInt (Neg (primMulNat vuz3190 vuz3170)) (gcd (vuz316 * Pos vuz3170 + vuz318 * Neg vuz3190) (Neg (primMulNat vuz3190 vuz3170)))",fontsize=16,color="black",shape="box"];7226 -> 7240[label="",style="solid", color="black", weight=3];
67.32/34.79	7227[label="primQuotInt (Pos (primMulNat vuz3190 vuz3170)) (gcd (vuz316 * Neg vuz3170 + vuz318 * Neg vuz3190) (Pos (primMulNat vuz3190 vuz3170)))",fontsize=16,color="black",shape="box"];7227 -> 7241[label="",style="solid", color="black", weight=3];
67.32/34.79	7551[label="vuz306100",fontsize=16,color="green",shape="box"];7552[label="Succ vuz307100",fontsize=16,color="green",shape="box"];7553[label="primPlusNat (Succ vuz3350) (Succ vuz307100)",fontsize=16,color="black",shape="box"];7553 -> 7564[label="",style="solid", color="black", weight=3];
67.32/34.79	7554[label="primPlusNat Zero (Succ vuz307100)",fontsize=16,color="black",shape="box"];7554 -> 7565[label="",style="solid", color="black", weight=3];
67.32/34.79	7234[label="primQuotInt (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (primMulInt vuz318 vuz319)) (reduce2D (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (primMulInt vuz318 vuz319)) (vuz319 * Pos vuz3170))",fontsize=16,color="burlywood",shape="box"];10865[label="vuz318/Pos vuz3180",fontsize=10,color="white",style="solid",shape="box"];7234 -> 10865[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10865 -> 7250[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	10866[label="vuz318/Neg vuz3180",fontsize=10,color="white",style="solid",shape="box"];7234 -> 10866[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10866 -> 7251[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	7235[label="primQuotInt (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (primMulInt vuz318 vuz319)) (reduce2D (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (primMulInt vuz318 vuz319)) (vuz319 * Neg vuz3170))",fontsize=16,color="burlywood",shape="box"];10867[label="vuz318/Pos vuz3180",fontsize=10,color="white",style="solid",shape="box"];7235 -> 10867[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10867 -> 7252[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	10868[label="vuz318/Neg vuz3180",fontsize=10,color="white",style="solid",shape="box"];7235 -> 10868[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10868 -> 7253[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	7236[label="primQuotInt (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (primMulInt vuz318 vuz319)) (reduce2D (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (primMulInt vuz318 vuz319)) (vuz319 * Pos vuz3170))",fontsize=16,color="burlywood",shape="box"];10869[label="vuz318/Pos vuz3180",fontsize=10,color="white",style="solid",shape="box"];7236 -> 10869[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10869 -> 7254[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	10870[label="vuz318/Neg vuz3180",fontsize=10,color="white",style="solid",shape="box"];7236 -> 10870[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10870 -> 7255[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	7237[label="primQuotInt (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (primMulInt vuz318 vuz319)) (reduce2D (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (primMulInt vuz318 vuz319)) (vuz319 * Neg vuz3170))",fontsize=16,color="burlywood",shape="box"];10871[label="vuz318/Pos vuz3180",fontsize=10,color="white",style="solid",shape="box"];7237 -> 10871[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10871 -> 7256[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	10872[label="vuz318/Neg vuz3180",fontsize=10,color="white",style="solid",shape="box"];7237 -> 10872[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10872 -> 7257[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	7238[label="primQuotInt (Pos (primMulNat vuz3190 vuz3170)) (gcd3 (vuz316 * Pos vuz3170 + vuz318 * Pos vuz3190) (Pos (primMulNat vuz3190 vuz3170)))",fontsize=16,color="black",shape="box"];7238 -> 7258[label="",style="solid", color="black", weight=3];
67.32/34.79	7239[label="primQuotInt (Neg (primMulNat vuz3190 vuz3170)) (gcd3 (vuz316 * Neg vuz3170 + vuz318 * Pos vuz3190) (Neg (primMulNat vuz3190 vuz3170)))",fontsize=16,color="black",shape="box"];7239 -> 7259[label="",style="solid", color="black", weight=3];
67.32/34.79	7240[label="primQuotInt (Neg (primMulNat vuz3190 vuz3170)) (gcd3 (vuz316 * Pos vuz3170 + vuz318 * Neg vuz3190) (Neg (primMulNat vuz3190 vuz3170)))",fontsize=16,color="black",shape="box"];7240 -> 7260[label="",style="solid", color="black", weight=3];
67.32/34.79	7241[label="primQuotInt (Pos (primMulNat vuz3190 vuz3170)) (gcd3 (vuz316 * Neg vuz3170 + vuz318 * Neg vuz3190) (Pos (primMulNat vuz3190 vuz3170)))",fontsize=16,color="black",shape="box"];7241 -> 7261[label="",style="solid", color="black", weight=3];
67.32/34.79	7564[label="Succ (Succ (primPlusNat vuz3350 vuz307100))",fontsize=16,color="green",shape="box"];7564 -> 7571[label="",style="dashed", color="green", weight=3];
67.32/34.79	7565[label="Succ vuz307100",fontsize=16,color="green",shape="box"];7250[label="primQuotInt (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (primMulInt (Pos vuz3180) vuz319)) (reduce2D (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (primMulInt (Pos vuz3180) vuz319)) (vuz319 * Pos vuz3170))",fontsize=16,color="burlywood",shape="box"];10873[label="vuz319/Pos vuz3190",fontsize=10,color="white",style="solid",shape="box"];7250 -> 10873[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10873 -> 7268[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	10874[label="vuz319/Neg vuz3190",fontsize=10,color="white",style="solid",shape="box"];7250 -> 10874[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10874 -> 7269[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	7251[label="primQuotInt (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (primMulInt (Neg vuz3180) vuz319)) (reduce2D (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (primMulInt (Neg vuz3180) vuz319)) (vuz319 * Pos vuz3170))",fontsize=16,color="burlywood",shape="box"];10875[label="vuz319/Pos vuz3190",fontsize=10,color="white",style="solid",shape="box"];7251 -> 10875[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10875 -> 7270[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	10876[label="vuz319/Neg vuz3190",fontsize=10,color="white",style="solid",shape="box"];7251 -> 10876[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10876 -> 7271[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	7252[label="primQuotInt (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (primMulInt (Pos vuz3180) vuz319)) (reduce2D (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (primMulInt (Pos vuz3180) vuz319)) (vuz319 * Neg vuz3170))",fontsize=16,color="burlywood",shape="box"];10877[label="vuz319/Pos vuz3190",fontsize=10,color="white",style="solid",shape="box"];7252 -> 10877[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10877 -> 7272[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	10878[label="vuz319/Neg vuz3190",fontsize=10,color="white",style="solid",shape="box"];7252 -> 10878[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10878 -> 7273[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	7253[label="primQuotInt (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (primMulInt (Neg vuz3180) vuz319)) (reduce2D (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (primMulInt (Neg vuz3180) vuz319)) (vuz319 * Neg vuz3170))",fontsize=16,color="burlywood",shape="box"];10879[label="vuz319/Pos vuz3190",fontsize=10,color="white",style="solid",shape="box"];7253 -> 10879[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10879 -> 7274[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	10880[label="vuz319/Neg vuz3190",fontsize=10,color="white",style="solid",shape="box"];7253 -> 10880[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10880 -> 7275[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	7254[label="primQuotInt (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (primMulInt (Pos vuz3180) vuz319)) (reduce2D (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (primMulInt (Pos vuz3180) vuz319)) (vuz319 * Pos vuz3170))",fontsize=16,color="burlywood",shape="box"];10881[label="vuz319/Pos vuz3190",fontsize=10,color="white",style="solid",shape="box"];7254 -> 10881[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10881 -> 7276[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	10882[label="vuz319/Neg vuz3190",fontsize=10,color="white",style="solid",shape="box"];7254 -> 10882[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10882 -> 7277[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	7255[label="primQuotInt (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (primMulInt (Neg vuz3180) vuz319)) (reduce2D (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (primMulInt (Neg vuz3180) vuz319)) (vuz319 * Pos vuz3170))",fontsize=16,color="burlywood",shape="box"];10883[label="vuz319/Pos vuz3190",fontsize=10,color="white",style="solid",shape="box"];7255 -> 10883[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10883 -> 7278[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	10884[label="vuz319/Neg vuz3190",fontsize=10,color="white",style="solid",shape="box"];7255 -> 10884[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10884 -> 7279[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	7256[label="primQuotInt (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (primMulInt (Pos vuz3180) vuz319)) (reduce2D (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (primMulInt (Pos vuz3180) vuz319)) (vuz319 * Neg vuz3170))",fontsize=16,color="burlywood",shape="box"];10885[label="vuz319/Pos vuz3190",fontsize=10,color="white",style="solid",shape="box"];7256 -> 10885[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10885 -> 7280[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	10886[label="vuz319/Neg vuz3190",fontsize=10,color="white",style="solid",shape="box"];7256 -> 10886[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10886 -> 7281[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	7257[label="primQuotInt (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (primMulInt (Neg vuz3180) vuz319)) (reduce2D (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (primMulInt (Neg vuz3180) vuz319)) (vuz319 * Neg vuz3170))",fontsize=16,color="burlywood",shape="box"];10887[label="vuz319/Pos vuz3190",fontsize=10,color="white",style="solid",shape="box"];7257 -> 10887[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10887 -> 7282[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	10888[label="vuz319/Neg vuz3190",fontsize=10,color="white",style="solid",shape="box"];7257 -> 10888[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10888 -> 7283[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	7258[label="primQuotInt (Pos (primMulNat vuz3190 vuz3170)) (gcd2 (vuz316 * Pos vuz3170 + vuz318 * Pos vuz3190 == fromInt (Pos Zero)) (vuz316 * Pos vuz3170 + vuz318 * Pos vuz3190) (Pos (primMulNat vuz3190 vuz3170)))",fontsize=16,color="black",shape="box"];7258 -> 7284[label="",style="solid", color="black", weight=3];
67.32/34.79	7259[label="primQuotInt (Neg (primMulNat vuz3190 vuz3170)) (gcd2 (vuz316 * Neg vuz3170 + vuz318 * Pos vuz3190 == fromInt (Pos Zero)) (vuz316 * Neg vuz3170 + vuz318 * Pos vuz3190) (Neg (primMulNat vuz3190 vuz3170)))",fontsize=16,color="black",shape="box"];7259 -> 7285[label="",style="solid", color="black", weight=3];
67.32/34.79	7260[label="primQuotInt (Neg (primMulNat vuz3190 vuz3170)) (gcd2 (vuz316 * Pos vuz3170 + vuz318 * Neg vuz3190 == fromInt (Pos Zero)) (vuz316 * Pos vuz3170 + vuz318 * Neg vuz3190) (Neg (primMulNat vuz3190 vuz3170)))",fontsize=16,color="black",shape="box"];7260 -> 7286[label="",style="solid", color="black", weight=3];
67.32/34.79	7261[label="primQuotInt (Pos (primMulNat vuz3190 vuz3170)) (gcd2 (vuz316 * Neg vuz3170 + vuz318 * Neg vuz3190 == fromInt (Pos Zero)) (vuz316 * Neg vuz3170 + vuz318 * Neg vuz3190) (Pos (primMulNat vuz3190 vuz3170)))",fontsize=16,color="black",shape="box"];7261 -> 7287[label="",style="solid", color="black", weight=3];
67.32/34.79	7571[label="primPlusNat vuz3350 vuz307100",fontsize=16,color="burlywood",shape="triangle"];10889[label="vuz3350/Succ vuz33500",fontsize=10,color="white",style="solid",shape="box"];7571 -> 10889[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10889 -> 7585[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	10890[label="vuz3350/Zero",fontsize=10,color="white",style="solid",shape="box"];7571 -> 10890[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10890 -> 7586[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	7268[label="primQuotInt (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (primMulInt (Pos vuz3180) (Pos vuz3190))) (reduce2D (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (primMulInt (Pos vuz3180) (Pos vuz3190))) (Pos vuz3190 * Pos vuz3170))",fontsize=16,color="black",shape="box"];7268 -> 7296[label="",style="solid", color="black", weight=3];
67.32/34.79	7269[label="primQuotInt (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (primMulInt (Pos vuz3180) (Neg vuz3190))) (reduce2D (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (primMulInt (Pos vuz3180) (Neg vuz3190))) (Neg vuz3190 * Pos vuz3170))",fontsize=16,color="black",shape="box"];7269 -> 7297[label="",style="solid", color="black", weight=3];
67.32/34.79	7270[label="primQuotInt (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (primMulInt (Neg vuz3180) (Pos vuz3190))) (reduce2D (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (primMulInt (Neg vuz3180) (Pos vuz3190))) (Pos vuz3190 * Pos vuz3170))",fontsize=16,color="black",shape="box"];7270 -> 7298[label="",style="solid", color="black", weight=3];
67.32/34.79	7271[label="primQuotInt (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (primMulInt (Neg vuz3180) (Neg vuz3190))) (reduce2D (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (primMulInt (Neg vuz3180) (Neg vuz3190))) (Neg vuz3190 * Pos vuz3170))",fontsize=16,color="black",shape="box"];7271 -> 7299[label="",style="solid", color="black", weight=3];
67.32/34.79	7272[label="primQuotInt (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (primMulInt (Pos vuz3180) (Pos vuz3190))) (reduce2D (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (primMulInt (Pos vuz3180) (Pos vuz3190))) (Pos vuz3190 * Neg vuz3170))",fontsize=16,color="black",shape="box"];7272 -> 7300[label="",style="solid", color="black", weight=3];
67.32/34.79	7273[label="primQuotInt (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (primMulInt (Pos vuz3180) (Neg vuz3190))) (reduce2D (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (primMulInt (Pos vuz3180) (Neg vuz3190))) (Neg vuz3190 * Neg vuz3170))",fontsize=16,color="black",shape="box"];7273 -> 7301[label="",style="solid", color="black", weight=3];
67.32/34.79	7274[label="primQuotInt (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (primMulInt (Neg vuz3180) (Pos vuz3190))) (reduce2D (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (primMulInt (Neg vuz3180) (Pos vuz3190))) (Pos vuz3190 * Neg vuz3170))",fontsize=16,color="black",shape="box"];7274 -> 7302[label="",style="solid", color="black", weight=3];
67.32/34.79	7275[label="primQuotInt (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (primMulInt (Neg vuz3180) (Neg vuz3190))) (reduce2D (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (primMulInt (Neg vuz3180) (Neg vuz3190))) (Neg vuz3190 * Neg vuz3170))",fontsize=16,color="black",shape="box"];7275 -> 7303[label="",style="solid", color="black", weight=3];
67.32/34.79	7276[label="primQuotInt (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (primMulInt (Pos vuz3180) (Pos vuz3190))) (reduce2D (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (primMulInt (Pos vuz3180) (Pos vuz3190))) (Pos vuz3190 * Pos vuz3170))",fontsize=16,color="black",shape="box"];7276 -> 7304[label="",style="solid", color="black", weight=3];
67.32/34.79	7277[label="primQuotInt (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (primMulInt (Pos vuz3180) (Neg vuz3190))) (reduce2D (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (primMulInt (Pos vuz3180) (Neg vuz3190))) (Neg vuz3190 * Pos vuz3170))",fontsize=16,color="black",shape="box"];7277 -> 7305[label="",style="solid", color="black", weight=3];
67.32/34.79	7278[label="primQuotInt (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (primMulInt (Neg vuz3180) (Pos vuz3190))) (reduce2D (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (primMulInt (Neg vuz3180) (Pos vuz3190))) (Pos vuz3190 * Pos vuz3170))",fontsize=16,color="black",shape="box"];7278 -> 7306[label="",style="solid", color="black", weight=3];
67.32/34.79	7279[label="primQuotInt (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (primMulInt (Neg vuz3180) (Neg vuz3190))) (reduce2D (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (primMulInt (Neg vuz3180) (Neg vuz3190))) (Neg vuz3190 * Pos vuz3170))",fontsize=16,color="black",shape="box"];7279 -> 7307[label="",style="solid", color="black", weight=3];
67.32/34.79	7280[label="primQuotInt (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (primMulInt (Pos vuz3180) (Pos vuz3190))) (reduce2D (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (primMulInt (Pos vuz3180) (Pos vuz3190))) (Pos vuz3190 * Neg vuz3170))",fontsize=16,color="black",shape="box"];7280 -> 7308[label="",style="solid", color="black", weight=3];
67.32/34.79	7281[label="primQuotInt (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (primMulInt (Pos vuz3180) (Neg vuz3190))) (reduce2D (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (primMulInt (Pos vuz3180) (Neg vuz3190))) (Neg vuz3190 * Neg vuz3170))",fontsize=16,color="black",shape="box"];7281 -> 7309[label="",style="solid", color="black", weight=3];
67.32/34.79	7282[label="primQuotInt (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (primMulInt (Neg vuz3180) (Pos vuz3190))) (reduce2D (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (primMulInt (Neg vuz3180) (Pos vuz3190))) (Pos vuz3190 * Neg vuz3170))",fontsize=16,color="black",shape="box"];7282 -> 7310[label="",style="solid", color="black", weight=3];
67.32/34.79	7283[label="primQuotInt (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (primMulInt (Neg vuz3180) (Neg vuz3190))) (reduce2D (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (primMulInt (Neg vuz3180) (Neg vuz3190))) (Neg vuz3190 * Neg vuz3170))",fontsize=16,color="black",shape="box"];7283 -> 7311[label="",style="solid", color="black", weight=3];
67.32/34.79	7284[label="primQuotInt (Pos (primMulNat vuz3190 vuz3170)) (gcd2 (primEqInt (vuz316 * Pos vuz3170 + vuz318 * Pos vuz3190) (fromInt (Pos Zero))) (vuz316 * Pos vuz3170 + vuz318 * Pos vuz3190) (Pos (primMulNat vuz3190 vuz3170)))",fontsize=16,color="black",shape="box"];7284 -> 7312[label="",style="solid", color="black", weight=3];
67.32/34.79	7285[label="primQuotInt (Neg (primMulNat vuz3190 vuz3170)) (gcd2 (primEqInt (vuz316 * Neg vuz3170 + vuz318 * Pos vuz3190) (fromInt (Pos Zero))) (vuz316 * Neg vuz3170 + vuz318 * Pos vuz3190) (Neg (primMulNat vuz3190 vuz3170)))",fontsize=16,color="black",shape="box"];7285 -> 7313[label="",style="solid", color="black", weight=3];
67.32/34.79	7286[label="primQuotInt (Neg (primMulNat vuz3190 vuz3170)) (gcd2 (primEqInt (vuz316 * Pos vuz3170 + vuz318 * Neg vuz3190) (fromInt (Pos Zero))) (vuz316 * Pos vuz3170 + vuz318 * Neg vuz3190) (Neg (primMulNat vuz3190 vuz3170)))",fontsize=16,color="black",shape="box"];7286 -> 7314[label="",style="solid", color="black", weight=3];
67.32/34.79	7287[label="primQuotInt (Pos (primMulNat vuz3190 vuz3170)) (gcd2 (primEqInt (vuz316 * Neg vuz3170 + vuz318 * Neg vuz3190) (fromInt (Pos Zero))) (vuz316 * Neg vuz3170 + vuz318 * Neg vuz3190) (Pos (primMulNat vuz3190 vuz3170)))",fontsize=16,color="black",shape="box"];7287 -> 7315[label="",style="solid", color="black", weight=3];
67.32/34.79	7585[label="primPlusNat (Succ vuz33500) vuz307100",fontsize=16,color="burlywood",shape="box"];10891[label="vuz307100/Succ vuz3071000",fontsize=10,color="white",style="solid",shape="box"];7585 -> 10891[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10891 -> 7590[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	10892[label="vuz307100/Zero",fontsize=10,color="white",style="solid",shape="box"];7585 -> 10892[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10892 -> 7591[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	7586[label="primPlusNat Zero vuz307100",fontsize=16,color="burlywood",shape="box"];10893[label="vuz307100/Succ vuz3071000",fontsize=10,color="white",style="solid",shape="box"];7586 -> 10893[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10893 -> 7592[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	10894[label="vuz307100/Zero",fontsize=10,color="white",style="solid",shape="box"];7586 -> 10894[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10894 -> 7593[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	7296[label="primQuotInt (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (Pos (primMulNat vuz3180 vuz3190))) (reduce2D (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (Pos (primMulNat vuz3180 vuz3190))) (Pos vuz3190 * Pos vuz3170))",fontsize=16,color="black",shape="box"];7296 -> 7324[label="",style="solid", color="black", weight=3];
67.32/34.79	7297[label="primQuotInt (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (Neg (primMulNat vuz3180 vuz3190))) (reduce2D (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (Neg (primMulNat vuz3180 vuz3190))) (Neg vuz3190 * Pos vuz3170))",fontsize=16,color="black",shape="box"];7297 -> 7325[label="",style="solid", color="black", weight=3];
67.32/34.79	7298[label="primQuotInt (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (Neg (primMulNat vuz3180 vuz3190))) (reduce2D (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (Neg (primMulNat vuz3180 vuz3190))) (Pos vuz3190 * Pos vuz3170))",fontsize=16,color="black",shape="box"];7298 -> 7326[label="",style="solid", color="black", weight=3];
67.32/34.79	7299[label="primQuotInt (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (Pos (primMulNat vuz3180 vuz3190))) (reduce2D (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (Pos (primMulNat vuz3180 vuz3190))) (Neg vuz3190 * Pos vuz3170))",fontsize=16,color="black",shape="box"];7299 -> 7327[label="",style="solid", color="black", weight=3];
67.32/34.79	7300[label="primQuotInt (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (Pos (primMulNat vuz3180 vuz3190))) (reduce2D (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (Pos (primMulNat vuz3180 vuz3190))) (Pos vuz3190 * Neg vuz3170))",fontsize=16,color="black",shape="box"];7300 -> 7328[label="",style="solid", color="black", weight=3];
67.32/34.79	7301[label="primQuotInt (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (Neg (primMulNat vuz3180 vuz3190))) (reduce2D (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (Neg (primMulNat vuz3180 vuz3190))) (Neg vuz3190 * Neg vuz3170))",fontsize=16,color="black",shape="box"];7301 -> 7329[label="",style="solid", color="black", weight=3];
67.32/34.79	7302[label="primQuotInt (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (Neg (primMulNat vuz3180 vuz3190))) (reduce2D (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (Neg (primMulNat vuz3180 vuz3190))) (Pos vuz3190 * Neg vuz3170))",fontsize=16,color="black",shape="box"];7302 -> 7330[label="",style="solid", color="black", weight=3];
67.32/34.79	7303[label="primQuotInt (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (Pos (primMulNat vuz3180 vuz3190))) (reduce2D (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (Pos (primMulNat vuz3180 vuz3190))) (Neg vuz3190 * Neg vuz3170))",fontsize=16,color="black",shape="box"];7303 -> 7331[label="",style="solid", color="black", weight=3];
67.32/34.79	7304[label="primQuotInt (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (Pos (primMulNat vuz3180 vuz3190))) (reduce2D (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (Pos (primMulNat vuz3180 vuz3190))) (Pos vuz3190 * Pos vuz3170))",fontsize=16,color="black",shape="box"];7304 -> 7332[label="",style="solid", color="black", weight=3];
67.32/34.79	7305[label="primQuotInt (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (Neg (primMulNat vuz3180 vuz3190))) (reduce2D (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (Neg (primMulNat vuz3180 vuz3190))) (Neg vuz3190 * Pos vuz3170))",fontsize=16,color="black",shape="box"];7305 -> 7333[label="",style="solid", color="black", weight=3];
67.32/34.79	7306[label="primQuotInt (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (Neg (primMulNat vuz3180 vuz3190))) (reduce2D (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (Neg (primMulNat vuz3180 vuz3190))) (Pos vuz3190 * Pos vuz3170))",fontsize=16,color="black",shape="box"];7306 -> 7334[label="",style="solid", color="black", weight=3];
67.32/34.79	7307[label="primQuotInt (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (Pos (primMulNat vuz3180 vuz3190))) (reduce2D (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (Pos (primMulNat vuz3180 vuz3190))) (Neg vuz3190 * Pos vuz3170))",fontsize=16,color="black",shape="box"];7307 -> 7335[label="",style="solid", color="black", weight=3];
67.32/34.79	7308[label="primQuotInt (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (Pos (primMulNat vuz3180 vuz3190))) (reduce2D (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (Pos (primMulNat vuz3180 vuz3190))) (Pos vuz3190 * Neg vuz3170))",fontsize=16,color="black",shape="box"];7308 -> 7336[label="",style="solid", color="black", weight=3];
67.32/34.79	7309[label="primQuotInt (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (Neg (primMulNat vuz3180 vuz3190))) (reduce2D (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (Neg (primMulNat vuz3180 vuz3190))) (Neg vuz3190 * Neg vuz3170))",fontsize=16,color="black",shape="box"];7309 -> 7337[label="",style="solid", color="black", weight=3];
67.32/34.79	7310[label="primQuotInt (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (Neg (primMulNat vuz3180 vuz3190))) (reduce2D (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (Neg (primMulNat vuz3180 vuz3190))) (Pos vuz3190 * Neg vuz3170))",fontsize=16,color="black",shape="box"];7310 -> 7338[label="",style="solid", color="black", weight=3];
67.32/34.79	7311[label="primQuotInt (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (Pos (primMulNat vuz3180 vuz3190))) (reduce2D (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (Pos (primMulNat vuz3180 vuz3190))) (Neg vuz3190 * Neg vuz3170))",fontsize=16,color="black",shape="box"];7311 -> 7339[label="",style="solid", color="black", weight=3];
67.32/34.79	7312[label="primQuotInt (Pos (primMulNat vuz3190 vuz3170)) (gcd2 (primEqInt (primPlusInt (vuz316 * Pos vuz3170) (vuz318 * Pos vuz3190)) (fromInt (Pos Zero))) (primPlusInt (vuz316 * Pos vuz3170) (vuz318 * Pos vuz3190)) (Pos (primMulNat vuz3190 vuz3170)))",fontsize=16,color="black",shape="box"];7312 -> 7340[label="",style="solid", color="black", weight=3];
67.32/34.79	7313[label="primQuotInt (Neg (primMulNat vuz3190 vuz3170)) (gcd2 (primEqInt (primPlusInt (vuz316 * Neg vuz3170) (vuz318 * Pos vuz3190)) (fromInt (Pos Zero))) (primPlusInt (vuz316 * Neg vuz3170) (vuz318 * Pos vuz3190)) (Neg (primMulNat vuz3190 vuz3170)))",fontsize=16,color="black",shape="box"];7313 -> 7341[label="",style="solid", color="black", weight=3];
67.32/34.79	7314[label="primQuotInt (Neg (primMulNat vuz3190 vuz3170)) (gcd2 (primEqInt (primPlusInt (vuz316 * Pos vuz3170) (vuz318 * Neg vuz3190)) (fromInt (Pos Zero))) (primPlusInt (vuz316 * Pos vuz3170) (vuz318 * Neg vuz3190)) (Neg (primMulNat vuz3190 vuz3170)))",fontsize=16,color="black",shape="box"];7314 -> 7342[label="",style="solid", color="black", weight=3];
67.32/34.79	7315[label="primQuotInt (Pos (primMulNat vuz3190 vuz3170)) (gcd2 (primEqInt (primPlusInt (vuz316 * Neg vuz3170) (vuz318 * Neg vuz3190)) (fromInt (Pos Zero))) (primPlusInt (vuz316 * Neg vuz3170) (vuz318 * Neg vuz3190)) (Pos (primMulNat vuz3190 vuz3170)))",fontsize=16,color="black",shape="box"];7315 -> 7343[label="",style="solid", color="black", weight=3];
67.32/34.79	7590[label="primPlusNat (Succ vuz33500) (Succ vuz3071000)",fontsize=16,color="black",shape="box"];7590 -> 7601[label="",style="solid", color="black", weight=3];
67.32/34.79	7591[label="primPlusNat (Succ vuz33500) Zero",fontsize=16,color="black",shape="box"];7591 -> 7602[label="",style="solid", color="black", weight=3];
67.32/34.79	7592[label="primPlusNat Zero (Succ vuz3071000)",fontsize=16,color="black",shape="box"];7592 -> 7603[label="",style="solid", color="black", weight=3];
67.32/34.79	7593[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="box"];7593 -> 7604[label="",style="solid", color="black", weight=3];
67.32/34.79	7324[label="primQuotInt (Pos (primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190))) (reduce2D (Pos (primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190))) (Pos vuz3190 * Pos vuz3170))",fontsize=16,color="black",shape="box"];7324 -> 7356[label="",style="solid", color="black", weight=3];
67.32/34.79	7325[label="primQuotInt (primMinusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190)) (reduce2D (primMinusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190)) (Neg vuz3190 * Pos vuz3170))",fontsize=16,color="burlywood",shape="box"];10895[label="vuz3160/Succ vuz31600",fontsize=10,color="white",style="solid",shape="box"];7325 -> 10895[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10895 -> 7357[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	10896[label="vuz3160/Zero",fontsize=10,color="white",style="solid",shape="box"];7325 -> 10896[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10896 -> 7358[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	7326[label="primQuotInt (primMinusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190)) (reduce2D (primMinusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190)) (Pos vuz3190 * Pos vuz3170))",fontsize=16,color="burlywood",shape="box"];10897[label="vuz3160/Succ vuz31600",fontsize=10,color="white",style="solid",shape="box"];7326 -> 10897[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10897 -> 7359[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	10898[label="vuz3160/Zero",fontsize=10,color="white",style="solid",shape="box"];7326 -> 10898[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10898 -> 7360[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	7327[label="primQuotInt (Pos (primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190))) (reduce2D (Pos (primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190))) (Neg vuz3190 * Pos vuz3170))",fontsize=16,color="black",shape="box"];7327 -> 7361[label="",style="solid", color="black", weight=3];
67.32/34.79	7328[label="primQuotInt (primMinusNat (primMulNat vuz3180 vuz3190) (primMulNat vuz3160 vuz3170)) (reduce2D (primMinusNat (primMulNat vuz3180 vuz3190) (primMulNat vuz3160 vuz3170)) (Pos vuz3190 * Neg vuz3170))",fontsize=16,color="burlywood",shape="box"];10899[label="vuz3180/Succ vuz31800",fontsize=10,color="white",style="solid",shape="box"];7328 -> 10899[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10899 -> 7362[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	10900[label="vuz3180/Zero",fontsize=10,color="white",style="solid",shape="box"];7328 -> 10900[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10900 -> 7363[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	7329[label="primQuotInt (Neg (primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190))) (reduce2D (Neg (primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190))) (Neg vuz3190 * Neg vuz3170))",fontsize=16,color="black",shape="box"];7329 -> 7364[label="",style="solid", color="black", weight=3];
67.32/34.79	7330[label="primQuotInt (Neg (primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190))) (reduce2D (Neg (primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190))) (Pos vuz3190 * Neg vuz3170))",fontsize=16,color="black",shape="box"];7330 -> 7365[label="",style="solid", color="black", weight=3];
67.32/34.79	7331[label="primQuotInt (primMinusNat (primMulNat vuz3180 vuz3190) (primMulNat vuz3160 vuz3170)) (reduce2D (primMinusNat (primMulNat vuz3180 vuz3190) (primMulNat vuz3160 vuz3170)) (Neg vuz3190 * Neg vuz3170))",fontsize=16,color="burlywood",shape="box"];10901[label="vuz3180/Succ vuz31800",fontsize=10,color="white",style="solid",shape="box"];7331 -> 10901[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10901 -> 7366[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	10902[label="vuz3180/Zero",fontsize=10,color="white",style="solid",shape="box"];7331 -> 10902[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10902 -> 7367[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	7332[label="primQuotInt (primMinusNat (primMulNat vuz3180 vuz3190) (primMulNat vuz3160 vuz3170)) (reduce2D (primMinusNat (primMulNat vuz3180 vuz3190) (primMulNat vuz3160 vuz3170)) (Pos vuz3190 * Pos vuz3170))",fontsize=16,color="burlywood",shape="box"];10903[label="vuz3180/Succ vuz31800",fontsize=10,color="white",style="solid",shape="box"];7332 -> 10903[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10903 -> 7368[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	10904[label="vuz3180/Zero",fontsize=10,color="white",style="solid",shape="box"];7332 -> 10904[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10904 -> 7369[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	7333[label="primQuotInt (Neg (primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190))) (reduce2D (Neg (primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190))) (Neg vuz3190 * Pos vuz3170))",fontsize=16,color="black",shape="box"];7333 -> 7370[label="",style="solid", color="black", weight=3];
67.32/34.79	7334[label="primQuotInt (Neg (primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190))) (reduce2D (Neg (primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190))) (Pos vuz3190 * Pos vuz3170))",fontsize=16,color="black",shape="box"];7334 -> 7371[label="",style="solid", color="black", weight=3];
67.32/34.79	7335[label="primQuotInt (primMinusNat (primMulNat vuz3180 vuz3190) (primMulNat vuz3160 vuz3170)) (reduce2D (primMinusNat (primMulNat vuz3180 vuz3190) (primMulNat vuz3160 vuz3170)) (Neg vuz3190 * Pos vuz3170))",fontsize=16,color="burlywood",shape="box"];10905[label="vuz3180/Succ vuz31800",fontsize=10,color="white",style="solid",shape="box"];7335 -> 10905[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10905 -> 7372[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	10906[label="vuz3180/Zero",fontsize=10,color="white",style="solid",shape="box"];7335 -> 10906[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10906 -> 7373[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	7336[label="primQuotInt (Pos (primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190))) (reduce2D (Pos (primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190))) (Pos vuz3190 * Neg vuz3170))",fontsize=16,color="black",shape="box"];7336 -> 7374[label="",style="solid", color="black", weight=3];
67.32/34.79	7337[label="primQuotInt (primMinusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190)) (reduce2D (primMinusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190)) (Neg vuz3190 * Neg vuz3170))",fontsize=16,color="burlywood",shape="box"];10907[label="vuz3160/Succ vuz31600",fontsize=10,color="white",style="solid",shape="box"];7337 -> 10907[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10907 -> 7375[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	10908[label="vuz3160/Zero",fontsize=10,color="white",style="solid",shape="box"];7337 -> 10908[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10908 -> 7376[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	7338[label="primQuotInt (primMinusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190)) (reduce2D (primMinusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190)) (Pos vuz3190 * Neg vuz3170))",fontsize=16,color="burlywood",shape="box"];10909[label="vuz3160/Succ vuz31600",fontsize=10,color="white",style="solid",shape="box"];7338 -> 10909[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10909 -> 7377[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	10910[label="vuz3160/Zero",fontsize=10,color="white",style="solid",shape="box"];7338 -> 10910[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10910 -> 7378[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	7339[label="primQuotInt (Pos (primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190))) (reduce2D (Pos (primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190))) (Neg vuz3190 * Neg vuz3170))",fontsize=16,color="black",shape="box"];7339 -> 7379[label="",style="solid", color="black", weight=3];
67.32/34.79	7340[label="primQuotInt (Pos (primMulNat vuz3190 vuz3170)) (gcd2 (primEqInt (primPlusInt (primMulInt vuz316 (Pos vuz3170)) (vuz318 * Pos vuz3190)) (fromInt (Pos Zero))) (primPlusInt (primMulInt vuz316 (Pos vuz3170)) (vuz318 * Pos vuz3190)) (Pos (primMulNat vuz3190 vuz3170)))",fontsize=16,color="burlywood",shape="box"];10911[label="vuz316/Pos vuz3160",fontsize=10,color="white",style="solid",shape="box"];7340 -> 10911[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10911 -> 7380[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	10912[label="vuz316/Neg vuz3160",fontsize=10,color="white",style="solid",shape="box"];7340 -> 10912[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10912 -> 7381[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	7341[label="primQuotInt (Neg (primMulNat vuz3190 vuz3170)) (gcd2 (primEqInt (primPlusInt (primMulInt vuz316 (Neg vuz3170)) (vuz318 * Pos vuz3190)) (fromInt (Pos Zero))) (primPlusInt (primMulInt vuz316 (Neg vuz3170)) (vuz318 * Pos vuz3190)) (Neg (primMulNat vuz3190 vuz3170)))",fontsize=16,color="burlywood",shape="box"];10913[label="vuz316/Pos vuz3160",fontsize=10,color="white",style="solid",shape="box"];7341 -> 10913[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10913 -> 7382[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	10914[label="vuz316/Neg vuz3160",fontsize=10,color="white",style="solid",shape="box"];7341 -> 10914[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10914 -> 7383[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	7342[label="primQuotInt (Neg (primMulNat vuz3190 vuz3170)) (gcd2 (primEqInt (primPlusInt (primMulInt vuz316 (Pos vuz3170)) (vuz318 * Neg vuz3190)) (fromInt (Pos Zero))) (primPlusInt (primMulInt vuz316 (Pos vuz3170)) (vuz318 * Neg vuz3190)) (Neg (primMulNat vuz3190 vuz3170)))",fontsize=16,color="burlywood",shape="box"];10915[label="vuz316/Pos vuz3160",fontsize=10,color="white",style="solid",shape="box"];7342 -> 10915[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10915 -> 7384[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	10916[label="vuz316/Neg vuz3160",fontsize=10,color="white",style="solid",shape="box"];7342 -> 10916[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10916 -> 7385[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	7343[label="primQuotInt (Pos (primMulNat vuz3190 vuz3170)) (gcd2 (primEqInt (primPlusInt (primMulInt vuz316 (Neg vuz3170)) (vuz318 * Neg vuz3190)) (fromInt (Pos Zero))) (primPlusInt (primMulInt vuz316 (Neg vuz3170)) (vuz318 * Neg vuz3190)) (Pos (primMulNat vuz3190 vuz3170)))",fontsize=16,color="burlywood",shape="box"];10917[label="vuz316/Pos vuz3160",fontsize=10,color="white",style="solid",shape="box"];7343 -> 10917[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10917 -> 7386[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	10918[label="vuz316/Neg vuz3160",fontsize=10,color="white",style="solid",shape="box"];7343 -> 10918[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10918 -> 7387[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	7601[label="Succ (Succ (primPlusNat vuz33500 vuz3071000))",fontsize=16,color="green",shape="box"];7601 -> 7616[label="",style="dashed", color="green", weight=3];
67.32/34.79	7602[label="Succ vuz33500",fontsize=16,color="green",shape="box"];7603[label="Succ vuz3071000",fontsize=16,color="green",shape="box"];7604[label="Zero",fontsize=16,color="green",shape="box"];7356[label="primQuotInt (Pos (primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190))) (gcd (Pos (primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190))) (Pos vuz3190 * Pos vuz3170))",fontsize=16,color="black",shape="box"];7356 -> 7427[label="",style="solid", color="black", weight=3];
67.32/34.79	7357[label="primQuotInt (primMinusNat (primMulNat (Succ vuz31600) vuz3170) (primMulNat vuz3180 vuz3190)) (reduce2D (primMinusNat (primMulNat (Succ vuz31600) vuz3170) (primMulNat vuz3180 vuz3190)) (Neg vuz3190 * Pos vuz3170))",fontsize=16,color="burlywood",shape="box"];10919[label="vuz3170/Succ vuz31700",fontsize=10,color="white",style="solid",shape="box"];7357 -> 10919[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10919 -> 7428[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	10920[label="vuz3170/Zero",fontsize=10,color="white",style="solid",shape="box"];7357 -> 10920[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10920 -> 7429[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	7358[label="primQuotInt (primMinusNat (primMulNat Zero vuz3170) (primMulNat vuz3180 vuz3190)) (reduce2D (primMinusNat (primMulNat Zero vuz3170) (primMulNat vuz3180 vuz3190)) (Neg vuz3190 * Pos vuz3170))",fontsize=16,color="burlywood",shape="box"];10921[label="vuz3170/Succ vuz31700",fontsize=10,color="white",style="solid",shape="box"];7358 -> 10921[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10921 -> 7430[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	10922[label="vuz3170/Zero",fontsize=10,color="white",style="solid",shape="box"];7358 -> 10922[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10922 -> 7431[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	7359[label="primQuotInt (primMinusNat (primMulNat (Succ vuz31600) vuz3170) (primMulNat vuz3180 vuz3190)) (reduce2D (primMinusNat (primMulNat (Succ vuz31600) vuz3170) (primMulNat vuz3180 vuz3190)) (Pos vuz3190 * Pos vuz3170))",fontsize=16,color="burlywood",shape="box"];10923[label="vuz3170/Succ vuz31700",fontsize=10,color="white",style="solid",shape="box"];7359 -> 10923[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10923 -> 7432[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	10924[label="vuz3170/Zero",fontsize=10,color="white",style="solid",shape="box"];7359 -> 10924[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10924 -> 7433[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	7360[label="primQuotInt (primMinusNat (primMulNat Zero vuz3170) (primMulNat vuz3180 vuz3190)) (reduce2D (primMinusNat (primMulNat Zero vuz3170) (primMulNat vuz3180 vuz3190)) (Pos vuz3190 * Pos vuz3170))",fontsize=16,color="burlywood",shape="box"];10925[label="vuz3170/Succ vuz31700",fontsize=10,color="white",style="solid",shape="box"];7360 -> 10925[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10925 -> 7434[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	10926[label="vuz3170/Zero",fontsize=10,color="white",style="solid",shape="box"];7360 -> 10926[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10926 -> 7435[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	7361[label="primQuotInt (Pos (primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190))) (gcd (Pos (primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190))) (Neg vuz3190 * Pos vuz3170))",fontsize=16,color="black",shape="box"];7361 -> 7436[label="",style="solid", color="black", weight=3];
67.32/34.79	7362[label="primQuotInt (primMinusNat (primMulNat (Succ vuz31800) vuz3190) (primMulNat vuz3160 vuz3170)) (reduce2D (primMinusNat (primMulNat (Succ vuz31800) vuz3190) (primMulNat vuz3160 vuz3170)) (Pos vuz3190 * Neg vuz3170))",fontsize=16,color="burlywood",shape="box"];10927[label="vuz3190/Succ vuz31900",fontsize=10,color="white",style="solid",shape="box"];7362 -> 10927[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10927 -> 7437[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	10928[label="vuz3190/Zero",fontsize=10,color="white",style="solid",shape="box"];7362 -> 10928[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10928 -> 7438[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	7363[label="primQuotInt (primMinusNat (primMulNat Zero vuz3190) (primMulNat vuz3160 vuz3170)) (reduce2D (primMinusNat (primMulNat Zero vuz3190) (primMulNat vuz3160 vuz3170)) (Pos vuz3190 * Neg vuz3170))",fontsize=16,color="burlywood",shape="box"];10929[label="vuz3190/Succ vuz31900",fontsize=10,color="white",style="solid",shape="box"];7363 -> 10929[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10929 -> 7439[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	10930[label="vuz3190/Zero",fontsize=10,color="white",style="solid",shape="box"];7363 -> 10930[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10930 -> 7440[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	7364[label="primQuotInt (Neg (primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190))) (gcd (Neg (primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190))) (Neg vuz3190 * Neg vuz3170))",fontsize=16,color="black",shape="box"];7364 -> 7441[label="",style="solid", color="black", weight=3];
67.32/34.79	7365[label="primQuotInt (Neg (primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190))) (gcd (Neg (primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190))) (Pos vuz3190 * Neg vuz3170))",fontsize=16,color="black",shape="box"];7365 -> 7442[label="",style="solid", color="black", weight=3];
67.32/34.79	7366[label="primQuotInt (primMinusNat (primMulNat (Succ vuz31800) vuz3190) (primMulNat vuz3160 vuz3170)) (reduce2D (primMinusNat (primMulNat (Succ vuz31800) vuz3190) (primMulNat vuz3160 vuz3170)) (Neg vuz3190 * Neg vuz3170))",fontsize=16,color="burlywood",shape="box"];10931[label="vuz3190/Succ vuz31900",fontsize=10,color="white",style="solid",shape="box"];7366 -> 10931[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10931 -> 7443[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	10932[label="vuz3190/Zero",fontsize=10,color="white",style="solid",shape="box"];7366 -> 10932[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10932 -> 7444[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	7367[label="primQuotInt (primMinusNat (primMulNat Zero vuz3190) (primMulNat vuz3160 vuz3170)) (reduce2D (primMinusNat (primMulNat Zero vuz3190) (primMulNat vuz3160 vuz3170)) (Neg vuz3190 * Neg vuz3170))",fontsize=16,color="burlywood",shape="box"];10933[label="vuz3190/Succ vuz31900",fontsize=10,color="white",style="solid",shape="box"];7367 -> 10933[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10933 -> 7445[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	10934[label="vuz3190/Zero",fontsize=10,color="white",style="solid",shape="box"];7367 -> 10934[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10934 -> 7446[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	7368[label="primQuotInt (primMinusNat (primMulNat (Succ vuz31800) vuz3190) (primMulNat vuz3160 vuz3170)) (reduce2D (primMinusNat (primMulNat (Succ vuz31800) vuz3190) (primMulNat vuz3160 vuz3170)) (Pos vuz3190 * Pos vuz3170))",fontsize=16,color="burlywood",shape="box"];10935[label="vuz3190/Succ vuz31900",fontsize=10,color="white",style="solid",shape="box"];7368 -> 10935[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10935 -> 7447[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	10936[label="vuz3190/Zero",fontsize=10,color="white",style="solid",shape="box"];7368 -> 10936[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10936 -> 7448[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	7369[label="primQuotInt (primMinusNat (primMulNat Zero vuz3190) (primMulNat vuz3160 vuz3170)) (reduce2D (primMinusNat (primMulNat Zero vuz3190) (primMulNat vuz3160 vuz3170)) (Pos vuz3190 * Pos vuz3170))",fontsize=16,color="burlywood",shape="box"];10937[label="vuz3190/Succ vuz31900",fontsize=10,color="white",style="solid",shape="box"];7369 -> 10937[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10937 -> 7449[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	10938[label="vuz3190/Zero",fontsize=10,color="white",style="solid",shape="box"];7369 -> 10938[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10938 -> 7450[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	7370[label="primQuotInt (Neg (primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190))) (gcd (Neg (primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190))) (Neg vuz3190 * Pos vuz3170))",fontsize=16,color="black",shape="box"];7370 -> 7451[label="",style="solid", color="black", weight=3];
67.32/34.79	7371[label="primQuotInt (Neg (primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190))) (gcd (Neg (primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190))) (Pos vuz3190 * Pos vuz3170))",fontsize=16,color="black",shape="box"];7371 -> 7452[label="",style="solid", color="black", weight=3];
67.32/34.79	7372[label="primQuotInt (primMinusNat (primMulNat (Succ vuz31800) vuz3190) (primMulNat vuz3160 vuz3170)) (reduce2D (primMinusNat (primMulNat (Succ vuz31800) vuz3190) (primMulNat vuz3160 vuz3170)) (Neg vuz3190 * Pos vuz3170))",fontsize=16,color="burlywood",shape="box"];10939[label="vuz3190/Succ vuz31900",fontsize=10,color="white",style="solid",shape="box"];7372 -> 10939[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10939 -> 7453[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	10940[label="vuz3190/Zero",fontsize=10,color="white",style="solid",shape="box"];7372 -> 10940[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10940 -> 7454[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	7373[label="primQuotInt (primMinusNat (primMulNat Zero vuz3190) (primMulNat vuz3160 vuz3170)) (reduce2D (primMinusNat (primMulNat Zero vuz3190) (primMulNat vuz3160 vuz3170)) (Neg vuz3190 * Pos vuz3170))",fontsize=16,color="burlywood",shape="box"];10941[label="vuz3190/Succ vuz31900",fontsize=10,color="white",style="solid",shape="box"];7373 -> 10941[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10941 -> 7455[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	10942[label="vuz3190/Zero",fontsize=10,color="white",style="solid",shape="box"];7373 -> 10942[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10942 -> 7456[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	7374[label="primQuotInt (Pos (primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190))) (gcd (Pos (primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190))) (Pos vuz3190 * Neg vuz3170))",fontsize=16,color="black",shape="box"];7374 -> 7457[label="",style="solid", color="black", weight=3];
67.32/34.79	7375[label="primQuotInt (primMinusNat (primMulNat (Succ vuz31600) vuz3170) (primMulNat vuz3180 vuz3190)) (reduce2D (primMinusNat (primMulNat (Succ vuz31600) vuz3170) (primMulNat vuz3180 vuz3190)) (Neg vuz3190 * Neg vuz3170))",fontsize=16,color="burlywood",shape="box"];10943[label="vuz3170/Succ vuz31700",fontsize=10,color="white",style="solid",shape="box"];7375 -> 10943[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10943 -> 7458[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	10944[label="vuz3170/Zero",fontsize=10,color="white",style="solid",shape="box"];7375 -> 10944[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10944 -> 7459[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	7376[label="primQuotInt (primMinusNat (primMulNat Zero vuz3170) (primMulNat vuz3180 vuz3190)) (reduce2D (primMinusNat (primMulNat Zero vuz3170) (primMulNat vuz3180 vuz3190)) (Neg vuz3190 * Neg vuz3170))",fontsize=16,color="burlywood",shape="box"];10945[label="vuz3170/Succ vuz31700",fontsize=10,color="white",style="solid",shape="box"];7376 -> 10945[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10945 -> 7460[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	10946[label="vuz3170/Zero",fontsize=10,color="white",style="solid",shape="box"];7376 -> 10946[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10946 -> 7461[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	7377[label="primQuotInt (primMinusNat (primMulNat (Succ vuz31600) vuz3170) (primMulNat vuz3180 vuz3190)) (reduce2D (primMinusNat (primMulNat (Succ vuz31600) vuz3170) (primMulNat vuz3180 vuz3190)) (Pos vuz3190 * Neg vuz3170))",fontsize=16,color="burlywood",shape="box"];10947[label="vuz3170/Succ vuz31700",fontsize=10,color="white",style="solid",shape="box"];7377 -> 10947[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10947 -> 7462[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	10948[label="vuz3170/Zero",fontsize=10,color="white",style="solid",shape="box"];7377 -> 10948[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10948 -> 7463[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	7378[label="primQuotInt (primMinusNat (primMulNat Zero vuz3170) (primMulNat vuz3180 vuz3190)) (reduce2D (primMinusNat (primMulNat Zero vuz3170) (primMulNat vuz3180 vuz3190)) (Pos vuz3190 * Neg vuz3170))",fontsize=16,color="burlywood",shape="box"];10949[label="vuz3170/Succ vuz31700",fontsize=10,color="white",style="solid",shape="box"];7378 -> 10949[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10949 -> 7464[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	10950[label="vuz3170/Zero",fontsize=10,color="white",style="solid",shape="box"];7378 -> 10950[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10950 -> 7465[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	7379[label="primQuotInt (Pos (primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190))) (gcd (Pos (primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190))) (Neg vuz3190 * Neg vuz3170))",fontsize=16,color="black",shape="box"];7379 -> 7466[label="",style="solid", color="black", weight=3];
67.32/34.79	7380[label="primQuotInt (Pos (primMulNat vuz3190 vuz3170)) (gcd2 (primEqInt (primPlusInt (primMulInt (Pos vuz3160) (Pos vuz3170)) (vuz318 * Pos vuz3190)) (fromInt (Pos Zero))) (primPlusInt (primMulInt (Pos vuz3160) (Pos vuz3170)) (vuz318 * Pos vuz3190)) (Pos (primMulNat vuz3190 vuz3170)))",fontsize=16,color="black",shape="box"];7380 -> 7467[label="",style="solid", color="black", weight=3];
67.32/34.79	7381[label="primQuotInt (Pos (primMulNat vuz3190 vuz3170)) (gcd2 (primEqInt (primPlusInt (primMulInt (Neg vuz3160) (Pos vuz3170)) (vuz318 * Pos vuz3190)) (fromInt (Pos Zero))) (primPlusInt (primMulInt (Neg vuz3160) (Pos vuz3170)) (vuz318 * Pos vuz3190)) (Pos (primMulNat vuz3190 vuz3170)))",fontsize=16,color="black",shape="box"];7381 -> 7468[label="",style="solid", color="black", weight=3];
67.32/34.79	7382[label="primQuotInt (Neg (primMulNat vuz3190 vuz3170)) (gcd2 (primEqInt (primPlusInt (primMulInt (Pos vuz3160) (Neg vuz3170)) (vuz318 * Pos vuz3190)) (fromInt (Pos Zero))) (primPlusInt (primMulInt (Pos vuz3160) (Neg vuz3170)) (vuz318 * Pos vuz3190)) (Neg (primMulNat vuz3190 vuz3170)))",fontsize=16,color="black",shape="box"];7382 -> 7469[label="",style="solid", color="black", weight=3];
67.32/34.79	7383[label="primQuotInt (Neg (primMulNat vuz3190 vuz3170)) (gcd2 (primEqInt (primPlusInt (primMulInt (Neg vuz3160) (Neg vuz3170)) (vuz318 * Pos vuz3190)) (fromInt (Pos Zero))) (primPlusInt (primMulInt (Neg vuz3160) (Neg vuz3170)) (vuz318 * Pos vuz3190)) (Neg (primMulNat vuz3190 vuz3170)))",fontsize=16,color="black",shape="box"];7383 -> 7470[label="",style="solid", color="black", weight=3];
67.32/34.79	7384[label="primQuotInt (Neg (primMulNat vuz3190 vuz3170)) (gcd2 (primEqInt (primPlusInt (primMulInt (Pos vuz3160) (Pos vuz3170)) (vuz318 * Neg vuz3190)) (fromInt (Pos Zero))) (primPlusInt (primMulInt (Pos vuz3160) (Pos vuz3170)) (vuz318 * Neg vuz3190)) (Neg (primMulNat vuz3190 vuz3170)))",fontsize=16,color="black",shape="box"];7384 -> 7471[label="",style="solid", color="black", weight=3];
67.32/34.79	7385[label="primQuotInt (Neg (primMulNat vuz3190 vuz3170)) (gcd2 (primEqInt (primPlusInt (primMulInt (Neg vuz3160) (Pos vuz3170)) (vuz318 * Neg vuz3190)) (fromInt (Pos Zero))) (primPlusInt (primMulInt (Neg vuz3160) (Pos vuz3170)) (vuz318 * Neg vuz3190)) (Neg (primMulNat vuz3190 vuz3170)))",fontsize=16,color="black",shape="box"];7385 -> 7472[label="",style="solid", color="black", weight=3];
67.32/34.79	7386[label="primQuotInt (Pos (primMulNat vuz3190 vuz3170)) (gcd2 (primEqInt (primPlusInt (primMulInt (Pos vuz3160) (Neg vuz3170)) (vuz318 * Neg vuz3190)) (fromInt (Pos Zero))) (primPlusInt (primMulInt (Pos vuz3160) (Neg vuz3170)) (vuz318 * Neg vuz3190)) (Pos (primMulNat vuz3190 vuz3170)))",fontsize=16,color="black",shape="box"];7386 -> 7473[label="",style="solid", color="black", weight=3];
67.32/34.79	7387[label="primQuotInt (Pos (primMulNat vuz3190 vuz3170)) (gcd2 (primEqInt (primPlusInt (primMulInt (Neg vuz3160) (Neg vuz3170)) (vuz318 * Neg vuz3190)) (fromInt (Pos Zero))) (primPlusInt (primMulInt (Neg vuz3160) (Neg vuz3170)) (vuz318 * Neg vuz3190)) (Pos (primMulNat vuz3190 vuz3170)))",fontsize=16,color="black",shape="box"];7387 -> 7474[label="",style="solid", color="black", weight=3];
67.32/34.79	7616 -> 7571[label="",style="dashed", color="red", weight=0];
67.32/34.79	7616[label="primPlusNat vuz33500 vuz3071000",fontsize=16,color="magenta"];7616 -> 7622[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7616 -> 7623[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7427 -> 7667[label="",style="dashed", color="red", weight=0];
67.32/34.79	7427[label="primQuotInt (Pos (primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190))) (gcd3 (Pos (primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190))) (Pos vuz3190 * Pos vuz3170))",fontsize=16,color="magenta"];7427 -> 7668[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7427 -> 7669[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7428[label="primQuotInt (primMinusNat (primMulNat (Succ vuz31600) (Succ vuz31700)) (primMulNat vuz3180 vuz3190)) (reduce2D (primMinusNat (primMulNat (Succ vuz31600) (Succ vuz31700)) (primMulNat vuz3180 vuz3190)) (Neg vuz3190 * Pos (Succ vuz31700)))",fontsize=16,color="black",shape="box"];7428 -> 7534[label="",style="solid", color="black", weight=3];
67.32/34.79	7429[label="primQuotInt (primMinusNat (primMulNat (Succ vuz31600) Zero) (primMulNat vuz3180 vuz3190)) (reduce2D (primMinusNat (primMulNat (Succ vuz31600) Zero) (primMulNat vuz3180 vuz3190)) (Neg vuz3190 * Pos Zero))",fontsize=16,color="black",shape="box"];7429 -> 7535[label="",style="solid", color="black", weight=3];
67.32/34.79	7430[label="primQuotInt (primMinusNat (primMulNat Zero (Succ vuz31700)) (primMulNat vuz3180 vuz3190)) (reduce2D (primMinusNat (primMulNat Zero (Succ vuz31700)) (primMulNat vuz3180 vuz3190)) (Neg vuz3190 * Pos (Succ vuz31700)))",fontsize=16,color="black",shape="box"];7430 -> 7536[label="",style="solid", color="black", weight=3];
67.32/34.79	7431[label="primQuotInt (primMinusNat (primMulNat Zero Zero) (primMulNat vuz3180 vuz3190)) (reduce2D (primMinusNat (primMulNat Zero Zero) (primMulNat vuz3180 vuz3190)) (Neg vuz3190 * Pos Zero))",fontsize=16,color="black",shape="box"];7431 -> 7537[label="",style="solid", color="black", weight=3];
67.32/34.79	7432[label="primQuotInt (primMinusNat (primMulNat (Succ vuz31600) (Succ vuz31700)) (primMulNat vuz3180 vuz3190)) (reduce2D (primMinusNat (primMulNat (Succ vuz31600) (Succ vuz31700)) (primMulNat vuz3180 vuz3190)) (Pos vuz3190 * Pos (Succ vuz31700)))",fontsize=16,color="black",shape="box"];7432 -> 7538[label="",style="solid", color="black", weight=3];
67.32/34.79	7433[label="primQuotInt (primMinusNat (primMulNat (Succ vuz31600) Zero) (primMulNat vuz3180 vuz3190)) (reduce2D (primMinusNat (primMulNat (Succ vuz31600) Zero) (primMulNat vuz3180 vuz3190)) (Pos vuz3190 * Pos Zero))",fontsize=16,color="black",shape="box"];7433 -> 7539[label="",style="solid", color="black", weight=3];
67.32/34.79	7434[label="primQuotInt (primMinusNat (primMulNat Zero (Succ vuz31700)) (primMulNat vuz3180 vuz3190)) (reduce2D (primMinusNat (primMulNat Zero (Succ vuz31700)) (primMulNat vuz3180 vuz3190)) (Pos vuz3190 * Pos (Succ vuz31700)))",fontsize=16,color="black",shape="box"];7434 -> 7540[label="",style="solid", color="black", weight=3];
67.32/34.79	7435[label="primQuotInt (primMinusNat (primMulNat Zero Zero) (primMulNat vuz3180 vuz3190)) (reduce2D (primMinusNat (primMulNat Zero Zero) (primMulNat vuz3180 vuz3190)) (Pos vuz3190 * Pos Zero))",fontsize=16,color="black",shape="box"];7435 -> 7541[label="",style="solid", color="black", weight=3];
67.32/34.79	7436 -> 7713[label="",style="dashed", color="red", weight=0];
67.32/34.79	7436[label="primQuotInt (Pos (primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190))) (gcd3 (Pos (primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190))) (Neg vuz3190 * Pos vuz3170))",fontsize=16,color="magenta"];7436 -> 7714[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7436 -> 7715[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7437[label="primQuotInt (primMinusNat (primMulNat (Succ vuz31800) (Succ vuz31900)) (primMulNat vuz3160 vuz3170)) (reduce2D (primMinusNat (primMulNat (Succ vuz31800) (Succ vuz31900)) (primMulNat vuz3160 vuz3170)) (Pos (Succ vuz31900) * Neg vuz3170))",fontsize=16,color="black",shape="box"];7437 -> 7555[label="",style="solid", color="black", weight=3];
67.32/34.79	7438[label="primQuotInt (primMinusNat (primMulNat (Succ vuz31800) Zero) (primMulNat vuz3160 vuz3170)) (reduce2D (primMinusNat (primMulNat (Succ vuz31800) Zero) (primMulNat vuz3160 vuz3170)) (Pos Zero * Neg vuz3170))",fontsize=16,color="black",shape="box"];7438 -> 7556[label="",style="solid", color="black", weight=3];
67.32/34.79	7439[label="primQuotInt (primMinusNat (primMulNat Zero (Succ vuz31900)) (primMulNat vuz3160 vuz3170)) (reduce2D (primMinusNat (primMulNat Zero (Succ vuz31900)) (primMulNat vuz3160 vuz3170)) (Pos (Succ vuz31900) * Neg vuz3170))",fontsize=16,color="black",shape="box"];7439 -> 7557[label="",style="solid", color="black", weight=3];
67.32/34.79	7440[label="primQuotInt (primMinusNat (primMulNat Zero Zero) (primMulNat vuz3160 vuz3170)) (reduce2D (primMinusNat (primMulNat Zero Zero) (primMulNat vuz3160 vuz3170)) (Pos Zero * Neg vuz3170))",fontsize=16,color="black",shape="box"];7440 -> 7558[label="",style="solid", color="black", weight=3];
67.32/34.79	7441 -> 7745[label="",style="dashed", color="red", weight=0];
67.32/34.79	7441[label="primQuotInt (Neg (primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190))) (gcd3 (Neg (primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190))) (Neg vuz3190 * Neg vuz3170))",fontsize=16,color="magenta"];7441 -> 7746[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7441 -> 7747[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7442 -> 7763[label="",style="dashed", color="red", weight=0];
67.32/34.79	7442[label="primQuotInt (Neg (primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190))) (gcd3 (Neg (primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190))) (Pos vuz3190 * Neg vuz3170))",fontsize=16,color="magenta"];7442 -> 7764[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7442 -> 7765[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7443[label="primQuotInt (primMinusNat (primMulNat (Succ vuz31800) (Succ vuz31900)) (primMulNat vuz3160 vuz3170)) (reduce2D (primMinusNat (primMulNat (Succ vuz31800) (Succ vuz31900)) (primMulNat vuz3160 vuz3170)) (Neg (Succ vuz31900) * Neg vuz3170))",fontsize=16,color="black",shape="box"];7443 -> 7572[label="",style="solid", color="black", weight=3];
67.32/34.79	7444[label="primQuotInt (primMinusNat (primMulNat (Succ vuz31800) Zero) (primMulNat vuz3160 vuz3170)) (reduce2D (primMinusNat (primMulNat (Succ vuz31800) Zero) (primMulNat vuz3160 vuz3170)) (Neg Zero * Neg vuz3170))",fontsize=16,color="black",shape="box"];7444 -> 7573[label="",style="solid", color="black", weight=3];
67.32/34.79	7445[label="primQuotInt (primMinusNat (primMulNat Zero (Succ vuz31900)) (primMulNat vuz3160 vuz3170)) (reduce2D (primMinusNat (primMulNat Zero (Succ vuz31900)) (primMulNat vuz3160 vuz3170)) (Neg (Succ vuz31900) * Neg vuz3170))",fontsize=16,color="black",shape="box"];7445 -> 7574[label="",style="solid", color="black", weight=3];
67.32/34.79	7446[label="primQuotInt (primMinusNat (primMulNat Zero Zero) (primMulNat vuz3160 vuz3170)) (reduce2D (primMinusNat (primMulNat Zero Zero) (primMulNat vuz3160 vuz3170)) (Neg Zero * Neg vuz3170))",fontsize=16,color="black",shape="box"];7446 -> 7575[label="",style="solid", color="black", weight=3];
67.32/34.79	7447[label="primQuotInt (primMinusNat (primMulNat (Succ vuz31800) (Succ vuz31900)) (primMulNat vuz3160 vuz3170)) (reduce2D (primMinusNat (primMulNat (Succ vuz31800) (Succ vuz31900)) (primMulNat vuz3160 vuz3170)) (Pos (Succ vuz31900) * Pos vuz3170))",fontsize=16,color="black",shape="box"];7447 -> 7576[label="",style="solid", color="black", weight=3];
67.32/34.79	7448[label="primQuotInt (primMinusNat (primMulNat (Succ vuz31800) Zero) (primMulNat vuz3160 vuz3170)) (reduce2D (primMinusNat (primMulNat (Succ vuz31800) Zero) (primMulNat vuz3160 vuz3170)) (Pos Zero * Pos vuz3170))",fontsize=16,color="black",shape="box"];7448 -> 7577[label="",style="solid", color="black", weight=3];
67.32/34.79	7449[label="primQuotInt (primMinusNat (primMulNat Zero (Succ vuz31900)) (primMulNat vuz3160 vuz3170)) (reduce2D (primMinusNat (primMulNat Zero (Succ vuz31900)) (primMulNat vuz3160 vuz3170)) (Pos (Succ vuz31900) * Pos vuz3170))",fontsize=16,color="black",shape="box"];7449 -> 7578[label="",style="solid", color="black", weight=3];
67.32/34.79	7450[label="primQuotInt (primMinusNat (primMulNat Zero Zero) (primMulNat vuz3160 vuz3170)) (reduce2D (primMinusNat (primMulNat Zero Zero) (primMulNat vuz3160 vuz3170)) (Pos Zero * Pos vuz3170))",fontsize=16,color="black",shape="box"];7450 -> 7579[label="",style="solid", color="black", weight=3];
67.32/34.79	7451 -> 7809[label="",style="dashed", color="red", weight=0];
67.32/34.79	7451[label="primQuotInt (Neg (primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190))) (gcd3 (Neg (primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190))) (Neg vuz3190 * Pos vuz3170))",fontsize=16,color="magenta"];7451 -> 7810[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7451 -> 7811[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7452 -> 7587[label="",style="dashed", color="red", weight=0];
67.32/34.79	7452[label="primQuotInt (Neg (primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190))) (gcd3 (Neg (primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190))) (Pos vuz3190 * Pos vuz3170))",fontsize=16,color="magenta"];7452 -> 7588[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7452 -> 7589[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7453[label="primQuotInt (primMinusNat (primMulNat (Succ vuz31800) (Succ vuz31900)) (primMulNat vuz3160 vuz3170)) (reduce2D (primMinusNat (primMulNat (Succ vuz31800) (Succ vuz31900)) (primMulNat vuz3160 vuz3170)) (Neg (Succ vuz31900) * Pos vuz3170))",fontsize=16,color="black",shape="box"];7453 -> 7594[label="",style="solid", color="black", weight=3];
67.32/34.79	7454[label="primQuotInt (primMinusNat (primMulNat (Succ vuz31800) Zero) (primMulNat vuz3160 vuz3170)) (reduce2D (primMinusNat (primMulNat (Succ vuz31800) Zero) (primMulNat vuz3160 vuz3170)) (Neg Zero * Pos vuz3170))",fontsize=16,color="black",shape="box"];7454 -> 7595[label="",style="solid", color="black", weight=3];
67.32/34.79	7455[label="primQuotInt (primMinusNat (primMulNat Zero (Succ vuz31900)) (primMulNat vuz3160 vuz3170)) (reduce2D (primMinusNat (primMulNat Zero (Succ vuz31900)) (primMulNat vuz3160 vuz3170)) (Neg (Succ vuz31900) * Pos vuz3170))",fontsize=16,color="black",shape="box"];7455 -> 7596[label="",style="solid", color="black", weight=3];
67.32/34.79	7456[label="primQuotInt (primMinusNat (primMulNat Zero Zero) (primMulNat vuz3160 vuz3170)) (reduce2D (primMinusNat (primMulNat Zero Zero) (primMulNat vuz3160 vuz3170)) (Neg Zero * Pos vuz3170))",fontsize=16,color="black",shape="box"];7456 -> 7597[label="",style="solid", color="black", weight=3];
67.32/34.79	7457 -> 7598[label="",style="dashed", color="red", weight=0];
67.32/34.79	7457[label="primQuotInt (Pos (primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190))) (gcd3 (Pos (primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190))) (Pos vuz3190 * Neg vuz3170))",fontsize=16,color="magenta"];7457 -> 7599[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7457 -> 7600[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7458[label="primQuotInt (primMinusNat (primMulNat (Succ vuz31600) (Succ vuz31700)) (primMulNat vuz3180 vuz3190)) (reduce2D (primMinusNat (primMulNat (Succ vuz31600) (Succ vuz31700)) (primMulNat vuz3180 vuz3190)) (Neg vuz3190 * Neg (Succ vuz31700)))",fontsize=16,color="black",shape="box"];7458 -> 7605[label="",style="solid", color="black", weight=3];
67.32/34.79	7459[label="primQuotInt (primMinusNat (primMulNat (Succ vuz31600) Zero) (primMulNat vuz3180 vuz3190)) (reduce2D (primMinusNat (primMulNat (Succ vuz31600) Zero) (primMulNat vuz3180 vuz3190)) (Neg vuz3190 * Neg Zero))",fontsize=16,color="black",shape="box"];7459 -> 7606[label="",style="solid", color="black", weight=3];
67.32/34.79	7460[label="primQuotInt (primMinusNat (primMulNat Zero (Succ vuz31700)) (primMulNat vuz3180 vuz3190)) (reduce2D (primMinusNat (primMulNat Zero (Succ vuz31700)) (primMulNat vuz3180 vuz3190)) (Neg vuz3190 * Neg (Succ vuz31700)))",fontsize=16,color="black",shape="box"];7460 -> 7607[label="",style="solid", color="black", weight=3];
67.32/34.79	7461[label="primQuotInt (primMinusNat (primMulNat Zero Zero) (primMulNat vuz3180 vuz3190)) (reduce2D (primMinusNat (primMulNat Zero Zero) (primMulNat vuz3180 vuz3190)) (Neg vuz3190 * Neg Zero))",fontsize=16,color="black",shape="box"];7461 -> 7608[label="",style="solid", color="black", weight=3];
67.32/34.79	7462[label="primQuotInt (primMinusNat (primMulNat (Succ vuz31600) (Succ vuz31700)) (primMulNat vuz3180 vuz3190)) (reduce2D (primMinusNat (primMulNat (Succ vuz31600) (Succ vuz31700)) (primMulNat vuz3180 vuz3190)) (Pos vuz3190 * Neg (Succ vuz31700)))",fontsize=16,color="black",shape="box"];7462 -> 7609[label="",style="solid", color="black", weight=3];
67.32/34.79	7463[label="primQuotInt (primMinusNat (primMulNat (Succ vuz31600) Zero) (primMulNat vuz3180 vuz3190)) (reduce2D (primMinusNat (primMulNat (Succ vuz31600) Zero) (primMulNat vuz3180 vuz3190)) (Pos vuz3190 * Neg Zero))",fontsize=16,color="black",shape="box"];7463 -> 7610[label="",style="solid", color="black", weight=3];
67.32/34.79	7464[label="primQuotInt (primMinusNat (primMulNat Zero (Succ vuz31700)) (primMulNat vuz3180 vuz3190)) (reduce2D (primMinusNat (primMulNat Zero (Succ vuz31700)) (primMulNat vuz3180 vuz3190)) (Pos vuz3190 * Neg (Succ vuz31700)))",fontsize=16,color="black",shape="box"];7464 -> 7611[label="",style="solid", color="black", weight=3];
67.32/34.79	7465[label="primQuotInt (primMinusNat (primMulNat Zero Zero) (primMulNat vuz3180 vuz3190)) (reduce2D (primMinusNat (primMulNat Zero Zero) (primMulNat vuz3180 vuz3190)) (Pos vuz3190 * Neg Zero))",fontsize=16,color="black",shape="box"];7465 -> 7612[label="",style="solid", color="black", weight=3];
67.32/34.79	7466 -> 7613[label="",style="dashed", color="red", weight=0];
67.32/34.79	7466[label="primQuotInt (Pos (primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190))) (gcd3 (Pos (primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190))) (Neg vuz3190 * Neg vuz3170))",fontsize=16,color="magenta"];7466 -> 7614[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7466 -> 7615[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7467 -> 7617[label="",style="dashed", color="red", weight=0];
67.32/34.79	7467[label="primQuotInt (Pos (primMulNat vuz3190 vuz3170)) (gcd2 (primEqInt (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (vuz318 * Pos vuz3190)) (fromInt (Pos Zero))) (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (vuz318 * Pos vuz3190)) (Pos (primMulNat vuz3190 vuz3170)))",fontsize=16,color="magenta"];7467 -> 7618[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7467 -> 7619[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7467 -> 7620[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7467 -> 7621[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7468 -> 7624[label="",style="dashed", color="red", weight=0];
67.32/34.79	7468[label="primQuotInt (Pos (primMulNat vuz3190 vuz3170)) (gcd2 (primEqInt (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (vuz318 * Pos vuz3190)) (fromInt (Pos Zero))) (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (vuz318 * Pos vuz3190)) (Pos (primMulNat vuz3190 vuz3170)))",fontsize=16,color="magenta"];7468 -> 7625[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7468 -> 7626[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7468 -> 7627[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7468 -> 7628[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7469 -> 7629[label="",style="dashed", color="red", weight=0];
67.32/34.79	7469[label="primQuotInt (Neg (primMulNat vuz3190 vuz3170)) (gcd2 (primEqInt (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (vuz318 * Pos vuz3190)) (fromInt (Pos Zero))) (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (vuz318 * Pos vuz3190)) (Neg (primMulNat vuz3190 vuz3170)))",fontsize=16,color="magenta"];7469 -> 7630[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7469 -> 7631[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7469 -> 7632[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7469 -> 7633[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7470 -> 7634[label="",style="dashed", color="red", weight=0];
67.32/34.79	7470[label="primQuotInt (Neg (primMulNat vuz3190 vuz3170)) (gcd2 (primEqInt (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (vuz318 * Pos vuz3190)) (fromInt (Pos Zero))) (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (vuz318 * Pos vuz3190)) (Neg (primMulNat vuz3190 vuz3170)))",fontsize=16,color="magenta"];7470 -> 7635[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7470 -> 7636[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7470 -> 7637[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7470 -> 7638[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7471 -> 7639[label="",style="dashed", color="red", weight=0];
67.32/34.79	7471[label="primQuotInt (Neg (primMulNat vuz3190 vuz3170)) (gcd2 (primEqInt (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (vuz318 * Neg vuz3190)) (fromInt (Pos Zero))) (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (vuz318 * Neg vuz3190)) (Neg (primMulNat vuz3190 vuz3170)))",fontsize=16,color="magenta"];7471 -> 7640[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7471 -> 7641[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7471 -> 7642[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7471 -> 7643[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7472 -> 7644[label="",style="dashed", color="red", weight=0];
67.32/34.79	7472[label="primQuotInt (Neg (primMulNat vuz3190 vuz3170)) (gcd2 (primEqInt (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (vuz318 * Neg vuz3190)) (fromInt (Pos Zero))) (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (vuz318 * Neg vuz3190)) (Neg (primMulNat vuz3190 vuz3170)))",fontsize=16,color="magenta"];7472 -> 7645[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7472 -> 7646[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7472 -> 7647[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7472 -> 7648[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7473 -> 7649[label="",style="dashed", color="red", weight=0];
67.32/34.79	7473[label="primQuotInt (Pos (primMulNat vuz3190 vuz3170)) (gcd2 (primEqInt (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (vuz318 * Neg vuz3190)) (fromInt (Pos Zero))) (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (vuz318 * Neg vuz3190)) (Pos (primMulNat vuz3190 vuz3170)))",fontsize=16,color="magenta"];7473 -> 7650[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7473 -> 7651[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7473 -> 7652[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7473 -> 7653[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7474 -> 7654[label="",style="dashed", color="red", weight=0];
67.32/34.79	7474[label="primQuotInt (Pos (primMulNat vuz3190 vuz3170)) (gcd2 (primEqInt (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (vuz318 * Neg vuz3190)) (fromInt (Pos Zero))) (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (vuz318 * Neg vuz3190)) (Pos (primMulNat vuz3190 vuz3170)))",fontsize=16,color="magenta"];7474 -> 7655[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7474 -> 7656[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7474 -> 7657[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7474 -> 7658[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7622[label="vuz33500",fontsize=16,color="green",shape="box"];7623[label="vuz3071000",fontsize=16,color="green",shape="box"];7668 -> 7571[label="",style="dashed", color="red", weight=0];
67.32/34.79	7668[label="primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190)",fontsize=16,color="magenta"];7668 -> 7672[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7668 -> 7673[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7669 -> 7571[label="",style="dashed", color="red", weight=0];
67.32/34.79	7669[label="primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190)",fontsize=16,color="magenta"];7669 -> 7674[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7669 -> 7675[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7667[label="primQuotInt (Pos vuz398) (gcd3 (Pos vuz399) (Pos vuz3190 * Pos vuz3170))",fontsize=16,color="black",shape="triangle"];7667 -> 7676[label="",style="solid", color="black", weight=3];
67.32/34.79	7534 -> 7677[label="",style="dashed", color="red", weight=0];
67.32/34.79	7534[label="primQuotInt (primMinusNat (primPlusNat (primMulNat vuz31600 (Succ vuz31700)) (Succ vuz31700)) (primMulNat vuz3180 vuz3190)) (reduce2D (primMinusNat (primPlusNat (primMulNat vuz31600 (Succ vuz31700)) (Succ vuz31700)) (primMulNat vuz3180 vuz3190)) (Neg vuz3190 * Pos (Succ vuz31700)))",fontsize=16,color="magenta"];7534 -> 7678[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7534 -> 7679[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7534 -> 7680[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7534 -> 7681[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7535 -> 7686[label="",style="dashed", color="red", weight=0];
67.32/34.79	7535[label="primQuotInt (primMinusNat Zero (primMulNat vuz3180 vuz3190)) (reduce2D (primMinusNat Zero (primMulNat vuz3180 vuz3190)) (Neg vuz3190 * Pos Zero))",fontsize=16,color="magenta"];7535 -> 7687[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7535 -> 7688[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7536 -> 7677[label="",style="dashed", color="red", weight=0];
67.32/34.79	7536[label="primQuotInt (primMinusNat Zero (primMulNat vuz3180 vuz3190)) (reduce2D (primMinusNat Zero (primMulNat vuz3180 vuz3190)) (Neg vuz3190 * Pos (Succ vuz31700)))",fontsize=16,color="magenta"];7536 -> 7682[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7536 -> 7683[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7536 -> 7684[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7536 -> 7685[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7537 -> 7686[label="",style="dashed", color="red", weight=0];
67.32/34.79	7537[label="primQuotInt (primMinusNat Zero (primMulNat vuz3180 vuz3190)) (reduce2D (primMinusNat Zero (primMulNat vuz3180 vuz3190)) (Neg vuz3190 * Pos Zero))",fontsize=16,color="magenta"];7537 -> 7689[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7537 -> 7690[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7538 -> 7691[label="",style="dashed", color="red", weight=0];
67.32/34.79	7538[label="primQuotInt (primMinusNat (primPlusNat (primMulNat vuz31600 (Succ vuz31700)) (Succ vuz31700)) (primMulNat vuz3180 vuz3190)) (reduce2D (primMinusNat (primPlusNat (primMulNat vuz31600 (Succ vuz31700)) (Succ vuz31700)) (primMulNat vuz3180 vuz3190)) (Pos vuz3190 * Pos (Succ vuz31700)))",fontsize=16,color="magenta"];7538 -> 7692[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7538 -> 7693[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7538 -> 7694[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7538 -> 7695[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7539 -> 7700[label="",style="dashed", color="red", weight=0];
67.32/34.79	7539[label="primQuotInt (primMinusNat Zero (primMulNat vuz3180 vuz3190)) (reduce2D (primMinusNat Zero (primMulNat vuz3180 vuz3190)) (Pos vuz3190 * Pos Zero))",fontsize=16,color="magenta"];7539 -> 7701[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7539 -> 7702[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7540 -> 7691[label="",style="dashed", color="red", weight=0];
67.32/34.79	7540[label="primQuotInt (primMinusNat Zero (primMulNat vuz3180 vuz3190)) (reduce2D (primMinusNat Zero (primMulNat vuz3180 vuz3190)) (Pos vuz3190 * Pos (Succ vuz31700)))",fontsize=16,color="magenta"];7540 -> 7696[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7540 -> 7697[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7540 -> 7698[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7540 -> 7699[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7541 -> 7700[label="",style="dashed", color="red", weight=0];
67.32/34.79	7541[label="primQuotInt (primMinusNat Zero (primMulNat vuz3180 vuz3190)) (reduce2D (primMinusNat Zero (primMulNat vuz3180 vuz3190)) (Pos vuz3190 * Pos Zero))",fontsize=16,color="magenta"];7541 -> 7703[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7541 -> 7704[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7714 -> 7571[label="",style="dashed", color="red", weight=0];
67.32/34.79	7714[label="primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190)",fontsize=16,color="magenta"];7714 -> 7718[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7714 -> 7719[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7715 -> 7571[label="",style="dashed", color="red", weight=0];
67.32/34.79	7715[label="primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190)",fontsize=16,color="magenta"];7715 -> 7720[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7715 -> 7721[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7713[label="primQuotInt (Pos vuz416) (gcd3 (Pos vuz417) (Neg vuz3190 * Pos vuz3170))",fontsize=16,color="black",shape="triangle"];7713 -> 7722[label="",style="solid", color="black", weight=3];
67.32/34.79	7555 -> 7723[label="",style="dashed", color="red", weight=0];
67.32/34.79	7555[label="primQuotInt (primMinusNat (primPlusNat (primMulNat vuz31800 (Succ vuz31900)) (Succ vuz31900)) (primMulNat vuz3160 vuz3170)) (reduce2D (primMinusNat (primPlusNat (primMulNat vuz31800 (Succ vuz31900)) (Succ vuz31900)) (primMulNat vuz3160 vuz3170)) (Pos (Succ vuz31900) * Neg vuz3170))",fontsize=16,color="magenta"];7555 -> 7724[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7555 -> 7725[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7555 -> 7726[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7555 -> 7727[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7556 -> 7732[label="",style="dashed", color="red", weight=0];
67.32/34.79	7556[label="primQuotInt (primMinusNat Zero (primMulNat vuz3160 vuz3170)) (reduce2D (primMinusNat Zero (primMulNat vuz3160 vuz3170)) (Pos Zero * Neg vuz3170))",fontsize=16,color="magenta"];7556 -> 7733[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7556 -> 7734[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7557 -> 7723[label="",style="dashed", color="red", weight=0];
67.32/34.79	7557[label="primQuotInt (primMinusNat Zero (primMulNat vuz3160 vuz3170)) (reduce2D (primMinusNat Zero (primMulNat vuz3160 vuz3170)) (Pos (Succ vuz31900) * Neg vuz3170))",fontsize=16,color="magenta"];7557 -> 7728[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7557 -> 7729[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7557 -> 7730[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7557 -> 7731[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7558 -> 7732[label="",style="dashed", color="red", weight=0];
67.32/34.79	7558[label="primQuotInt (primMinusNat Zero (primMulNat vuz3160 vuz3170)) (reduce2D (primMinusNat Zero (primMulNat vuz3160 vuz3170)) (Pos Zero * Neg vuz3170))",fontsize=16,color="magenta"];7558 -> 7735[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7558 -> 7736[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7746 -> 7571[label="",style="dashed", color="red", weight=0];
67.32/34.79	7746[label="primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190)",fontsize=16,color="magenta"];7746 -> 7750[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7746 -> 7751[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7747 -> 7571[label="",style="dashed", color="red", weight=0];
67.32/34.79	7747[label="primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190)",fontsize=16,color="magenta"];7747 -> 7752[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7747 -> 7753[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7745[label="primQuotInt (Neg vuz426) (gcd3 (Neg vuz427) (Neg vuz3190 * Neg vuz3170))",fontsize=16,color="black",shape="triangle"];7745 -> 7754[label="",style="solid", color="black", weight=3];
67.32/34.79	7764 -> 7571[label="",style="dashed", color="red", weight=0];
67.32/34.79	7764[label="primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190)",fontsize=16,color="magenta"];7764 -> 7768[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7764 -> 7769[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7765 -> 7571[label="",style="dashed", color="red", weight=0];
67.32/34.79	7765[label="primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190)",fontsize=16,color="magenta"];7765 -> 7770[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7765 -> 7771[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7763[label="primQuotInt (Neg vuz428) (gcd3 (Neg vuz429) (Pos vuz3190 * Neg vuz3170))",fontsize=16,color="black",shape="triangle"];7763 -> 7772[label="",style="solid", color="black", weight=3];
67.32/34.79	7572 -> 7773[label="",style="dashed", color="red", weight=0];
67.32/34.79	7572[label="primQuotInt (primMinusNat (primPlusNat (primMulNat vuz31800 (Succ vuz31900)) (Succ vuz31900)) (primMulNat vuz3160 vuz3170)) (reduce2D (primMinusNat (primPlusNat (primMulNat vuz31800 (Succ vuz31900)) (Succ vuz31900)) (primMulNat vuz3160 vuz3170)) (Neg (Succ vuz31900) * Neg vuz3170))",fontsize=16,color="magenta"];7572 -> 7774[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7572 -> 7775[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7572 -> 7776[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7572 -> 7777[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7573 -> 7782[label="",style="dashed", color="red", weight=0];
67.32/34.79	7573[label="primQuotInt (primMinusNat Zero (primMulNat vuz3160 vuz3170)) (reduce2D (primMinusNat Zero (primMulNat vuz3160 vuz3170)) (Neg Zero * Neg vuz3170))",fontsize=16,color="magenta"];7573 -> 7783[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7573 -> 7784[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7574 -> 7773[label="",style="dashed", color="red", weight=0];
67.32/34.79	7574[label="primQuotInt (primMinusNat Zero (primMulNat vuz3160 vuz3170)) (reduce2D (primMinusNat Zero (primMulNat vuz3160 vuz3170)) (Neg (Succ vuz31900) * Neg vuz3170))",fontsize=16,color="magenta"];7574 -> 7778[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7574 -> 7779[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7574 -> 7780[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7574 -> 7781[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7575 -> 7782[label="",style="dashed", color="red", weight=0];
67.32/34.79	7575[label="primQuotInt (primMinusNat Zero (primMulNat vuz3160 vuz3170)) (reduce2D (primMinusNat Zero (primMulNat vuz3160 vuz3170)) (Neg Zero * Neg vuz3170))",fontsize=16,color="magenta"];7575 -> 7785[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7575 -> 7786[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7576 -> 7787[label="",style="dashed", color="red", weight=0];
67.32/34.79	7576[label="primQuotInt (primMinusNat (primPlusNat (primMulNat vuz31800 (Succ vuz31900)) (Succ vuz31900)) (primMulNat vuz3160 vuz3170)) (reduce2D (primMinusNat (primPlusNat (primMulNat vuz31800 (Succ vuz31900)) (Succ vuz31900)) (primMulNat vuz3160 vuz3170)) (Pos (Succ vuz31900) * Pos vuz3170))",fontsize=16,color="magenta"];7576 -> 7788[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7576 -> 7789[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7576 -> 7790[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7576 -> 7791[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7577 -> 7796[label="",style="dashed", color="red", weight=0];
67.32/34.79	7577[label="primQuotInt (primMinusNat Zero (primMulNat vuz3160 vuz3170)) (reduce2D (primMinusNat Zero (primMulNat vuz3160 vuz3170)) (Pos Zero * Pos vuz3170))",fontsize=16,color="magenta"];7577 -> 7797[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7577 -> 7798[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7578 -> 7787[label="",style="dashed", color="red", weight=0];
67.32/34.79	7578[label="primQuotInt (primMinusNat Zero (primMulNat vuz3160 vuz3170)) (reduce2D (primMinusNat Zero (primMulNat vuz3160 vuz3170)) (Pos (Succ vuz31900) * Pos vuz3170))",fontsize=16,color="magenta"];7578 -> 7792[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7578 -> 7793[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7578 -> 7794[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7578 -> 7795[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7579 -> 7796[label="",style="dashed", color="red", weight=0];
67.32/34.79	7579[label="primQuotInt (primMinusNat Zero (primMulNat vuz3160 vuz3170)) (reduce2D (primMinusNat Zero (primMulNat vuz3160 vuz3170)) (Pos Zero * Pos vuz3170))",fontsize=16,color="magenta"];7579 -> 7799[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7579 -> 7800[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7810 -> 7571[label="",style="dashed", color="red", weight=0];
67.32/34.79	7810[label="primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190)",fontsize=16,color="magenta"];7810 -> 7814[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7810 -> 7815[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7811 -> 7571[label="",style="dashed", color="red", weight=0];
67.32/34.79	7811[label="primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190)",fontsize=16,color="magenta"];7811 -> 7816[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7811 -> 7817[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7809[label="primQuotInt (Neg vuz446) (gcd3 (Neg vuz447) (Neg vuz3190 * Pos vuz3170))",fontsize=16,color="black",shape="triangle"];7809 -> 7818[label="",style="solid", color="black", weight=3];
67.32/34.79	7588 -> 7571[label="",style="dashed", color="red", weight=0];
67.32/34.79	7588[label="primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190)",fontsize=16,color="magenta"];7588 -> 7819[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7588 -> 7820[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7589 -> 7571[label="",style="dashed", color="red", weight=0];
67.32/34.79	7589[label="primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190)",fontsize=16,color="magenta"];7589 -> 7821[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7589 -> 7822[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7587[label="primQuotInt (Neg vuz348) (gcd3 (Neg vuz349) (Pos vuz3190 * Pos vuz3170))",fontsize=16,color="black",shape="triangle"];7587 -> 7823[label="",style="solid", color="black", weight=3];
67.32/34.79	7594 -> 7824[label="",style="dashed", color="red", weight=0];
67.32/34.79	7594[label="primQuotInt (primMinusNat (primPlusNat (primMulNat vuz31800 (Succ vuz31900)) (Succ vuz31900)) (primMulNat vuz3160 vuz3170)) (reduce2D (primMinusNat (primPlusNat (primMulNat vuz31800 (Succ vuz31900)) (Succ vuz31900)) (primMulNat vuz3160 vuz3170)) (Neg (Succ vuz31900) * Pos vuz3170))",fontsize=16,color="magenta"];7594 -> 7825[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7594 -> 7826[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7594 -> 7827[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7594 -> 7828[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7595 -> 7833[label="",style="dashed", color="red", weight=0];
67.32/34.79	7595[label="primQuotInt (primMinusNat Zero (primMulNat vuz3160 vuz3170)) (reduce2D (primMinusNat Zero (primMulNat vuz3160 vuz3170)) (Neg Zero * Pos vuz3170))",fontsize=16,color="magenta"];7595 -> 7834[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7595 -> 7835[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7596 -> 7824[label="",style="dashed", color="red", weight=0];
67.32/34.79	7596[label="primQuotInt (primMinusNat Zero (primMulNat vuz3160 vuz3170)) (reduce2D (primMinusNat Zero (primMulNat vuz3160 vuz3170)) (Neg (Succ vuz31900) * Pos vuz3170))",fontsize=16,color="magenta"];7596 -> 7829[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7596 -> 7830[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7596 -> 7831[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7596 -> 7832[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7597 -> 7833[label="",style="dashed", color="red", weight=0];
67.32/34.79	7597[label="primQuotInt (primMinusNat Zero (primMulNat vuz3160 vuz3170)) (reduce2D (primMinusNat Zero (primMulNat vuz3160 vuz3170)) (Neg Zero * Pos vuz3170))",fontsize=16,color="magenta"];7597 -> 7836[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7597 -> 7837[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7599 -> 7571[label="",style="dashed", color="red", weight=0];
67.32/34.79	7599[label="primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190)",fontsize=16,color="magenta"];7599 -> 7838[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7599 -> 7839[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7600 -> 7571[label="",style="dashed", color="red", weight=0];
67.32/34.79	7600[label="primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190)",fontsize=16,color="magenta"];7600 -> 7840[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7600 -> 7841[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7598[label="primQuotInt (Pos vuz354) (gcd3 (Pos vuz355) (Pos vuz3190 * Neg vuz3170))",fontsize=16,color="black",shape="triangle"];7598 -> 7842[label="",style="solid", color="black", weight=3];
67.32/34.79	7605 -> 7843[label="",style="dashed", color="red", weight=0];
67.32/34.79	7605[label="primQuotInt (primMinusNat (primPlusNat (primMulNat vuz31600 (Succ vuz31700)) (Succ vuz31700)) (primMulNat vuz3180 vuz3190)) (reduce2D (primMinusNat (primPlusNat (primMulNat vuz31600 (Succ vuz31700)) (Succ vuz31700)) (primMulNat vuz3180 vuz3190)) (Neg vuz3190 * Neg (Succ vuz31700)))",fontsize=16,color="magenta"];7605 -> 7844[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7605 -> 7845[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7605 -> 7846[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7605 -> 7847[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7606 -> 7852[label="",style="dashed", color="red", weight=0];
67.32/34.79	7606[label="primQuotInt (primMinusNat Zero (primMulNat vuz3180 vuz3190)) (reduce2D (primMinusNat Zero (primMulNat vuz3180 vuz3190)) (Neg vuz3190 * Neg Zero))",fontsize=16,color="magenta"];7606 -> 7853[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7606 -> 7854[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7607 -> 7843[label="",style="dashed", color="red", weight=0];
67.32/34.79	7607[label="primQuotInt (primMinusNat Zero (primMulNat vuz3180 vuz3190)) (reduce2D (primMinusNat Zero (primMulNat vuz3180 vuz3190)) (Neg vuz3190 * Neg (Succ vuz31700)))",fontsize=16,color="magenta"];7607 -> 7848[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7607 -> 7849[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7607 -> 7850[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7607 -> 7851[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7608 -> 7852[label="",style="dashed", color="red", weight=0];
67.32/34.79	7608[label="primQuotInt (primMinusNat Zero (primMulNat vuz3180 vuz3190)) (reduce2D (primMinusNat Zero (primMulNat vuz3180 vuz3190)) (Neg vuz3190 * Neg Zero))",fontsize=16,color="magenta"];7608 -> 7855[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7608 -> 7856[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7609 -> 7857[label="",style="dashed", color="red", weight=0];
67.32/34.79	7609[label="primQuotInt (primMinusNat (primPlusNat (primMulNat vuz31600 (Succ vuz31700)) (Succ vuz31700)) (primMulNat vuz3180 vuz3190)) (reduce2D (primMinusNat (primPlusNat (primMulNat vuz31600 (Succ vuz31700)) (Succ vuz31700)) (primMulNat vuz3180 vuz3190)) (Pos vuz3190 * Neg (Succ vuz31700)))",fontsize=16,color="magenta"];7609 -> 7858[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7609 -> 7859[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7609 -> 7860[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7609 -> 7861[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7610 -> 7866[label="",style="dashed", color="red", weight=0];
67.32/34.79	7610[label="primQuotInt (primMinusNat Zero (primMulNat vuz3180 vuz3190)) (reduce2D (primMinusNat Zero (primMulNat vuz3180 vuz3190)) (Pos vuz3190 * Neg Zero))",fontsize=16,color="magenta"];7610 -> 7867[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7610 -> 7868[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7611 -> 7857[label="",style="dashed", color="red", weight=0];
67.32/34.79	7611[label="primQuotInt (primMinusNat Zero (primMulNat vuz3180 vuz3190)) (reduce2D (primMinusNat Zero (primMulNat vuz3180 vuz3190)) (Pos vuz3190 * Neg (Succ vuz31700)))",fontsize=16,color="magenta"];7611 -> 7862[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7611 -> 7863[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7611 -> 7864[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7611 -> 7865[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7612 -> 7866[label="",style="dashed", color="red", weight=0];
67.32/34.79	7612[label="primQuotInt (primMinusNat Zero (primMulNat vuz3180 vuz3190)) (reduce2D (primMinusNat Zero (primMulNat vuz3180 vuz3190)) (Pos vuz3190 * Neg Zero))",fontsize=16,color="magenta"];7612 -> 7869[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7612 -> 7870[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7614 -> 7571[label="",style="dashed", color="red", weight=0];
67.32/34.79	7614[label="primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190)",fontsize=16,color="magenta"];7614 -> 7871[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7614 -> 7872[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7615 -> 7571[label="",style="dashed", color="red", weight=0];
67.32/34.79	7615[label="primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190)",fontsize=16,color="magenta"];7615 -> 7873[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7615 -> 7874[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7613[label="primQuotInt (Pos vuz360) (gcd3 (Pos vuz361) (Neg vuz3190 * Neg vuz3170))",fontsize=16,color="black",shape="triangle"];7613 -> 7875[label="",style="solid", color="black", weight=3];
67.32/34.79	7618 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7618[label="primMulNat vuz3190 vuz3170",fontsize=16,color="magenta"];7618 -> 7876[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7618 -> 7877[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7619 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7619[label="primMulNat vuz3160 vuz3170",fontsize=16,color="magenta"];7619 -> 7878[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7619 -> 7879[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7620 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7620[label="primMulNat vuz3160 vuz3170",fontsize=16,color="magenta"];7620 -> 7880[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7620 -> 7881[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7621 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7621[label="primMulNat vuz3190 vuz3170",fontsize=16,color="magenta"];7621 -> 7882[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7621 -> 7883[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7617[label="primQuotInt (Pos vuz366) (gcd2 (primEqInt (primPlusInt (Pos vuz369) (vuz318 * Pos vuz3190)) (fromInt (Pos Zero))) (primPlusInt (Pos vuz368) (vuz318 * Pos vuz3190)) (Pos vuz367))",fontsize=16,color="black",shape="triangle"];7617 -> 7884[label="",style="solid", color="black", weight=3];
67.32/34.79	7625 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7625[label="primMulNat vuz3160 vuz3170",fontsize=16,color="magenta"];7625 -> 7885[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7625 -> 7886[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7626 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7626[label="primMulNat vuz3160 vuz3170",fontsize=16,color="magenta"];7626 -> 7887[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7626 -> 7888[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7627 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7627[label="primMulNat vuz3190 vuz3170",fontsize=16,color="magenta"];7627 -> 7889[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7627 -> 7890[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7628 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7628[label="primMulNat vuz3190 vuz3170",fontsize=16,color="magenta"];7628 -> 7891[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7628 -> 7892[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7624[label="primQuotInt (Pos vuz370) (gcd2 (primEqInt (primPlusInt (Neg vuz373) (vuz318 * Pos vuz3190)) (fromInt (Pos Zero))) (primPlusInt (Neg vuz372) (vuz318 * Pos vuz3190)) (Pos vuz371))",fontsize=16,color="black",shape="triangle"];7624 -> 7893[label="",style="solid", color="black", weight=3];
67.32/34.79	7630 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7630[label="primMulNat vuz3190 vuz3170",fontsize=16,color="magenta"];7630 -> 7894[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7630 -> 7895[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7631 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7631[label="primMulNat vuz3160 vuz3170",fontsize=16,color="magenta"];7631 -> 7896[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7631 -> 7897[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7632 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7632[label="primMulNat vuz3190 vuz3170",fontsize=16,color="magenta"];7632 -> 7898[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7632 -> 7899[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7633 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7633[label="primMulNat vuz3160 vuz3170",fontsize=16,color="magenta"];7633 -> 7900[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7633 -> 7901[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7629[label="primQuotInt (Neg vuz374) (gcd2 (primEqInt (primPlusInt (Neg vuz377) (vuz318 * Pos vuz3190)) (fromInt (Pos Zero))) (primPlusInt (Neg vuz376) (vuz318 * Pos vuz3190)) (Neg vuz375))",fontsize=16,color="black",shape="triangle"];7629 -> 7902[label="",style="solid", color="black", weight=3];
67.32/34.79	7635 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7635[label="primMulNat vuz3190 vuz3170",fontsize=16,color="magenta"];7635 -> 7903[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7635 -> 7904[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7636 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7636[label="primMulNat vuz3160 vuz3170",fontsize=16,color="magenta"];7636 -> 7905[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7636 -> 7906[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7637 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7637[label="primMulNat vuz3160 vuz3170",fontsize=16,color="magenta"];7637 -> 7907[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7637 -> 7908[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7638 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7638[label="primMulNat vuz3190 vuz3170",fontsize=16,color="magenta"];7638 -> 7909[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7638 -> 7910[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7634[label="primQuotInt (Neg vuz378) (gcd2 (primEqInt (primPlusInt (Pos vuz381) (vuz318 * Pos vuz3190)) (fromInt (Pos Zero))) (primPlusInt (Pos vuz380) (vuz318 * Pos vuz3190)) (Neg vuz379))",fontsize=16,color="black",shape="triangle"];7634 -> 7911[label="",style="solid", color="black", weight=3];
67.32/34.79	7640 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7640[label="primMulNat vuz3190 vuz3170",fontsize=16,color="magenta"];7640 -> 7912[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7640 -> 7913[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7641 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7641[label="primMulNat vuz3190 vuz3170",fontsize=16,color="magenta"];7641 -> 7914[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7641 -> 7915[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7642 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7642[label="primMulNat vuz3160 vuz3170",fontsize=16,color="magenta"];7642 -> 7916[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7642 -> 7917[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7643 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7643[label="primMulNat vuz3160 vuz3170",fontsize=16,color="magenta"];7643 -> 7918[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7643 -> 7919[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7639[label="primQuotInt (Neg vuz382) (gcd2 (primEqInt (primPlusInt (Pos vuz385) (vuz318 * Neg vuz3190)) (fromInt (Pos Zero))) (primPlusInt (Pos vuz384) (vuz318 * Neg vuz3190)) (Neg vuz383))",fontsize=16,color="black",shape="triangle"];7639 -> 7920[label="",style="solid", color="black", weight=3];
67.32/34.79	7645 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7645[label="primMulNat vuz3190 vuz3170",fontsize=16,color="magenta"];7645 -> 7921[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7645 -> 7922[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7646 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7646[label="primMulNat vuz3160 vuz3170",fontsize=16,color="magenta"];7646 -> 7923[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7646 -> 7924[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7647 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7647[label="primMulNat vuz3160 vuz3170",fontsize=16,color="magenta"];7647 -> 7925[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7647 -> 7926[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7648 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7648[label="primMulNat vuz3190 vuz3170",fontsize=16,color="magenta"];7648 -> 7927[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7648 -> 7928[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7644[label="primQuotInt (Neg vuz386) (gcd2 (primEqInt (primPlusInt (Neg vuz389) (vuz318 * Neg vuz3190)) (fromInt (Pos Zero))) (primPlusInt (Neg vuz388) (vuz318 * Neg vuz3190)) (Neg vuz387))",fontsize=16,color="black",shape="triangle"];7644 -> 7929[label="",style="solid", color="black", weight=3];
67.32/34.79	7650 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7650[label="primMulNat vuz3190 vuz3170",fontsize=16,color="magenta"];7650 -> 7930[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7650 -> 7931[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7651 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7651[label="primMulNat vuz3160 vuz3170",fontsize=16,color="magenta"];7651 -> 7932[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7651 -> 7933[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7652 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7652[label="primMulNat vuz3160 vuz3170",fontsize=16,color="magenta"];7652 -> 7934[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7652 -> 7935[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7653 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7653[label="primMulNat vuz3190 vuz3170",fontsize=16,color="magenta"];7653 -> 7936[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7653 -> 7937[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7649[label="primQuotInt (Pos vuz390) (gcd2 (primEqInt (primPlusInt (Neg vuz393) (vuz318 * Neg vuz3190)) (fromInt (Pos Zero))) (primPlusInt (Neg vuz392) (vuz318 * Neg vuz3190)) (Pos vuz391))",fontsize=16,color="black",shape="triangle"];7649 -> 7938[label="",style="solid", color="black", weight=3];
67.32/34.79	7655 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7655[label="primMulNat vuz3190 vuz3170",fontsize=16,color="magenta"];7655 -> 7939[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7655 -> 7940[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7656 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7656[label="primMulNat vuz3160 vuz3170",fontsize=16,color="magenta"];7656 -> 7941[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7656 -> 7942[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7657 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7657[label="primMulNat vuz3190 vuz3170",fontsize=16,color="magenta"];7657 -> 7943[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7657 -> 7944[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7658 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7658[label="primMulNat vuz3160 vuz3170",fontsize=16,color="magenta"];7658 -> 7945[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7658 -> 7946[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7654[label="primQuotInt (Pos vuz394) (gcd2 (primEqInt (primPlusInt (Pos vuz397) (vuz318 * Neg vuz3190)) (fromInt (Pos Zero))) (primPlusInt (Pos vuz396) (vuz318 * Neg vuz3190)) (Pos vuz395))",fontsize=16,color="black",shape="triangle"];7654 -> 7947[label="",style="solid", color="black", weight=3];
67.32/34.79	7672 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7672[label="primMulNat vuz3160 vuz3170",fontsize=16,color="magenta"];7672 -> 7948[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7672 -> 7949[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7673 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7673[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];7673 -> 7950[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7673 -> 7951[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7674 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7674[label="primMulNat vuz3160 vuz3170",fontsize=16,color="magenta"];7674 -> 7952[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7674 -> 7953[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7675 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7675[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];7675 -> 7954[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7675 -> 7955[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7676 -> 8228[label="",style="dashed", color="red", weight=0];
67.32/34.79	7676[label="primQuotInt (Pos vuz398) (gcd2 (Pos vuz399 == fromInt (Pos Zero)) (Pos vuz399) (Pos vuz3190 * Pos vuz3170))",fontsize=16,color="magenta"];7676 -> 8229[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7678 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7678[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];7678 -> 7957[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7678 -> 7958[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7679 -> 7571[label="",style="dashed", color="red", weight=0];
67.32/34.79	7679[label="primPlusNat (primMulNat vuz31600 (Succ vuz31700)) (Succ vuz31700)",fontsize=16,color="magenta"];7679 -> 7959[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7679 -> 7960[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7680 -> 7571[label="",style="dashed", color="red", weight=0];
67.32/34.79	7680[label="primPlusNat (primMulNat vuz31600 (Succ vuz31700)) (Succ vuz31700)",fontsize=16,color="magenta"];7680 -> 7961[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7680 -> 7962[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7681 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7681[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];7681 -> 7963[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7681 -> 7964[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7677[label="primQuotInt (primMinusNat vuz401 vuz400) (reduce2D (primMinusNat vuz403 vuz402) (Neg vuz3190 * Pos (Succ vuz31700)))",fontsize=16,color="burlywood",shape="triangle"];10951[label="vuz401/Succ vuz4010",fontsize=10,color="white",style="solid",shape="box"];7677 -> 10951[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10951 -> 7965[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	10952[label="vuz401/Zero",fontsize=10,color="white",style="solid",shape="box"];7677 -> 10952[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10952 -> 7966[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	7687 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7687[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];7687 -> 7967[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7687 -> 7968[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7688 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7688[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];7688 -> 7969[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7688 -> 7970[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7686[label="primQuotInt (primMinusNat Zero vuz406) (reduce2D (primMinusNat Zero vuz407) (Neg vuz3190 * Pos Zero))",fontsize=16,color="burlywood",shape="triangle"];10953[label="vuz406/Succ vuz4060",fontsize=10,color="white",style="solid",shape="box"];7686 -> 10953[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10953 -> 7971[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	10954[label="vuz406/Zero",fontsize=10,color="white",style="solid",shape="box"];7686 -> 10954[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10954 -> 7972[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	7682 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7682[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];7682 -> 7973[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7682 -> 7974[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7683[label="Zero",fontsize=16,color="green",shape="box"];7684[label="Zero",fontsize=16,color="green",shape="box"];7685 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7685[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];7685 -> 7975[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7685 -> 7976[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7689 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7689[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];7689 -> 7977[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7689 -> 7978[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7690 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7690[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];7690 -> 7979[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7690 -> 7980[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7692 -> 7571[label="",style="dashed", color="red", weight=0];
67.32/34.79	7692[label="primPlusNat (primMulNat vuz31600 (Succ vuz31700)) (Succ vuz31700)",fontsize=16,color="magenta"];7692 -> 7981[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7692 -> 7982[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7693 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7693[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];7693 -> 7983[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7693 -> 7984[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7694 -> 7571[label="",style="dashed", color="red", weight=0];
67.32/34.79	7694[label="primPlusNat (primMulNat vuz31600 (Succ vuz31700)) (Succ vuz31700)",fontsize=16,color="magenta"];7694 -> 7985[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7694 -> 7986[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7695 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7695[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];7695 -> 7987[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7695 -> 7988[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7691[label="primQuotInt (primMinusNat vuz409 vuz408) (reduce2D (primMinusNat vuz411 vuz410) (Pos vuz3190 * Pos (Succ vuz31700)))",fontsize=16,color="burlywood",shape="triangle"];10955[label="vuz409/Succ vuz4090",fontsize=10,color="white",style="solid",shape="box"];7691 -> 10955[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10955 -> 7989[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	10956[label="vuz409/Zero",fontsize=10,color="white",style="solid",shape="box"];7691 -> 10956[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10956 -> 7990[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	7701 -> 7480[label="",style="dashed", color="red", weight=0];
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67.32/34.79	7701 -> 7992[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7702 -> 7480[label="",style="dashed", color="red", weight=0];
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67.32/34.79	7702 -> 7994[label="",style="dashed", color="magenta", weight=3];
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67.32/34.79	10957 -> 7995[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	10958[label="vuz414/Zero",fontsize=10,color="white",style="solid",shape="box"];7700 -> 10958[label="",style="solid", color="burlywood", weight=9];
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67.32/34.79	7697 -> 7998[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7698[label="Zero",fontsize=16,color="green",shape="box"];7699 -> 7480[label="",style="dashed", color="red", weight=0];
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67.32/34.79	7703[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];7703 -> 8001[label="",style="dashed", color="magenta", weight=3];
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67.32/34.79	7704[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];7704 -> 8003[label="",style="dashed", color="magenta", weight=3];
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67.32/34.79	7718 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7718[label="primMulNat vuz3160 vuz3170",fontsize=16,color="magenta"];7718 -> 8005[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7718 -> 8006[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7719 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7719[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];7719 -> 8007[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7719 -> 8008[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7720 -> 7480[label="",style="dashed", color="red", weight=0];
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67.32/34.79	7721 -> 7480[label="",style="dashed", color="red", weight=0];
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67.32/34.79	7722 -> 8254[label="",style="dashed", color="red", weight=0];
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67.32/34.79	7724 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7724[label="primMulNat vuz3160 vuz3170",fontsize=16,color="magenta"];7724 -> 8014[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7724 -> 8015[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7725 -> 7571[label="",style="dashed", color="red", weight=0];
67.32/34.79	7725[label="primPlusNat (primMulNat vuz31800 (Succ vuz31900)) (Succ vuz31900)",fontsize=16,color="magenta"];7725 -> 8016[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7725 -> 8017[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7726 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7726[label="primMulNat vuz3160 vuz3170",fontsize=16,color="magenta"];7726 -> 8018[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7726 -> 8019[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7727 -> 7571[label="",style="dashed", color="red", weight=0];
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67.32/34.79	7727 -> 8021[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7723[label="primQuotInt (primMinusNat vuz419 vuz418) (reduce2D (primMinusNat vuz421 vuz420) (Pos (Succ vuz31900) * Neg vuz3170))",fontsize=16,color="burlywood",shape="triangle"];10959[label="vuz419/Succ vuz4190",fontsize=10,color="white",style="solid",shape="box"];7723 -> 10959[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10959 -> 8022[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	10960[label="vuz419/Zero",fontsize=10,color="white",style="solid",shape="box"];7723 -> 10960[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10960 -> 8023[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	7733 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7733[label="primMulNat vuz3160 vuz3170",fontsize=16,color="magenta"];7733 -> 8024[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7733 -> 8025[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7734 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7734[label="primMulNat vuz3160 vuz3170",fontsize=16,color="magenta"];7734 -> 8026[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7734 -> 8027[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7732[label="primQuotInt (primMinusNat Zero vuz424) (reduce2D (primMinusNat Zero vuz425) (Pos Zero * Neg vuz3170))",fontsize=16,color="burlywood",shape="triangle"];10961[label="vuz424/Succ vuz4240",fontsize=10,color="white",style="solid",shape="box"];7732 -> 10961[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10961 -> 8028[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	10962[label="vuz424/Zero",fontsize=10,color="white",style="solid",shape="box"];7732 -> 10962[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10962 -> 8029[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	7728 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7728[label="primMulNat vuz3160 vuz3170",fontsize=16,color="magenta"];7728 -> 8030[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7728 -> 8031[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7729[label="Zero",fontsize=16,color="green",shape="box"];7730 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7730[label="primMulNat vuz3160 vuz3170",fontsize=16,color="magenta"];7730 -> 8032[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7730 -> 8033[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7731[label="Zero",fontsize=16,color="green",shape="box"];7735 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7735[label="primMulNat vuz3160 vuz3170",fontsize=16,color="magenta"];7735 -> 8034[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7735 -> 8035[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7736 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7736[label="primMulNat vuz3160 vuz3170",fontsize=16,color="magenta"];7736 -> 8036[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7736 -> 8037[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7750 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7750[label="primMulNat vuz3160 vuz3170",fontsize=16,color="magenta"];7750 -> 8038[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7750 -> 8039[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7751 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7751[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];7751 -> 8040[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7751 -> 8041[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7752 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7752[label="primMulNat vuz3160 vuz3170",fontsize=16,color="magenta"];7752 -> 8042[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7752 -> 8043[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7753 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7753[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];7753 -> 8044[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7753 -> 8045[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7754 -> 8270[label="",style="dashed", color="red", weight=0];
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67.32/34.79	7768 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7768[label="primMulNat vuz3160 vuz3170",fontsize=16,color="magenta"];7768 -> 8047[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7768 -> 8048[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7769 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7769[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];7769 -> 8049[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7769 -> 8050[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7770 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7770[label="primMulNat vuz3160 vuz3170",fontsize=16,color="magenta"];7770 -> 8051[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7770 -> 8052[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7771 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7771[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];7771 -> 8053[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7771 -> 8054[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7772 -> 8276[label="",style="dashed", color="red", weight=0];
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67.32/34.79	7774 -> 7571[label="",style="dashed", color="red", weight=0];
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67.32/34.79	7774 -> 8057[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7775 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7775[label="primMulNat vuz3160 vuz3170",fontsize=16,color="magenta"];7775 -> 8058[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7775 -> 8059[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7776 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7776[label="primMulNat vuz3160 vuz3170",fontsize=16,color="magenta"];7776 -> 8060[label="",style="dashed", color="magenta", weight=3];
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67.32/34.79	7777 -> 7571[label="",style="dashed", color="red", weight=0];
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67.32/34.79	7777 -> 8063[label="",style="dashed", color="magenta", weight=3];
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67.32/34.79	10963 -> 8064[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	10964[label="vuz431/Zero",fontsize=10,color="white",style="solid",shape="box"];7773 -> 10964[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10964 -> 8065[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	7783 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7783[label="primMulNat vuz3160 vuz3170",fontsize=16,color="magenta"];7783 -> 8066[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7783 -> 8067[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7784 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7784[label="primMulNat vuz3160 vuz3170",fontsize=16,color="magenta"];7784 -> 8068[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7784 -> 8069[label="",style="dashed", color="magenta", weight=3];
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67.32/34.79	10965 -> 8070[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	10966[label="vuz436/Zero",fontsize=10,color="white",style="solid",shape="box"];7782 -> 10966[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10966 -> 8071[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	7778[label="Zero",fontsize=16,color="green",shape="box"];7779 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7779[label="primMulNat vuz3160 vuz3170",fontsize=16,color="magenta"];7779 -> 8072[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7779 -> 8073[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7780 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7780[label="primMulNat vuz3160 vuz3170",fontsize=16,color="magenta"];7780 -> 8074[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7780 -> 8075[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7781[label="Zero",fontsize=16,color="green",shape="box"];7785 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7785[label="primMulNat vuz3160 vuz3170",fontsize=16,color="magenta"];7785 -> 8076[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7785 -> 8077[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7786 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7786[label="primMulNat vuz3160 vuz3170",fontsize=16,color="magenta"];7786 -> 8078[label="",style="dashed", color="magenta", weight=3];
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67.32/34.79	7788 -> 7571[label="",style="dashed", color="red", weight=0];
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67.32/34.79	7788 -> 8081[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7789 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7789[label="primMulNat vuz3160 vuz3170",fontsize=16,color="magenta"];7789 -> 8082[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7789 -> 8083[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7790 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7790[label="primMulNat vuz3160 vuz3170",fontsize=16,color="magenta"];7790 -> 8084[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7790 -> 8085[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7791 -> 7571[label="",style="dashed", color="red", weight=0];
67.32/34.79	7791[label="primPlusNat (primMulNat vuz31800 (Succ vuz31900)) (Succ vuz31900)",fontsize=16,color="magenta"];7791 -> 8086[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7791 -> 8087[label="",style="dashed", color="magenta", weight=3];
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67.32/34.79	10967 -> 8088[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	10968[label="vuz439/Zero",fontsize=10,color="white",style="solid",shape="box"];7787 -> 10968[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10968 -> 8089[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	7797 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7797[label="primMulNat vuz3160 vuz3170",fontsize=16,color="magenta"];7797 -> 8090[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7797 -> 8091[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7798 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7798[label="primMulNat vuz3160 vuz3170",fontsize=16,color="magenta"];7798 -> 8092[label="",style="dashed", color="magenta", weight=3];
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67.32/34.79	10969 -> 8094[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	10970[label="vuz444/Zero",fontsize=10,color="white",style="solid",shape="box"];7796 -> 10970[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10970 -> 8095[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	7792[label="Zero",fontsize=16,color="green",shape="box"];7793 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7793[label="primMulNat vuz3160 vuz3170",fontsize=16,color="magenta"];7793 -> 8096[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7793 -> 8097[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7794 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7794[label="primMulNat vuz3160 vuz3170",fontsize=16,color="magenta"];7794 -> 8098[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7794 -> 8099[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7795[label="Zero",fontsize=16,color="green",shape="box"];7799 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7799[label="primMulNat vuz3160 vuz3170",fontsize=16,color="magenta"];7799 -> 8100[label="",style="dashed", color="magenta", weight=3];
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67.32/34.79	7800 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7800[label="primMulNat vuz3160 vuz3170",fontsize=16,color="magenta"];7800 -> 8102[label="",style="dashed", color="magenta", weight=3];
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67.32/34.79	7814 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7814[label="primMulNat vuz3160 vuz3170",fontsize=16,color="magenta"];7814 -> 8104[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7814 -> 8105[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7815 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7815[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];7815 -> 8106[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7815 -> 8107[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7816 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7816[label="primMulNat vuz3160 vuz3170",fontsize=16,color="magenta"];7816 -> 8108[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7816 -> 8109[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7817 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7817[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];7817 -> 8110[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7817 -> 8111[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7818 -> 8302[label="",style="dashed", color="red", weight=0];
67.32/34.79	7818[label="primQuotInt (Neg vuz446) (gcd2 (Neg vuz447 == fromInt (Pos Zero)) (Neg vuz447) (Neg vuz3190 * Pos vuz3170))",fontsize=16,color="magenta"];7818 -> 8303[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7819 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7819[label="primMulNat vuz3160 vuz3170",fontsize=16,color="magenta"];7819 -> 8113[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7819 -> 8114[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7820 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7820[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];7820 -> 8115[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7820 -> 8116[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7821 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7821[label="primMulNat vuz3160 vuz3170",fontsize=16,color="magenta"];7821 -> 8117[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7821 -> 8118[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7822 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7822[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];7822 -> 8119[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7822 -> 8120[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7823 -> 8308[label="",style="dashed", color="red", weight=0];
67.32/34.79	7823[label="primQuotInt (Neg vuz348) (gcd2 (Neg vuz349 == fromInt (Pos Zero)) (Neg vuz349) (Pos vuz3190 * Pos vuz3170))",fontsize=16,color="magenta"];7823 -> 8309[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7825 -> 7571[label="",style="dashed", color="red", weight=0];
67.32/34.79	7825[label="primPlusNat (primMulNat vuz31800 (Succ vuz31900)) (Succ vuz31900)",fontsize=16,color="magenta"];7825 -> 8122[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7825 -> 8123[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7826 -> 7571[label="",style="dashed", color="red", weight=0];
67.32/34.79	7826[label="primPlusNat (primMulNat vuz31800 (Succ vuz31900)) (Succ vuz31900)",fontsize=16,color="magenta"];7826 -> 8124[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7826 -> 8125[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7827 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7827[label="primMulNat vuz3160 vuz3170",fontsize=16,color="magenta"];7827 -> 8126[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7827 -> 8127[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7828 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7828[label="primMulNat vuz3160 vuz3170",fontsize=16,color="magenta"];7828 -> 8128[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7828 -> 8129[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7824[label="primQuotInt (primMinusNat vuz449 vuz448) (reduce2D (primMinusNat vuz451 vuz450) (Neg (Succ vuz31900) * Pos vuz3170))",fontsize=16,color="burlywood",shape="triangle"];10971[label="vuz449/Succ vuz4490",fontsize=10,color="white",style="solid",shape="box"];7824 -> 10971[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10971 -> 8130[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	10972[label="vuz449/Zero",fontsize=10,color="white",style="solid",shape="box"];7824 -> 10972[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10972 -> 8131[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	7834 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7834[label="primMulNat vuz3160 vuz3170",fontsize=16,color="magenta"];7834 -> 8132[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7834 -> 8133[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7835 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7835[label="primMulNat vuz3160 vuz3170",fontsize=16,color="magenta"];7835 -> 8134[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7835 -> 8135[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7833[label="primQuotInt (primMinusNat Zero vuz454) (reduce2D (primMinusNat Zero vuz455) (Neg Zero * Pos vuz3170))",fontsize=16,color="burlywood",shape="triangle"];10973[label="vuz454/Succ vuz4540",fontsize=10,color="white",style="solid",shape="box"];7833 -> 10973[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10973 -> 8136[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	10974[label="vuz454/Zero",fontsize=10,color="white",style="solid",shape="box"];7833 -> 10974[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10974 -> 8137[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	7829[label="Zero",fontsize=16,color="green",shape="box"];7830[label="Zero",fontsize=16,color="green",shape="box"];7831 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7831[label="primMulNat vuz3160 vuz3170",fontsize=16,color="magenta"];7831 -> 8138[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7831 -> 8139[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7832 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7832[label="primMulNat vuz3160 vuz3170",fontsize=16,color="magenta"];7832 -> 8140[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7832 -> 8141[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7836 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7836[label="primMulNat vuz3160 vuz3170",fontsize=16,color="magenta"];7836 -> 8142[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7836 -> 8143[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7837 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7837[label="primMulNat vuz3160 vuz3170",fontsize=16,color="magenta"];7837 -> 8144[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7837 -> 8145[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7838 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7838[label="primMulNat vuz3160 vuz3170",fontsize=16,color="magenta"];7838 -> 8146[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7838 -> 8147[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7839 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7839[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];7839 -> 8148[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7839 -> 8149[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7840 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7840[label="primMulNat vuz3160 vuz3170",fontsize=16,color="magenta"];7840 -> 8150[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7840 -> 8151[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7841 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7841[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];7841 -> 8152[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7841 -> 8153[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7842 -> 8324[label="",style="dashed", color="red", weight=0];
67.32/34.79	7842[label="primQuotInt (Pos vuz354) (gcd2 (Pos vuz355 == fromInt (Pos Zero)) (Pos vuz355) (Pos vuz3190 * Neg vuz3170))",fontsize=16,color="magenta"];7842 -> 8325[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7844 -> 7571[label="",style="dashed", color="red", weight=0];
67.32/34.79	7844[label="primPlusNat (primMulNat vuz31600 (Succ vuz31700)) (Succ vuz31700)",fontsize=16,color="magenta"];7844 -> 8155[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7844 -> 8156[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7845 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7845[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];7845 -> 8157[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7845 -> 8158[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7846 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7846[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];7846 -> 8159[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7846 -> 8160[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7847 -> 7571[label="",style="dashed", color="red", weight=0];
67.32/34.79	7847[label="primPlusNat (primMulNat vuz31600 (Succ vuz31700)) (Succ vuz31700)",fontsize=16,color="magenta"];7847 -> 8161[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7847 -> 8162[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7843[label="primQuotInt (primMinusNat vuz457 vuz456) (reduce2D (primMinusNat vuz459 vuz458) (Neg vuz3190 * Neg (Succ vuz31700)))",fontsize=16,color="burlywood",shape="triangle"];10975[label="vuz457/Succ vuz4570",fontsize=10,color="white",style="solid",shape="box"];7843 -> 10975[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10975 -> 8163[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	10976[label="vuz457/Zero",fontsize=10,color="white",style="solid",shape="box"];7843 -> 10976[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10976 -> 8164[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	7853 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7853[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];7853 -> 8165[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7853 -> 8166[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7854 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7854[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];7854 -> 8167[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7854 -> 8168[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7852[label="primQuotInt (primMinusNat Zero vuz462) (reduce2D (primMinusNat Zero vuz463) (Neg vuz3190 * Neg Zero))",fontsize=16,color="burlywood",shape="triangle"];10977[label="vuz462/Succ vuz4620",fontsize=10,color="white",style="solid",shape="box"];7852 -> 10977[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10977 -> 8169[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	10978[label="vuz462/Zero",fontsize=10,color="white",style="solid",shape="box"];7852 -> 10978[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10978 -> 8170[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	7848[label="Zero",fontsize=16,color="green",shape="box"];7849 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7849[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];7849 -> 8171[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7849 -> 8172[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7850 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7850[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];7850 -> 8173[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7850 -> 8174[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7851[label="Zero",fontsize=16,color="green",shape="box"];7855 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7855[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];7855 -> 8175[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7855 -> 8176[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7856 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7856[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];7856 -> 8177[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7856 -> 8178[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7858 -> 7571[label="",style="dashed", color="red", weight=0];
67.32/34.79	7858[label="primPlusNat (primMulNat vuz31600 (Succ vuz31700)) (Succ vuz31700)",fontsize=16,color="magenta"];7858 -> 8179[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7858 -> 8180[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7859 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7859[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];7859 -> 8181[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7859 -> 8182[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7860 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7860[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];7860 -> 8183[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7860 -> 8184[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7861 -> 7571[label="",style="dashed", color="red", weight=0];
67.32/34.79	7861[label="primPlusNat (primMulNat vuz31600 (Succ vuz31700)) (Succ vuz31700)",fontsize=16,color="magenta"];7861 -> 8185[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7861 -> 8186[label="",style="dashed", color="magenta", weight=3];
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67.32/34.79	10979 -> 8187[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	10980[label="vuz465/Zero",fontsize=10,color="white",style="solid",shape="box"];7857 -> 10980[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10980 -> 8188[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	7867 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7867[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];7867 -> 8189[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7867 -> 8190[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7868 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7868[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];7868 -> 8191[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7868 -> 8192[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7866[label="primQuotInt (primMinusNat Zero vuz470) (reduce2D (primMinusNat Zero vuz471) (Pos vuz3190 * Neg Zero))",fontsize=16,color="burlywood",shape="triangle"];10981[label="vuz470/Succ vuz4700",fontsize=10,color="white",style="solid",shape="box"];7866 -> 10981[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10981 -> 8193[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	10982[label="vuz470/Zero",fontsize=10,color="white",style="solid",shape="box"];7866 -> 10982[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10982 -> 8194[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	7862[label="Zero",fontsize=16,color="green",shape="box"];7863 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7863[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];7863 -> 8195[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7863 -> 8196[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7864 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7864[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];7864 -> 8197[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7864 -> 8198[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7865[label="Zero",fontsize=16,color="green",shape="box"];7869 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7869[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];7869 -> 8199[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7869 -> 8200[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7870 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7870[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];7870 -> 8201[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7870 -> 8202[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7871 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7871[label="primMulNat vuz3160 vuz3170",fontsize=16,color="magenta"];7871 -> 8203[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7871 -> 8204[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7872 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7872[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];7872 -> 8205[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7872 -> 8206[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7873 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7873[label="primMulNat vuz3160 vuz3170",fontsize=16,color="magenta"];7873 -> 8207[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7873 -> 8208[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7874 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7874[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];7874 -> 8209[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7874 -> 8210[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7875 -> 8350[label="",style="dashed", color="red", weight=0];
67.32/34.79	7875[label="primQuotInt (Pos vuz360) (gcd2 (Pos vuz361 == fromInt (Pos Zero)) (Pos vuz361) (Neg vuz3190 * Neg vuz3170))",fontsize=16,color="magenta"];7875 -> 8351[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7876[label="vuz3190",fontsize=16,color="green",shape="box"];7877[label="vuz3170",fontsize=16,color="green",shape="box"];7878[label="vuz3160",fontsize=16,color="green",shape="box"];7879[label="vuz3170",fontsize=16,color="green",shape="box"];7880[label="vuz3160",fontsize=16,color="green",shape="box"];7881[label="vuz3170",fontsize=16,color="green",shape="box"];7882[label="vuz3190",fontsize=16,color="green",shape="box"];7883[label="vuz3170",fontsize=16,color="green",shape="box"];7884[label="primQuotInt (Pos vuz366) (gcd2 (primEqInt (primPlusInt (Pos vuz369) (primMulInt vuz318 (Pos vuz3190))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz368) (primMulInt vuz318 (Pos vuz3190))) (Pos vuz367))",fontsize=16,color="burlywood",shape="box"];10983[label="vuz318/Pos vuz3180",fontsize=10,color="white",style="solid",shape="box"];7884 -> 10983[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10983 -> 8212[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	10984[label="vuz318/Neg vuz3180",fontsize=10,color="white",style="solid",shape="box"];7884 -> 10984[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10984 -> 8213[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	7885[label="vuz3160",fontsize=16,color="green",shape="box"];7886[label="vuz3170",fontsize=16,color="green",shape="box"];7887[label="vuz3160",fontsize=16,color="green",shape="box"];7888[label="vuz3170",fontsize=16,color="green",shape="box"];7889[label="vuz3190",fontsize=16,color="green",shape="box"];7890[label="vuz3170",fontsize=16,color="green",shape="box"];7891[label="vuz3190",fontsize=16,color="green",shape="box"];7892[label="vuz3170",fontsize=16,color="green",shape="box"];7893[label="primQuotInt (Pos vuz370) (gcd2 (primEqInt (primPlusInt (Neg vuz373) (primMulInt vuz318 (Pos vuz3190))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz372) (primMulInt vuz318 (Pos vuz3190))) (Pos vuz371))",fontsize=16,color="burlywood",shape="box"];10985[label="vuz318/Pos vuz3180",fontsize=10,color="white",style="solid",shape="box"];7893 -> 10985[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10985 -> 8214[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	10986[label="vuz318/Neg vuz3180",fontsize=10,color="white",style="solid",shape="box"];7893 -> 10986[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10986 -> 8215[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	7894[label="vuz3190",fontsize=16,color="green",shape="box"];7895[label="vuz3170",fontsize=16,color="green",shape="box"];7896[label="vuz3160",fontsize=16,color="green",shape="box"];7897[label="vuz3170",fontsize=16,color="green",shape="box"];7898[label="vuz3190",fontsize=16,color="green",shape="box"];7899[label="vuz3170",fontsize=16,color="green",shape="box"];7900[label="vuz3160",fontsize=16,color="green",shape="box"];7901[label="vuz3170",fontsize=16,color="green",shape="box"];7902[label="primQuotInt (Neg vuz374) (gcd2 (primEqInt (primPlusInt (Neg vuz377) (primMulInt vuz318 (Pos vuz3190))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz376) (primMulInt vuz318 (Pos vuz3190))) (Neg vuz375))",fontsize=16,color="burlywood",shape="box"];10987[label="vuz318/Pos vuz3180",fontsize=10,color="white",style="solid",shape="box"];7902 -> 10987[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10987 -> 8216[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	10988[label="vuz318/Neg vuz3180",fontsize=10,color="white",style="solid",shape="box"];7902 -> 10988[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10988 -> 8217[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	7903[label="vuz3190",fontsize=16,color="green",shape="box"];7904[label="vuz3170",fontsize=16,color="green",shape="box"];7905[label="vuz3160",fontsize=16,color="green",shape="box"];7906[label="vuz3170",fontsize=16,color="green",shape="box"];7907[label="vuz3160",fontsize=16,color="green",shape="box"];7908[label="vuz3170",fontsize=16,color="green",shape="box"];7909[label="vuz3190",fontsize=16,color="green",shape="box"];7910[label="vuz3170",fontsize=16,color="green",shape="box"];7911[label="primQuotInt (Neg vuz378) (gcd2 (primEqInt (primPlusInt (Pos vuz381) (primMulInt vuz318 (Pos vuz3190))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz380) (primMulInt vuz318 (Pos vuz3190))) (Neg vuz379))",fontsize=16,color="burlywood",shape="box"];10989[label="vuz318/Pos vuz3180",fontsize=10,color="white",style="solid",shape="box"];7911 -> 10989[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10989 -> 8218[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	10990[label="vuz318/Neg vuz3180",fontsize=10,color="white",style="solid",shape="box"];7911 -> 10990[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10990 -> 8219[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	7912[label="vuz3190",fontsize=16,color="green",shape="box"];7913[label="vuz3170",fontsize=16,color="green",shape="box"];7914[label="vuz3190",fontsize=16,color="green",shape="box"];7915[label="vuz3170",fontsize=16,color="green",shape="box"];7916[label="vuz3160",fontsize=16,color="green",shape="box"];7917[label="vuz3170",fontsize=16,color="green",shape="box"];7918[label="vuz3160",fontsize=16,color="green",shape="box"];7919[label="vuz3170",fontsize=16,color="green",shape="box"];7920[label="primQuotInt (Neg vuz382) (gcd2 (primEqInt (primPlusInt (Pos vuz385) (primMulInt vuz318 (Neg vuz3190))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz384) (primMulInt vuz318 (Neg vuz3190))) (Neg vuz383))",fontsize=16,color="burlywood",shape="box"];10991[label="vuz318/Pos vuz3180",fontsize=10,color="white",style="solid",shape="box"];7920 -> 10991[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10991 -> 8220[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	10992[label="vuz318/Neg vuz3180",fontsize=10,color="white",style="solid",shape="box"];7920 -> 10992[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10992 -> 8221[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	7921[label="vuz3190",fontsize=16,color="green",shape="box"];7922[label="vuz3170",fontsize=16,color="green",shape="box"];7923[label="vuz3160",fontsize=16,color="green",shape="box"];7924[label="vuz3170",fontsize=16,color="green",shape="box"];7925[label="vuz3160",fontsize=16,color="green",shape="box"];7926[label="vuz3170",fontsize=16,color="green",shape="box"];7927[label="vuz3190",fontsize=16,color="green",shape="box"];7928[label="vuz3170",fontsize=16,color="green",shape="box"];7929[label="primQuotInt (Neg vuz386) (gcd2 (primEqInt (primPlusInt (Neg vuz389) (primMulInt vuz318 (Neg vuz3190))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz388) (primMulInt vuz318 (Neg vuz3190))) (Neg vuz387))",fontsize=16,color="burlywood",shape="box"];10993[label="vuz318/Pos vuz3180",fontsize=10,color="white",style="solid",shape="box"];7929 -> 10993[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10993 -> 8222[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	10994[label="vuz318/Neg vuz3180",fontsize=10,color="white",style="solid",shape="box"];7929 -> 10994[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10994 -> 8223[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	7930[label="vuz3190",fontsize=16,color="green",shape="box"];7931[label="vuz3170",fontsize=16,color="green",shape="box"];7932[label="vuz3160",fontsize=16,color="green",shape="box"];7933[label="vuz3170",fontsize=16,color="green",shape="box"];7934[label="vuz3160",fontsize=16,color="green",shape="box"];7935[label="vuz3170",fontsize=16,color="green",shape="box"];7936[label="vuz3190",fontsize=16,color="green",shape="box"];7937[label="vuz3170",fontsize=16,color="green",shape="box"];7938[label="primQuotInt (Pos vuz390) (gcd2 (primEqInt (primPlusInt (Neg vuz393) (primMulInt vuz318 (Neg vuz3190))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz392) (primMulInt vuz318 (Neg vuz3190))) (Pos vuz391))",fontsize=16,color="burlywood",shape="box"];10995[label="vuz318/Pos vuz3180",fontsize=10,color="white",style="solid",shape="box"];7938 -> 10995[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10995 -> 8224[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	10996[label="vuz318/Neg vuz3180",fontsize=10,color="white",style="solid",shape="box"];7938 -> 10996[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10996 -> 8225[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	7939[label="vuz3190",fontsize=16,color="green",shape="box"];7940[label="vuz3170",fontsize=16,color="green",shape="box"];7941[label="vuz3160",fontsize=16,color="green",shape="box"];7942[label="vuz3170",fontsize=16,color="green",shape="box"];7943[label="vuz3190",fontsize=16,color="green",shape="box"];7944[label="vuz3170",fontsize=16,color="green",shape="box"];7945[label="vuz3160",fontsize=16,color="green",shape="box"];7946[label="vuz3170",fontsize=16,color="green",shape="box"];7947[label="primQuotInt (Pos vuz394) (gcd2 (primEqInt (primPlusInt (Pos vuz397) (primMulInt vuz318 (Neg vuz3190))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz396) (primMulInt vuz318 (Neg vuz3190))) (Pos vuz395))",fontsize=16,color="burlywood",shape="box"];10997[label="vuz318/Pos vuz3180",fontsize=10,color="white",style="solid",shape="box"];7947 -> 10997[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10997 -> 8226[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	10998[label="vuz318/Neg vuz3180",fontsize=10,color="white",style="solid",shape="box"];7947 -> 10998[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10998 -> 8227[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	7948[label="vuz3160",fontsize=16,color="green",shape="box"];7949[label="vuz3170",fontsize=16,color="green",shape="box"];7950[label="vuz3180",fontsize=16,color="green",shape="box"];7951[label="vuz3190",fontsize=16,color="green",shape="box"];7952[label="vuz3160",fontsize=16,color="green",shape="box"];7953[label="vuz3170",fontsize=16,color="green",shape="box"];7954[label="vuz3180",fontsize=16,color="green",shape="box"];7955[label="vuz3190",fontsize=16,color="green",shape="box"];8229 -> 9987[label="",style="dashed", color="red", weight=0];
67.32/34.79	8229[label="Pos vuz399 == fromInt (Pos Zero)",fontsize=16,color="magenta"];8229 -> 9989[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	8228[label="primQuotInt (Pos vuz398) (gcd2 vuz472 (Pos vuz399) (Pos vuz3190 * Pos vuz3170))",fontsize=16,color="burlywood",shape="triangle"];10999[label="vuz472/False",fontsize=10,color="white",style="solid",shape="box"];8228 -> 10999[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	10999 -> 8232[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	11000[label="vuz472/True",fontsize=10,color="white",style="solid",shape="box"];8228 -> 11000[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	11000 -> 8233[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	7957[label="vuz3180",fontsize=16,color="green",shape="box"];7958[label="vuz3190",fontsize=16,color="green",shape="box"];7959 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7959[label="primMulNat vuz31600 (Succ vuz31700)",fontsize=16,color="magenta"];7959 -> 8234[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7959 -> 8235[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7960[label="Succ vuz31700",fontsize=16,color="green",shape="box"];7961 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7961[label="primMulNat vuz31600 (Succ vuz31700)",fontsize=16,color="magenta"];7961 -> 8236[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7961 -> 8237[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7962[label="Succ vuz31700",fontsize=16,color="green",shape="box"];7963[label="vuz3180",fontsize=16,color="green",shape="box"];7964[label="vuz3190",fontsize=16,color="green",shape="box"];7965[label="primQuotInt (primMinusNat (Succ vuz4010) vuz400) (reduce2D (primMinusNat vuz403 vuz402) (Neg vuz3190 * Pos (Succ vuz31700)))",fontsize=16,color="burlywood",shape="box"];11001[label="vuz400/Succ vuz4000",fontsize=10,color="white",style="solid",shape="box"];7965 -> 11001[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	11001 -> 8238[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	11002[label="vuz400/Zero",fontsize=10,color="white",style="solid",shape="box"];7965 -> 11002[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	11002 -> 8239[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	7966[label="primQuotInt (primMinusNat Zero vuz400) (reduce2D (primMinusNat vuz403 vuz402) (Neg vuz3190 * Pos (Succ vuz31700)))",fontsize=16,color="burlywood",shape="box"];11003[label="vuz400/Succ vuz4000",fontsize=10,color="white",style="solid",shape="box"];7966 -> 11003[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	11003 -> 8240[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	11004[label="vuz400/Zero",fontsize=10,color="white",style="solid",shape="box"];7966 -> 11004[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	11004 -> 8241[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	7967[label="vuz3180",fontsize=16,color="green",shape="box"];7968[label="vuz3190",fontsize=16,color="green",shape="box"];7969[label="vuz3180",fontsize=16,color="green",shape="box"];7970[label="vuz3190",fontsize=16,color="green",shape="box"];7971[label="primQuotInt (primMinusNat Zero (Succ vuz4060)) (reduce2D (primMinusNat Zero vuz407) (Neg vuz3190 * Pos Zero))",fontsize=16,color="black",shape="box"];7971 -> 8242[label="",style="solid", color="black", weight=3];
67.32/34.79	7972[label="primQuotInt (primMinusNat Zero Zero) (reduce2D (primMinusNat Zero vuz407) (Neg vuz3190 * Pos Zero))",fontsize=16,color="black",shape="box"];7972 -> 8243[label="",style="solid", color="black", weight=3];
67.32/34.79	7973[label="vuz3180",fontsize=16,color="green",shape="box"];7974[label="vuz3190",fontsize=16,color="green",shape="box"];7975[label="vuz3180",fontsize=16,color="green",shape="box"];7976[label="vuz3190",fontsize=16,color="green",shape="box"];7977[label="vuz3180",fontsize=16,color="green",shape="box"];7978[label="vuz3190",fontsize=16,color="green",shape="box"];7979[label="vuz3180",fontsize=16,color="green",shape="box"];7980[label="vuz3190",fontsize=16,color="green",shape="box"];7981 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7981[label="primMulNat vuz31600 (Succ vuz31700)",fontsize=16,color="magenta"];7981 -> 8244[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7981 -> 8245[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7982[label="Succ vuz31700",fontsize=16,color="green",shape="box"];7983[label="vuz3180",fontsize=16,color="green",shape="box"];7984[label="vuz3190",fontsize=16,color="green",shape="box"];7985 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	7985[label="primMulNat vuz31600 (Succ vuz31700)",fontsize=16,color="magenta"];7985 -> 8246[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7985 -> 8247[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	7986[label="Succ vuz31700",fontsize=16,color="green",shape="box"];7987[label="vuz3180",fontsize=16,color="green",shape="box"];7988[label="vuz3190",fontsize=16,color="green",shape="box"];7989[label="primQuotInt (primMinusNat (Succ vuz4090) vuz408) (reduce2D (primMinusNat vuz411 vuz410) (Pos vuz3190 * Pos (Succ vuz31700)))",fontsize=16,color="burlywood",shape="box"];11005[label="vuz408/Succ vuz4080",fontsize=10,color="white",style="solid",shape="box"];7989 -> 11005[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	11005 -> 8248[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	11006[label="vuz408/Zero",fontsize=10,color="white",style="solid",shape="box"];7989 -> 11006[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	11006 -> 8249[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	7990[label="primQuotInt (primMinusNat Zero vuz408) (reduce2D (primMinusNat vuz411 vuz410) (Pos vuz3190 * Pos (Succ vuz31700)))",fontsize=16,color="burlywood",shape="box"];11007[label="vuz408/Succ vuz4080",fontsize=10,color="white",style="solid",shape="box"];7990 -> 11007[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	11007 -> 8250[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	11008[label="vuz408/Zero",fontsize=10,color="white",style="solid",shape="box"];7990 -> 11008[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	11008 -> 8251[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	7991[label="vuz3180",fontsize=16,color="green",shape="box"];7992[label="vuz3190",fontsize=16,color="green",shape="box"];7993[label="vuz3180",fontsize=16,color="green",shape="box"];7994[label="vuz3190",fontsize=16,color="green",shape="box"];7995[label="primQuotInt (primMinusNat Zero (Succ vuz4140)) (reduce2D (primMinusNat Zero vuz415) (Pos vuz3190 * Pos Zero))",fontsize=16,color="black",shape="box"];7995 -> 8252[label="",style="solid", color="black", weight=3];
67.32/34.79	7996[label="primQuotInt (primMinusNat Zero Zero) (reduce2D (primMinusNat Zero vuz415) (Pos vuz3190 * Pos Zero))",fontsize=16,color="black",shape="box"];7996 -> 8253[label="",style="solid", color="black", weight=3];
67.32/34.79	7997[label="vuz3180",fontsize=16,color="green",shape="box"];7998[label="vuz3190",fontsize=16,color="green",shape="box"];7999[label="vuz3180",fontsize=16,color="green",shape="box"];8000[label="vuz3190",fontsize=16,color="green",shape="box"];8001[label="vuz3180",fontsize=16,color="green",shape="box"];8002[label="vuz3190",fontsize=16,color="green",shape="box"];8003[label="vuz3180",fontsize=16,color="green",shape="box"];8004[label="vuz3190",fontsize=16,color="green",shape="box"];8005[label="vuz3160",fontsize=16,color="green",shape="box"];8006[label="vuz3170",fontsize=16,color="green",shape="box"];8007[label="vuz3180",fontsize=16,color="green",shape="box"];8008[label="vuz3190",fontsize=16,color="green",shape="box"];8009[label="vuz3160",fontsize=16,color="green",shape="box"];8010[label="vuz3170",fontsize=16,color="green",shape="box"];8011[label="vuz3180",fontsize=16,color="green",shape="box"];8012[label="vuz3190",fontsize=16,color="green",shape="box"];8255 -> 9987[label="",style="dashed", color="red", weight=0];
67.32/34.79	8255[label="Pos vuz417 == fromInt (Pos Zero)",fontsize=16,color="magenta"];8255 -> 9990[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	8254[label="primQuotInt (Pos vuz416) (gcd2 vuz473 (Pos vuz417) (Neg vuz3190 * Pos vuz3170))",fontsize=16,color="burlywood",shape="triangle"];11009[label="vuz473/False",fontsize=10,color="white",style="solid",shape="box"];8254 -> 11009[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	11009 -> 8258[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	11010[label="vuz473/True",fontsize=10,color="white",style="solid",shape="box"];8254 -> 11010[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	11010 -> 8259[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	8014[label="vuz3160",fontsize=16,color="green",shape="box"];8015[label="vuz3170",fontsize=16,color="green",shape="box"];8016 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	8016[label="primMulNat vuz31800 (Succ vuz31900)",fontsize=16,color="magenta"];8016 -> 8260[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	8016 -> 8261[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	8017[label="Succ vuz31900",fontsize=16,color="green",shape="box"];8018[label="vuz3160",fontsize=16,color="green",shape="box"];8019[label="vuz3170",fontsize=16,color="green",shape="box"];8020 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	8020[label="primMulNat vuz31800 (Succ vuz31900)",fontsize=16,color="magenta"];8020 -> 8262[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	8020 -> 8263[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	8021[label="Succ vuz31900",fontsize=16,color="green",shape="box"];8022[label="primQuotInt (primMinusNat (Succ vuz4190) vuz418) (reduce2D (primMinusNat vuz421 vuz420) (Pos (Succ vuz31900) * Neg vuz3170))",fontsize=16,color="burlywood",shape="box"];11011[label="vuz418/Succ vuz4180",fontsize=10,color="white",style="solid",shape="box"];8022 -> 11011[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	11011 -> 8264[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	11012[label="vuz418/Zero",fontsize=10,color="white",style="solid",shape="box"];8022 -> 11012[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	11012 -> 8265[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	8023[label="primQuotInt (primMinusNat Zero vuz418) (reduce2D (primMinusNat vuz421 vuz420) (Pos (Succ vuz31900) * Neg vuz3170))",fontsize=16,color="burlywood",shape="box"];11013[label="vuz418/Succ vuz4180",fontsize=10,color="white",style="solid",shape="box"];8023 -> 11013[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	11013 -> 8266[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	11014[label="vuz418/Zero",fontsize=10,color="white",style="solid",shape="box"];8023 -> 11014[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	11014 -> 8267[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	8024[label="vuz3160",fontsize=16,color="green",shape="box"];8025[label="vuz3170",fontsize=16,color="green",shape="box"];8026[label="vuz3160",fontsize=16,color="green",shape="box"];8027[label="vuz3170",fontsize=16,color="green",shape="box"];8028[label="primQuotInt (primMinusNat Zero (Succ vuz4240)) (reduce2D (primMinusNat Zero vuz425) (Pos Zero * Neg vuz3170))",fontsize=16,color="black",shape="box"];8028 -> 8268[label="",style="solid", color="black", weight=3];
67.32/34.79	8029[label="primQuotInt (primMinusNat Zero Zero) (reduce2D (primMinusNat Zero vuz425) (Pos Zero * Neg vuz3170))",fontsize=16,color="black",shape="box"];8029 -> 8269[label="",style="solid", color="black", weight=3];
67.32/34.79	8030[label="vuz3160",fontsize=16,color="green",shape="box"];8031[label="vuz3170",fontsize=16,color="green",shape="box"];8032[label="vuz3160",fontsize=16,color="green",shape="box"];8033[label="vuz3170",fontsize=16,color="green",shape="box"];8034[label="vuz3160",fontsize=16,color="green",shape="box"];8035[label="vuz3170",fontsize=16,color="green",shape="box"];8036[label="vuz3160",fontsize=16,color="green",shape="box"];8037[label="vuz3170",fontsize=16,color="green",shape="box"];8038[label="vuz3160",fontsize=16,color="green",shape="box"];8039[label="vuz3170",fontsize=16,color="green",shape="box"];8040[label="vuz3180",fontsize=16,color="green",shape="box"];8041[label="vuz3190",fontsize=16,color="green",shape="box"];8042[label="vuz3160",fontsize=16,color="green",shape="box"];8043[label="vuz3170",fontsize=16,color="green",shape="box"];8044[label="vuz3180",fontsize=16,color="green",shape="box"];8045[label="vuz3190",fontsize=16,color="green",shape="box"];8271 -> 9987[label="",style="dashed", color="red", weight=0];
67.32/34.79	8271[label="Neg vuz427 == fromInt (Pos Zero)",fontsize=16,color="magenta"];8271 -> 9991[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	8270[label="primQuotInt (Neg vuz426) (gcd2 vuz474 (Neg vuz427) (Neg vuz3190 * Neg vuz3170))",fontsize=16,color="burlywood",shape="triangle"];11015[label="vuz474/False",fontsize=10,color="white",style="solid",shape="box"];8270 -> 11015[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	11015 -> 8274[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	11016[label="vuz474/True",fontsize=10,color="white",style="solid",shape="box"];8270 -> 11016[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	11016 -> 8275[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	8047[label="vuz3160",fontsize=16,color="green",shape="box"];8048[label="vuz3170",fontsize=16,color="green",shape="box"];8049[label="vuz3180",fontsize=16,color="green",shape="box"];8050[label="vuz3190",fontsize=16,color="green",shape="box"];8051[label="vuz3160",fontsize=16,color="green",shape="box"];8052[label="vuz3170",fontsize=16,color="green",shape="box"];8053[label="vuz3180",fontsize=16,color="green",shape="box"];8054[label="vuz3190",fontsize=16,color="green",shape="box"];8277 -> 9987[label="",style="dashed", color="red", weight=0];
67.32/34.79	8277[label="Neg vuz429 == fromInt (Pos Zero)",fontsize=16,color="magenta"];8277 -> 9992[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	8276[label="primQuotInt (Neg vuz428) (gcd2 vuz475 (Neg vuz429) (Pos vuz3190 * Neg vuz3170))",fontsize=16,color="burlywood",shape="triangle"];11017[label="vuz475/False",fontsize=10,color="white",style="solid",shape="box"];8276 -> 11017[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	11017 -> 8280[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	11018[label="vuz475/True",fontsize=10,color="white",style="solid",shape="box"];8276 -> 11018[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	11018 -> 8281[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	8056 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	8056[label="primMulNat vuz31800 (Succ vuz31900)",fontsize=16,color="magenta"];8056 -> 8282[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	8056 -> 8283[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	8057[label="Succ vuz31900",fontsize=16,color="green",shape="box"];8058[label="vuz3160",fontsize=16,color="green",shape="box"];8059[label="vuz3170",fontsize=16,color="green",shape="box"];8060[label="vuz3160",fontsize=16,color="green",shape="box"];8061[label="vuz3170",fontsize=16,color="green",shape="box"];8062 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	8062[label="primMulNat vuz31800 (Succ vuz31900)",fontsize=16,color="magenta"];8062 -> 8284[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	8062 -> 8285[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	8063[label="Succ vuz31900",fontsize=16,color="green",shape="box"];8064[label="primQuotInt (primMinusNat (Succ vuz4310) vuz430) (reduce2D (primMinusNat vuz433 vuz432) (Neg (Succ vuz31900) * Neg vuz3170))",fontsize=16,color="burlywood",shape="box"];11019[label="vuz430/Succ vuz4300",fontsize=10,color="white",style="solid",shape="box"];8064 -> 11019[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	11019 -> 8286[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	11020[label="vuz430/Zero",fontsize=10,color="white",style="solid",shape="box"];8064 -> 11020[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	11020 -> 8287[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	8065[label="primQuotInt (primMinusNat Zero vuz430) (reduce2D (primMinusNat vuz433 vuz432) (Neg (Succ vuz31900) * Neg vuz3170))",fontsize=16,color="burlywood",shape="box"];11021[label="vuz430/Succ vuz4300",fontsize=10,color="white",style="solid",shape="box"];8065 -> 11021[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	11021 -> 8288[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	11022[label="vuz430/Zero",fontsize=10,color="white",style="solid",shape="box"];8065 -> 11022[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	11022 -> 8289[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	8066[label="vuz3160",fontsize=16,color="green",shape="box"];8067[label="vuz3170",fontsize=16,color="green",shape="box"];8068[label="vuz3160",fontsize=16,color="green",shape="box"];8069[label="vuz3170",fontsize=16,color="green",shape="box"];8070[label="primQuotInt (primMinusNat Zero (Succ vuz4360)) (reduce2D (primMinusNat Zero vuz437) (Neg Zero * Neg vuz3170))",fontsize=16,color="black",shape="box"];8070 -> 8290[label="",style="solid", color="black", weight=3];
67.32/34.79	8071[label="primQuotInt (primMinusNat Zero Zero) (reduce2D (primMinusNat Zero vuz437) (Neg Zero * Neg vuz3170))",fontsize=16,color="black",shape="box"];8071 -> 8291[label="",style="solid", color="black", weight=3];
67.32/34.79	8072[label="vuz3160",fontsize=16,color="green",shape="box"];8073[label="vuz3170",fontsize=16,color="green",shape="box"];8074[label="vuz3160",fontsize=16,color="green",shape="box"];8075[label="vuz3170",fontsize=16,color="green",shape="box"];8076[label="vuz3160",fontsize=16,color="green",shape="box"];8077[label="vuz3170",fontsize=16,color="green",shape="box"];8078[label="vuz3160",fontsize=16,color="green",shape="box"];8079[label="vuz3170",fontsize=16,color="green",shape="box"];8080 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	8080[label="primMulNat vuz31800 (Succ vuz31900)",fontsize=16,color="magenta"];8080 -> 8292[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	8080 -> 8293[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	8081[label="Succ vuz31900",fontsize=16,color="green",shape="box"];8082[label="vuz3160",fontsize=16,color="green",shape="box"];8083[label="vuz3170",fontsize=16,color="green",shape="box"];8084[label="vuz3160",fontsize=16,color="green",shape="box"];8085[label="vuz3170",fontsize=16,color="green",shape="box"];8086 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	8086[label="primMulNat vuz31800 (Succ vuz31900)",fontsize=16,color="magenta"];8086 -> 8294[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	8086 -> 8295[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	8087[label="Succ vuz31900",fontsize=16,color="green",shape="box"];8088[label="primQuotInt (primMinusNat (Succ vuz4390) vuz438) (reduce2D (primMinusNat vuz441 vuz440) (Pos (Succ vuz31900) * Pos vuz3170))",fontsize=16,color="burlywood",shape="box"];11023[label="vuz438/Succ vuz4380",fontsize=10,color="white",style="solid",shape="box"];8088 -> 11023[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	11023 -> 8296[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	11024[label="vuz438/Zero",fontsize=10,color="white",style="solid",shape="box"];8088 -> 11024[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	11024 -> 8297[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	8089[label="primQuotInt (primMinusNat Zero vuz438) (reduce2D (primMinusNat vuz441 vuz440) (Pos (Succ vuz31900) * Pos vuz3170))",fontsize=16,color="burlywood",shape="box"];11025[label="vuz438/Succ vuz4380",fontsize=10,color="white",style="solid",shape="box"];8089 -> 11025[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	11025 -> 8298[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	11026[label="vuz438/Zero",fontsize=10,color="white",style="solid",shape="box"];8089 -> 11026[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	11026 -> 8299[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	8090[label="vuz3160",fontsize=16,color="green",shape="box"];8091[label="vuz3170",fontsize=16,color="green",shape="box"];8092[label="vuz3160",fontsize=16,color="green",shape="box"];8093[label="vuz3170",fontsize=16,color="green",shape="box"];8094[label="primQuotInt (primMinusNat Zero (Succ vuz4440)) (reduce2D (primMinusNat Zero vuz445) (Pos Zero * Pos vuz3170))",fontsize=16,color="black",shape="box"];8094 -> 8300[label="",style="solid", color="black", weight=3];
67.32/34.79	8095[label="primQuotInt (primMinusNat Zero Zero) (reduce2D (primMinusNat Zero vuz445) (Pos Zero * Pos vuz3170))",fontsize=16,color="black",shape="box"];8095 -> 8301[label="",style="solid", color="black", weight=3];
67.32/34.79	8096[label="vuz3160",fontsize=16,color="green",shape="box"];8097[label="vuz3170",fontsize=16,color="green",shape="box"];8098[label="vuz3160",fontsize=16,color="green",shape="box"];8099[label="vuz3170",fontsize=16,color="green",shape="box"];8100[label="vuz3160",fontsize=16,color="green",shape="box"];8101[label="vuz3170",fontsize=16,color="green",shape="box"];8102[label="vuz3160",fontsize=16,color="green",shape="box"];8103[label="vuz3170",fontsize=16,color="green",shape="box"];8104[label="vuz3160",fontsize=16,color="green",shape="box"];8105[label="vuz3170",fontsize=16,color="green",shape="box"];8106[label="vuz3180",fontsize=16,color="green",shape="box"];8107[label="vuz3190",fontsize=16,color="green",shape="box"];8108[label="vuz3160",fontsize=16,color="green",shape="box"];8109[label="vuz3170",fontsize=16,color="green",shape="box"];8110[label="vuz3180",fontsize=16,color="green",shape="box"];8111[label="vuz3190",fontsize=16,color="green",shape="box"];8303 -> 9987[label="",style="dashed", color="red", weight=0];
67.32/34.79	8303[label="Neg vuz447 == fromInt (Pos Zero)",fontsize=16,color="magenta"];8303 -> 9993[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	8302[label="primQuotInt (Neg vuz446) (gcd2 vuz476 (Neg vuz447) (Neg vuz3190 * Pos vuz3170))",fontsize=16,color="burlywood",shape="triangle"];11027[label="vuz476/False",fontsize=10,color="white",style="solid",shape="box"];8302 -> 11027[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	11027 -> 8306[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	11028[label="vuz476/True",fontsize=10,color="white",style="solid",shape="box"];8302 -> 11028[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	11028 -> 8307[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	8113[label="vuz3160",fontsize=16,color="green",shape="box"];8114[label="vuz3170",fontsize=16,color="green",shape="box"];8115[label="vuz3180",fontsize=16,color="green",shape="box"];8116[label="vuz3190",fontsize=16,color="green",shape="box"];8117[label="vuz3160",fontsize=16,color="green",shape="box"];8118[label="vuz3170",fontsize=16,color="green",shape="box"];8119[label="vuz3180",fontsize=16,color="green",shape="box"];8120[label="vuz3190",fontsize=16,color="green",shape="box"];8309 -> 9987[label="",style="dashed", color="red", weight=0];
67.32/34.79	8309[label="Neg vuz349 == fromInt (Pos Zero)",fontsize=16,color="magenta"];8309 -> 9994[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	8308[label="primQuotInt (Neg vuz348) (gcd2 vuz477 (Neg vuz349) (Pos vuz3190 * Pos vuz3170))",fontsize=16,color="burlywood",shape="triangle"];11029[label="vuz477/False",fontsize=10,color="white",style="solid",shape="box"];8308 -> 11029[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	11029 -> 8312[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	11030[label="vuz477/True",fontsize=10,color="white",style="solid",shape="box"];8308 -> 11030[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	11030 -> 8313[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	8122 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	8122[label="primMulNat vuz31800 (Succ vuz31900)",fontsize=16,color="magenta"];8122 -> 8314[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	8122 -> 8315[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	8123[label="Succ vuz31900",fontsize=16,color="green",shape="box"];8124 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	8124[label="primMulNat vuz31800 (Succ vuz31900)",fontsize=16,color="magenta"];8124 -> 8316[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	8124 -> 8317[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	8125[label="Succ vuz31900",fontsize=16,color="green",shape="box"];8126[label="vuz3160",fontsize=16,color="green",shape="box"];8127[label="vuz3170",fontsize=16,color="green",shape="box"];8128[label="vuz3160",fontsize=16,color="green",shape="box"];8129[label="vuz3170",fontsize=16,color="green",shape="box"];8130[label="primQuotInt (primMinusNat (Succ vuz4490) vuz448) (reduce2D (primMinusNat vuz451 vuz450) (Neg (Succ vuz31900) * Pos vuz3170))",fontsize=16,color="burlywood",shape="box"];11031[label="vuz448/Succ vuz4480",fontsize=10,color="white",style="solid",shape="box"];8130 -> 11031[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	11031 -> 8318[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	11032[label="vuz448/Zero",fontsize=10,color="white",style="solid",shape="box"];8130 -> 11032[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	11032 -> 8319[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	8131[label="primQuotInt (primMinusNat Zero vuz448) (reduce2D (primMinusNat vuz451 vuz450) (Neg (Succ vuz31900) * Pos vuz3170))",fontsize=16,color="burlywood",shape="box"];11033[label="vuz448/Succ vuz4480",fontsize=10,color="white",style="solid",shape="box"];8131 -> 11033[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	11033 -> 8320[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	11034[label="vuz448/Zero",fontsize=10,color="white",style="solid",shape="box"];8131 -> 11034[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	11034 -> 8321[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	8132[label="vuz3160",fontsize=16,color="green",shape="box"];8133[label="vuz3170",fontsize=16,color="green",shape="box"];8134[label="vuz3160",fontsize=16,color="green",shape="box"];8135[label="vuz3170",fontsize=16,color="green",shape="box"];8136[label="primQuotInt (primMinusNat Zero (Succ vuz4540)) (reduce2D (primMinusNat Zero vuz455) (Neg Zero * Pos vuz3170))",fontsize=16,color="black",shape="box"];8136 -> 8322[label="",style="solid", color="black", weight=3];
67.32/34.79	8137[label="primQuotInt (primMinusNat Zero Zero) (reduce2D (primMinusNat Zero vuz455) (Neg Zero * Pos vuz3170))",fontsize=16,color="black",shape="box"];8137 -> 8323[label="",style="solid", color="black", weight=3];
67.32/34.79	8138[label="vuz3160",fontsize=16,color="green",shape="box"];8139[label="vuz3170",fontsize=16,color="green",shape="box"];8140[label="vuz3160",fontsize=16,color="green",shape="box"];8141[label="vuz3170",fontsize=16,color="green",shape="box"];8142[label="vuz3160",fontsize=16,color="green",shape="box"];8143[label="vuz3170",fontsize=16,color="green",shape="box"];8144[label="vuz3160",fontsize=16,color="green",shape="box"];8145[label="vuz3170",fontsize=16,color="green",shape="box"];8146[label="vuz3160",fontsize=16,color="green",shape="box"];8147[label="vuz3170",fontsize=16,color="green",shape="box"];8148[label="vuz3180",fontsize=16,color="green",shape="box"];8149[label="vuz3190",fontsize=16,color="green",shape="box"];8150[label="vuz3160",fontsize=16,color="green",shape="box"];8151[label="vuz3170",fontsize=16,color="green",shape="box"];8152[label="vuz3180",fontsize=16,color="green",shape="box"];8153[label="vuz3190",fontsize=16,color="green",shape="box"];8325 -> 9987[label="",style="dashed", color="red", weight=0];
67.32/34.79	8325[label="Pos vuz355 == fromInt (Pos Zero)",fontsize=16,color="magenta"];8325 -> 9995[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	8324[label="primQuotInt (Pos vuz354) (gcd2 vuz478 (Pos vuz355) (Pos vuz3190 * Neg vuz3170))",fontsize=16,color="burlywood",shape="triangle"];11035[label="vuz478/False",fontsize=10,color="white",style="solid",shape="box"];8324 -> 11035[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	11035 -> 8328[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	11036[label="vuz478/True",fontsize=10,color="white",style="solid",shape="box"];8324 -> 11036[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	11036 -> 8329[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	8155 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	8155[label="primMulNat vuz31600 (Succ vuz31700)",fontsize=16,color="magenta"];8155 -> 8330[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	8155 -> 8331[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	8156[label="Succ vuz31700",fontsize=16,color="green",shape="box"];8157[label="vuz3180",fontsize=16,color="green",shape="box"];8158[label="vuz3190",fontsize=16,color="green",shape="box"];8159[label="vuz3180",fontsize=16,color="green",shape="box"];8160[label="vuz3190",fontsize=16,color="green",shape="box"];8161 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	8161[label="primMulNat vuz31600 (Succ vuz31700)",fontsize=16,color="magenta"];8161 -> 8332[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	8161 -> 8333[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	8162[label="Succ vuz31700",fontsize=16,color="green",shape="box"];8163[label="primQuotInt (primMinusNat (Succ vuz4570) vuz456) (reduce2D (primMinusNat vuz459 vuz458) (Neg vuz3190 * Neg (Succ vuz31700)))",fontsize=16,color="burlywood",shape="box"];11037[label="vuz456/Succ vuz4560",fontsize=10,color="white",style="solid",shape="box"];8163 -> 11037[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	11037 -> 8334[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	11038[label="vuz456/Zero",fontsize=10,color="white",style="solid",shape="box"];8163 -> 11038[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	11038 -> 8335[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	8164[label="primQuotInt (primMinusNat Zero vuz456) (reduce2D (primMinusNat vuz459 vuz458) (Neg vuz3190 * Neg (Succ vuz31700)))",fontsize=16,color="burlywood",shape="box"];11039[label="vuz456/Succ vuz4560",fontsize=10,color="white",style="solid",shape="box"];8164 -> 11039[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	11039 -> 8336[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	11040[label="vuz456/Zero",fontsize=10,color="white",style="solid",shape="box"];8164 -> 11040[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	11040 -> 8337[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	8165[label="vuz3180",fontsize=16,color="green",shape="box"];8166[label="vuz3190",fontsize=16,color="green",shape="box"];8167[label="vuz3180",fontsize=16,color="green",shape="box"];8168[label="vuz3190",fontsize=16,color="green",shape="box"];8169[label="primQuotInt (primMinusNat Zero (Succ vuz4620)) (reduce2D (primMinusNat Zero vuz463) (Neg vuz3190 * Neg Zero))",fontsize=16,color="black",shape="box"];8169 -> 8338[label="",style="solid", color="black", weight=3];
67.32/34.79	8170[label="primQuotInt (primMinusNat Zero Zero) (reduce2D (primMinusNat Zero vuz463) (Neg vuz3190 * Neg Zero))",fontsize=16,color="black",shape="box"];8170 -> 8339[label="",style="solid", color="black", weight=3];
67.32/34.79	8171[label="vuz3180",fontsize=16,color="green",shape="box"];8172[label="vuz3190",fontsize=16,color="green",shape="box"];8173[label="vuz3180",fontsize=16,color="green",shape="box"];8174[label="vuz3190",fontsize=16,color="green",shape="box"];8175[label="vuz3180",fontsize=16,color="green",shape="box"];8176[label="vuz3190",fontsize=16,color="green",shape="box"];8177[label="vuz3180",fontsize=16,color="green",shape="box"];8178[label="vuz3190",fontsize=16,color="green",shape="box"];8179 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	8179[label="primMulNat vuz31600 (Succ vuz31700)",fontsize=16,color="magenta"];8179 -> 8340[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	8179 -> 8341[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	8180[label="Succ vuz31700",fontsize=16,color="green",shape="box"];8181[label="vuz3180",fontsize=16,color="green",shape="box"];8182[label="vuz3190",fontsize=16,color="green",shape="box"];8183[label="vuz3180",fontsize=16,color="green",shape="box"];8184[label="vuz3190",fontsize=16,color="green",shape="box"];8185 -> 7480[label="",style="dashed", color="red", weight=0];
67.32/34.79	8185[label="primMulNat vuz31600 (Succ vuz31700)",fontsize=16,color="magenta"];8185 -> 8342[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	8185 -> 8343[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	8186[label="Succ vuz31700",fontsize=16,color="green",shape="box"];8187[label="primQuotInt (primMinusNat (Succ vuz4650) vuz464) (reduce2D (primMinusNat vuz467 vuz466) (Pos vuz3190 * Neg (Succ vuz31700)))",fontsize=16,color="burlywood",shape="box"];11041[label="vuz464/Succ vuz4640",fontsize=10,color="white",style="solid",shape="box"];8187 -> 11041[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	11041 -> 8344[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	11042[label="vuz464/Zero",fontsize=10,color="white",style="solid",shape="box"];8187 -> 11042[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	11042 -> 8345[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	8188[label="primQuotInt (primMinusNat Zero vuz464) (reduce2D (primMinusNat vuz467 vuz466) (Pos vuz3190 * Neg (Succ vuz31700)))",fontsize=16,color="burlywood",shape="box"];11043[label="vuz464/Succ vuz4640",fontsize=10,color="white",style="solid",shape="box"];8188 -> 11043[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	11043 -> 8346[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	11044[label="vuz464/Zero",fontsize=10,color="white",style="solid",shape="box"];8188 -> 11044[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	11044 -> 8347[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	8189[label="vuz3180",fontsize=16,color="green",shape="box"];8190[label="vuz3190",fontsize=16,color="green",shape="box"];8191[label="vuz3180",fontsize=16,color="green",shape="box"];8192[label="vuz3190",fontsize=16,color="green",shape="box"];8193[label="primQuotInt (primMinusNat Zero (Succ vuz4700)) (reduce2D (primMinusNat Zero vuz471) (Pos vuz3190 * Neg Zero))",fontsize=16,color="black",shape="box"];8193 -> 8348[label="",style="solid", color="black", weight=3];
67.32/34.79	8194[label="primQuotInt (primMinusNat Zero Zero) (reduce2D (primMinusNat Zero vuz471) (Pos vuz3190 * Neg Zero))",fontsize=16,color="black",shape="box"];8194 -> 8349[label="",style="solid", color="black", weight=3];
67.32/34.79	8195[label="vuz3180",fontsize=16,color="green",shape="box"];8196[label="vuz3190",fontsize=16,color="green",shape="box"];8197[label="vuz3180",fontsize=16,color="green",shape="box"];8198[label="vuz3190",fontsize=16,color="green",shape="box"];8199[label="vuz3180",fontsize=16,color="green",shape="box"];8200[label="vuz3190",fontsize=16,color="green",shape="box"];8201[label="vuz3180",fontsize=16,color="green",shape="box"];8202[label="vuz3190",fontsize=16,color="green",shape="box"];8203[label="vuz3160",fontsize=16,color="green",shape="box"];8204[label="vuz3170",fontsize=16,color="green",shape="box"];8205[label="vuz3180",fontsize=16,color="green",shape="box"];8206[label="vuz3190",fontsize=16,color="green",shape="box"];8207[label="vuz3160",fontsize=16,color="green",shape="box"];8208[label="vuz3170",fontsize=16,color="green",shape="box"];8209[label="vuz3180",fontsize=16,color="green",shape="box"];8210[label="vuz3190",fontsize=16,color="green",shape="box"];8351 -> 9987[label="",style="dashed", color="red", weight=0];
67.32/34.79	8351[label="Pos vuz361 == fromInt (Pos Zero)",fontsize=16,color="magenta"];8351 -> 9996[label="",style="dashed", color="magenta", weight=3];
67.32/34.79	8350[label="primQuotInt (Pos vuz360) (gcd2 vuz479 (Pos vuz361) (Neg vuz3190 * Neg vuz3170))",fontsize=16,color="burlywood",shape="triangle"];11045[label="vuz479/False",fontsize=10,color="white",style="solid",shape="box"];8350 -> 11045[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	11045 -> 8354[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	11046[label="vuz479/True",fontsize=10,color="white",style="solid",shape="box"];8350 -> 11046[label="",style="solid", color="burlywood", weight=9];
67.32/34.79	11046 -> 8355[label="",style="solid", color="burlywood", weight=3];
67.32/34.79	8212[label="primQuotInt (Pos vuz366) (gcd2 (primEqInt (primPlusInt (Pos vuz369) (primMulInt (Pos vuz3180) (Pos vuz3190))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz368) (primMulInt (Pos vuz3180) (Pos vuz3190))) (Pos vuz367))",fontsize=16,color="black",shape="box"];8212 -> 8356[label="",style="solid", color="black", weight=3];
67.32/34.79	8213[label="primQuotInt (Pos vuz366) (gcd2 (primEqInt (primPlusInt (Pos vuz369) (primMulInt (Neg vuz3180) (Pos vuz3190))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz368) (primMulInt (Neg vuz3180) (Pos vuz3190))) (Pos vuz367))",fontsize=16,color="black",shape="box"];8213 -> 8357[label="",style="solid", color="black", weight=3];
67.32/34.79	8214[label="primQuotInt (Pos vuz370) (gcd2 (primEqInt (primPlusInt (Neg vuz373) (primMulInt (Pos vuz3180) (Pos vuz3190))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz372) (primMulInt (Pos vuz3180) (Pos vuz3190))) (Pos vuz371))",fontsize=16,color="black",shape="box"];8214 -> 8358[label="",style="solid", color="black", weight=3];
67.32/34.79	8215[label="primQuotInt (Pos vuz370) (gcd2 (primEqInt (primPlusInt (Neg vuz373) (primMulInt (Neg vuz3180) (Pos vuz3190))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz372) (primMulInt (Neg vuz3180) (Pos vuz3190))) (Pos vuz371))",fontsize=16,color="black",shape="box"];8215 -> 8359[label="",style="solid", color="black", weight=3];
67.32/34.79	8216[label="primQuotInt (Neg vuz374) (gcd2 (primEqInt (primPlusInt (Neg vuz377) (primMulInt (Pos vuz3180) (Pos vuz3190))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz376) (primMulInt (Pos vuz3180) (Pos vuz3190))) (Neg vuz375))",fontsize=16,color="black",shape="box"];8216 -> 8360[label="",style="solid", color="black", weight=3];
67.32/34.79	8217[label="primQuotInt (Neg vuz374) (gcd2 (primEqInt (primPlusInt (Neg vuz377) (primMulInt (Neg vuz3180) (Pos vuz3190))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz376) (primMulInt (Neg vuz3180) (Pos vuz3190))) (Neg vuz375))",fontsize=16,color="black",shape="box"];8217 -> 8361[label="",style="solid", color="black", weight=3];
67.32/34.79	8218[label="primQuotInt (Neg vuz378) (gcd2 (primEqInt (primPlusInt (Pos vuz381) (primMulInt (Pos vuz3180) (Pos vuz3190))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz380) (primMulInt (Pos vuz3180) (Pos vuz3190))) (Neg vuz379))",fontsize=16,color="black",shape="box"];8218 -> 8362[label="",style="solid", color="black", weight=3];
67.32/34.79	8219[label="primQuotInt (Neg vuz378) (gcd2 (primEqInt (primPlusInt (Pos vuz381) (primMulInt (Neg vuz3180) (Pos vuz3190))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz380) (primMulInt (Neg vuz3180) (Pos vuz3190))) (Neg vuz379))",fontsize=16,color="black",shape="box"];8219 -> 8363[label="",style="solid", color="black", weight=3];
67.32/34.79	8220[label="primQuotInt (Neg vuz382) (gcd2 (primEqInt (primPlusInt (Pos vuz385) (primMulInt (Pos vuz3180) (Neg vuz3190))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz384) (primMulInt (Pos vuz3180) (Neg vuz3190))) (Neg vuz383))",fontsize=16,color="black",shape="box"];8220 -> 8364[label="",style="solid", color="black", weight=3];
67.32/34.79	8221[label="primQuotInt (Neg vuz382) (gcd2 (primEqInt (primPlusInt (Pos vuz385) (primMulInt (Neg vuz3180) (Neg vuz3190))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz384) (primMulInt (Neg vuz3180) (Neg vuz3190))) (Neg vuz383))",fontsize=16,color="black",shape="box"];8221 -> 8365[label="",style="solid", color="black", weight=3];
67.32/34.79	8222[label="primQuotInt (Neg vuz386) (gcd2 (primEqInt (primPlusInt (Neg vuz389) (primMulInt (Pos vuz3180) (Neg vuz3190))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz388) (primMulInt (Pos vuz3180) (Neg vuz3190))) (Neg vuz387))",fontsize=16,color="black",shape="box"];8222 -> 8366[label="",style="solid", color="black", weight=3];
67.32/34.79	8223[label="primQuotInt (Neg vuz386) (gcd2 (primEqInt (primPlusInt (Neg vuz389) (primMulInt (Neg vuz3180) (Neg vuz3190))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz388) (primMulInt (Neg vuz3180) (Neg vuz3190))) (Neg vuz387))",fontsize=16,color="black",shape="box"];8223 -> 8367[label="",style="solid", color="black", weight=3];
67.32/34.79	8224[label="primQuotInt (Pos vuz390) (gcd2 (primEqInt (primPlusInt (Neg vuz393) (primMulInt (Pos vuz3180) (Neg vuz3190))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz392) (primMulInt (Pos vuz3180) (Neg vuz3190))) (Pos vuz391))",fontsize=16,color="black",shape="box"];8224 -> 8368[label="",style="solid", color="black", weight=3];
67.32/34.79	8225[label="primQuotInt (Pos vuz390) (gcd2 (primEqInt (primPlusInt (Neg vuz393) (primMulInt (Neg vuz3180) (Neg vuz3190))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz392) (primMulInt (Neg vuz3180) (Neg vuz3190))) (Pos vuz391))",fontsize=16,color="black",shape="box"];8225 -> 8369[label="",style="solid", color="black", weight=3];
67.32/34.79	8226[label="primQuotInt (Pos vuz394) (gcd2 (primEqInt (primPlusInt (Pos vuz397) (primMulInt (Pos vuz3180) (Neg vuz3190))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz396) (primMulInt (Pos vuz3180) (Neg vuz3190))) (Pos vuz395))",fontsize=16,color="black",shape="box"];8226 -> 8370[label="",style="solid", color="black", weight=3];
67.32/34.79	8227[label="primQuotInt (Pos vuz394) (gcd2 (primEqInt (primPlusInt (Pos vuz397) (primMulInt (Neg vuz3180) (Neg vuz3190))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz396) (primMulInt (Neg vuz3180) (Neg vuz3190))) (Pos vuz395))",fontsize=16,color="black",shape="box"];8227 -> 8371[label="",style="solid", color="black", weight=3];
67.32/34.79	9989[label="Pos vuz399",fontsize=16,color="green",shape="box"];8232[label="primQuotInt (Pos vuz398) (gcd2 False (Pos vuz399) (Pos vuz3190 * Pos vuz3170))",fontsize=16,color="black",shape="box"];8232 -> 8373[label="",style="solid", color="black", weight=3];
67.32/34.79	8233[label="primQuotInt (Pos vuz398) (gcd2 True (Pos vuz399) (Pos vuz3190 * Pos vuz3170))",fontsize=16,color="black",shape="box"];8233 -> 8374[label="",style="solid", color="black", weight=3];
67.32/34.79	8234[label="vuz31600",fontsize=16,color="green",shape="box"];8235[label="Succ vuz31700",fontsize=16,color="green",shape="box"];8236[label="vuz31600",fontsize=16,color="green",shape="box"];8237[label="Succ vuz31700",fontsize=16,color="green",shape="box"];8238[label="primQuotInt (primMinusNat (Succ vuz4010) (Succ vuz4000)) (reduce2D (primMinusNat vuz403 vuz402) (Neg vuz3190 * Pos (Succ vuz31700)))",fontsize=16,color="black",shape="box"];8238 -> 8375[label="",style="solid", color="black", weight=3];
67.32/34.79	8239[label="primQuotInt (primMinusNat (Succ vuz4010) Zero) (reduce2D (primMinusNat vuz403 vuz402) (Neg vuz3190 * Pos (Succ vuz31700)))",fontsize=16,color="black",shape="box"];8239 -> 8376[label="",style="solid", color="black", weight=3];
67.32/34.79	8240[label="primQuotInt (primMinusNat Zero (Succ vuz4000)) (reduce2D (primMinusNat vuz403 vuz402) (Neg vuz3190 * Pos (Succ vuz31700)))",fontsize=16,color="black",shape="box"];8240 -> 8377[label="",style="solid", color="black", weight=3];
67.32/34.79	8241[label="primQuotInt (primMinusNat Zero Zero) (reduce2D (primMinusNat vuz403 vuz402) (Neg vuz3190 * Pos (Succ vuz31700)))",fontsize=16,color="black",shape="box"];8241 -> 8378[label="",style="solid", color="black", weight=3];
67.32/34.79	8242[label="primQuotInt (Neg (Succ vuz4060)) (reduce2D (Neg (Succ vuz4060)) (Neg vuz3190 * Pos Zero))",fontsize=16,color="black",shape="box"];8242 -> 8379[label="",style="solid", color="black", weight=3];
67.32/34.79	8243[label="primQuotInt (Pos Zero) (reduce2D (Pos Zero) (Neg vuz3190 * Pos Zero))",fontsize=16,color="black",shape="box"];8243 -> 8380[label="",style="solid", color="black", weight=3];
67.32/34.79	8244[label="vuz31600",fontsize=16,color="green",shape="box"];8245[label="Succ vuz31700",fontsize=16,color="green",shape="box"];8246[label="vuz31600",fontsize=16,color="green",shape="box"];8247[label="Succ vuz31700",fontsize=16,color="green",shape="box"];8248[label="primQuotInt (primMinusNat (Succ vuz4090) (Succ vuz4080)) (reduce2D (primMinusNat vuz411 vuz410) (Pos vuz3190 * Pos (Succ vuz31700)))",fontsize=16,color="black",shape="box"];8248 -> 8381[label="",style="solid", color="black", weight=3];
67.32/34.79	8249[label="primQuotInt (primMinusNat (Succ vuz4090) Zero) (reduce2D (primMinusNat vuz411 vuz410) (Pos vuz3190 * Pos (Succ vuz31700)))",fontsize=16,color="black",shape="box"];8249 -> 8382[label="",style="solid", color="black", weight=3];
67.32/34.79	8250[label="primQuotInt (primMinusNat Zero (Succ vuz4080)) (reduce2D (primMinusNat vuz411 vuz410) (Pos vuz3190 * Pos (Succ vuz31700)))",fontsize=16,color="black",shape="box"];8250 -> 8383[label="",style="solid", color="black", weight=3];
67.32/34.79	8251[label="primQuotInt (primMinusNat Zero Zero) (reduce2D (primMinusNat vuz411 vuz410) (Pos vuz3190 * Pos (Succ vuz31700)))",fontsize=16,color="black",shape="box"];8251 -> 8384[label="",style="solid", color="black", weight=3];
67.32/34.79	8252[label="primQuotInt (Neg (Succ vuz4140)) (reduce2D (Neg (Succ vuz4140)) (Pos vuz3190 * Pos Zero))",fontsize=16,color="black",shape="box"];8252 -> 8385[label="",style="solid", color="black", weight=3];
67.32/34.79	8253[label="primQuotInt (Pos Zero) (reduce2D (Pos Zero) (Pos vuz3190 * Pos Zero))",fontsize=16,color="black",shape="box"];8253 -> 8386[label="",style="solid", color="black", weight=3];
67.32/34.79	9990[label="Pos vuz417",fontsize=16,color="green",shape="box"];8258[label="primQuotInt (Pos vuz416) (gcd2 False (Pos vuz417) (Neg vuz3190 * Pos vuz3170))",fontsize=16,color="black",shape="box"];8258 -> 8387[label="",style="solid", color="black", weight=3];
67.32/34.79	8259[label="primQuotInt (Pos vuz416) (gcd2 True (Pos vuz417) (Neg vuz3190 * Pos vuz3170))",fontsize=16,color="black",shape="box"];8259 -> 8388[label="",style="solid", color="black", weight=3];
67.32/34.79	8260[label="vuz31800",fontsize=16,color="green",shape="box"];8261[label="Succ vuz31900",fontsize=16,color="green",shape="box"];8262[label="vuz31800",fontsize=16,color="green",shape="box"];8263[label="Succ vuz31900",fontsize=16,color="green",shape="box"];8264[label="primQuotInt (primMinusNat (Succ vuz4190) (Succ vuz4180)) (reduce2D (primMinusNat vuz421 vuz420) (Pos (Succ vuz31900) * Neg vuz3170))",fontsize=16,color="black",shape="box"];8264 -> 8389[label="",style="solid", color="black", weight=3];
67.32/34.79	8265[label="primQuotInt (primMinusNat (Succ vuz4190) Zero) (reduce2D (primMinusNat vuz421 vuz420) (Pos (Succ vuz31900) * Neg vuz3170))",fontsize=16,color="black",shape="box"];8265 -> 8390[label="",style="solid", color="black", weight=3];
67.32/34.79	8266[label="primQuotInt (primMinusNat Zero (Succ vuz4180)) (reduce2D (primMinusNat vuz421 vuz420) (Pos (Succ vuz31900) * Neg vuz3170))",fontsize=16,color="black",shape="box"];8266 -> 8391[label="",style="solid", color="black", weight=3];
67.32/34.79	8267[label="primQuotInt (primMinusNat Zero Zero) (reduce2D (primMinusNat vuz421 vuz420) (Pos (Succ vuz31900) * Neg vuz3170))",fontsize=16,color="black",shape="box"];8267 -> 8392[label="",style="solid", color="black", weight=3];
67.32/34.79	8268[label="primQuotInt (Neg (Succ vuz4240)) (reduce2D (Neg (Succ vuz4240)) (Pos Zero * Neg vuz3170))",fontsize=16,color="black",shape="box"];8268 -> 8393[label="",style="solid", color="black", weight=3];
67.32/34.79	8269[label="primQuotInt (Pos Zero) (reduce2D (Pos Zero) (Pos Zero * Neg vuz3170))",fontsize=16,color="black",shape="box"];8269 -> 8394[label="",style="solid", color="black", weight=3];
67.32/34.79	9991[label="Neg vuz427",fontsize=16,color="green",shape="box"];8274[label="primQuotInt (Neg vuz426) (gcd2 False (Neg vuz427) (Neg vuz3190 * Neg vuz3170))",fontsize=16,color="black",shape="box"];8274 -> 8396[label="",style="solid", color="black", weight=3];
67.32/34.79	8275[label="primQuotInt (Neg vuz426) (gcd2 True (Neg vuz427) (Neg vuz3190 * Neg vuz3170))",fontsize=16,color="black",shape="box"];8275 -> 8397[label="",style="solid", color="black", weight=3];
67.32/34.79	9992[label="Neg vuz429",fontsize=16,color="green",shape="box"];8280[label="primQuotInt (Neg vuz428) (gcd2 False (Neg vuz429) (Pos vuz3190 * Neg vuz3170))",fontsize=16,color="black",shape="box"];8280 -> 8398[label="",style="solid", color="black", weight=3];
67.32/34.79	8281[label="primQuotInt (Neg vuz428) (gcd2 True (Neg vuz429) (Pos vuz3190 * Neg vuz3170))",fontsize=16,color="black",shape="box"];8281 -> 8399[label="",style="solid", color="black", weight=3];
67.32/34.79	8282[label="vuz31800",fontsize=16,color="green",shape="box"];8283[label="Succ vuz31900",fontsize=16,color="green",shape="box"];8284[label="vuz31800",fontsize=16,color="green",shape="box"];8285[label="Succ vuz31900",fontsize=16,color="green",shape="box"];8286[label="primQuotInt (primMinusNat (Succ vuz4310) (Succ vuz4300)) (reduce2D (primMinusNat vuz433 vuz432) (Neg (Succ vuz31900) * Neg vuz3170))",fontsize=16,color="black",shape="box"];8286 -> 8400[label="",style="solid", color="black", weight=3];
67.32/34.79	8287[label="primQuotInt (primMinusNat (Succ vuz4310) Zero) (reduce2D (primMinusNat vuz433 vuz432) (Neg (Succ vuz31900) * Neg vuz3170))",fontsize=16,color="black",shape="box"];8287 -> 8401[label="",style="solid", color="black", weight=3];
67.32/34.79	8288[label="primQuotInt (primMinusNat Zero (Succ vuz4300)) (reduce2D (primMinusNat vuz433 vuz432) (Neg (Succ vuz31900) * Neg vuz3170))",fontsize=16,color="black",shape="box"];8288 -> 8402[label="",style="solid", color="black", weight=3];
67.32/34.79	8289[label="primQuotInt (primMinusNat Zero Zero) (reduce2D (primMinusNat vuz433 vuz432) (Neg (Succ vuz31900) * Neg vuz3170))",fontsize=16,color="black",shape="box"];8289 -> 8403[label="",style="solid", color="black", weight=3];
67.32/34.79	8290[label="primQuotInt (Neg (Succ vuz4360)) (reduce2D (Neg (Succ vuz4360)) (Neg Zero * Neg vuz3170))",fontsize=16,color="black",shape="box"];8290 -> 8404[label="",style="solid", color="black", weight=3];
67.32/34.79	8291[label="primQuotInt (Pos Zero) (reduce2D (Pos Zero) (Neg Zero * Neg vuz3170))",fontsize=16,color="black",shape="box"];8291 -> 8405[label="",style="solid", color="black", weight=3];
67.32/34.79	8292[label="vuz31800",fontsize=16,color="green",shape="box"];8293[label="Succ vuz31900",fontsize=16,color="green",shape="box"];8294[label="vuz31800",fontsize=16,color="green",shape="box"];8295[label="Succ vuz31900",fontsize=16,color="green",shape="box"];8296[label="primQuotInt (primMinusNat (Succ vuz4390) (Succ vuz4380)) (reduce2D (primMinusNat vuz441 vuz440) (Pos (Succ vuz31900) * Pos vuz3170))",fontsize=16,color="black",shape="box"];8296 -> 8406[label="",style="solid", color="black", weight=3];
67.32/34.79	8297[label="primQuotInt (primMinusNat (Succ vuz4390) Zero) (reduce2D (primMinusNat vuz441 vuz440) (Pos (Succ vuz31900) * Pos vuz3170))",fontsize=16,color="black",shape="box"];8297 -> 8407[label="",style="solid", color="black", weight=3];
67.32/34.79	8298[label="primQuotInt (primMinusNat Zero (Succ vuz4380)) (reduce2D (primMinusNat vuz441 vuz440) (Pos (Succ vuz31900) * Pos vuz3170))",fontsize=16,color="black",shape="box"];8298 -> 8408[label="",style="solid", color="black", weight=3];
67.32/34.79	8299[label="primQuotInt (primMinusNat Zero Zero) (reduce2D (primMinusNat vuz441 vuz440) (Pos (Succ vuz31900) * Pos vuz3170))",fontsize=16,color="black",shape="box"];8299 -> 8409[label="",style="solid", color="black", weight=3];
67.32/34.79	8300[label="primQuotInt (Neg (Succ vuz4440)) (reduce2D (Neg (Succ vuz4440)) (Pos Zero * Pos vuz3170))",fontsize=16,color="black",shape="box"];8300 -> 8410[label="",style="solid", color="black", weight=3];
67.32/34.79	8301[label="primQuotInt (Pos Zero) (reduce2D (Pos Zero) (Pos Zero * Pos vuz3170))",fontsize=16,color="black",shape="box"];8301 -> 8411[label="",style="solid", color="black", weight=3];
67.32/34.79	9993[label="Neg vuz447",fontsize=16,color="green",shape="box"];8306[label="primQuotInt (Neg vuz446) (gcd2 False (Neg vuz447) (Neg vuz3190 * Pos vuz3170))",fontsize=16,color="black",shape="box"];8306 -> 8412[label="",style="solid", color="black", weight=3];
67.32/34.79	8307[label="primQuotInt (Neg vuz446) (gcd2 True (Neg vuz447) (Neg vuz3190 * Pos vuz3170))",fontsize=16,color="black",shape="box"];8307 -> 8413[label="",style="solid", color="black", weight=3];
67.32/34.79	9994[label="Neg vuz349",fontsize=16,color="green",shape="box"];8312[label="primQuotInt (Neg vuz348) (gcd2 False (Neg vuz349) (Pos vuz3190 * Pos vuz3170))",fontsize=16,color="black",shape="box"];8312 -> 8414[label="",style="solid", color="black", weight=3];
67.32/34.79	8313[label="primQuotInt (Neg vuz348) (gcd2 True (Neg vuz349) (Pos vuz3190 * Pos vuz3170))",fontsize=16,color="black",shape="box"];8313 -> 8415[label="",style="solid", color="black", weight=3];
67.32/34.79	8314[label="vuz31800",fontsize=16,color="green",shape="box"];8315[label="Succ vuz31900",fontsize=16,color="green",shape="box"];8316[label="vuz31800",fontsize=16,color="green",shape="box"];8317[label="Succ vuz31900",fontsize=16,color="green",shape="box"];8318[label="primQuotInt (primMinusNat (Succ vuz4490) (Succ vuz4480)) (reduce2D (primMinusNat vuz451 vuz450) (Neg (Succ vuz31900) * Pos vuz3170))",fontsize=16,color="black",shape="box"];8318 -> 8416[label="",style="solid", color="black", weight=3];
67.32/34.79	8319[label="primQuotInt (primMinusNat (Succ vuz4490) Zero) (reduce2D (primMinusNat vuz451 vuz450) (Neg (Succ vuz31900) * Pos vuz3170))",fontsize=16,color="black",shape="box"];8319 -> 8417[label="",style="solid", color="black", weight=3];
67.71/34.80	8320[label="primQuotInt (primMinusNat Zero (Succ vuz4480)) (reduce2D (primMinusNat vuz451 vuz450) (Neg (Succ vuz31900) * Pos vuz3170))",fontsize=16,color="black",shape="box"];8320 -> 8418[label="",style="solid", color="black", weight=3];
67.71/34.80	8321[label="primQuotInt (primMinusNat Zero Zero) (reduce2D (primMinusNat vuz451 vuz450) (Neg (Succ vuz31900) * Pos vuz3170))",fontsize=16,color="black",shape="box"];8321 -> 8419[label="",style="solid", color="black", weight=3];
67.71/34.80	8322[label="primQuotInt (Neg (Succ vuz4540)) (reduce2D (Neg (Succ vuz4540)) (Neg Zero * Pos vuz3170))",fontsize=16,color="black",shape="box"];8322 -> 8420[label="",style="solid", color="black", weight=3];
67.71/34.80	8323[label="primQuotInt (Pos Zero) (reduce2D (Pos Zero) (Neg Zero * Pos vuz3170))",fontsize=16,color="black",shape="box"];8323 -> 8421[label="",style="solid", color="black", weight=3];
67.71/34.80	9995[label="Pos vuz355",fontsize=16,color="green",shape="box"];8328[label="primQuotInt (Pos vuz354) (gcd2 False (Pos vuz355) (Pos vuz3190 * Neg vuz3170))",fontsize=16,color="black",shape="box"];8328 -> 8422[label="",style="solid", color="black", weight=3];
67.71/34.80	8329[label="primQuotInt (Pos vuz354) (gcd2 True (Pos vuz355) (Pos vuz3190 * Neg vuz3170))",fontsize=16,color="black",shape="box"];8329 -> 8423[label="",style="solid", color="black", weight=3];
67.71/34.80	8330[label="vuz31600",fontsize=16,color="green",shape="box"];8331[label="Succ vuz31700",fontsize=16,color="green",shape="box"];8332[label="vuz31600",fontsize=16,color="green",shape="box"];8333[label="Succ vuz31700",fontsize=16,color="green",shape="box"];8334[label="primQuotInt (primMinusNat (Succ vuz4570) (Succ vuz4560)) (reduce2D (primMinusNat vuz459 vuz458) (Neg vuz3190 * Neg (Succ vuz31700)))",fontsize=16,color="black",shape="box"];8334 -> 8424[label="",style="solid", color="black", weight=3];
67.71/34.80	8335[label="primQuotInt (primMinusNat (Succ vuz4570) Zero) (reduce2D (primMinusNat vuz459 vuz458) (Neg vuz3190 * Neg (Succ vuz31700)))",fontsize=16,color="black",shape="box"];8335 -> 8425[label="",style="solid", color="black", weight=3];
67.71/34.80	8336[label="primQuotInt (primMinusNat Zero (Succ vuz4560)) (reduce2D (primMinusNat vuz459 vuz458) (Neg vuz3190 * Neg (Succ vuz31700)))",fontsize=16,color="black",shape="box"];8336 -> 8426[label="",style="solid", color="black", weight=3];
67.71/34.80	8337[label="primQuotInt (primMinusNat Zero Zero) (reduce2D (primMinusNat vuz459 vuz458) (Neg vuz3190 * Neg (Succ vuz31700)))",fontsize=16,color="black",shape="box"];8337 -> 8427[label="",style="solid", color="black", weight=3];
67.71/34.80	8338[label="primQuotInt (Neg (Succ vuz4620)) (reduce2D (Neg (Succ vuz4620)) (Neg vuz3190 * Neg Zero))",fontsize=16,color="black",shape="box"];8338 -> 8428[label="",style="solid", color="black", weight=3];
67.71/34.80	8339[label="primQuotInt (Pos Zero) (reduce2D (Pos Zero) (Neg vuz3190 * Neg Zero))",fontsize=16,color="black",shape="box"];8339 -> 8429[label="",style="solid", color="black", weight=3];
67.71/34.80	8340[label="vuz31600",fontsize=16,color="green",shape="box"];8341[label="Succ vuz31700",fontsize=16,color="green",shape="box"];8342[label="vuz31600",fontsize=16,color="green",shape="box"];8343[label="Succ vuz31700",fontsize=16,color="green",shape="box"];8344[label="primQuotInt (primMinusNat (Succ vuz4650) (Succ vuz4640)) (reduce2D (primMinusNat vuz467 vuz466) (Pos vuz3190 * Neg (Succ vuz31700)))",fontsize=16,color="black",shape="box"];8344 -> 8430[label="",style="solid", color="black", weight=3];
67.71/34.80	8345[label="primQuotInt (primMinusNat (Succ vuz4650) Zero) (reduce2D (primMinusNat vuz467 vuz466) (Pos vuz3190 * Neg (Succ vuz31700)))",fontsize=16,color="black",shape="box"];8345 -> 8431[label="",style="solid", color="black", weight=3];
67.71/34.80	8346[label="primQuotInt (primMinusNat Zero (Succ vuz4640)) (reduce2D (primMinusNat vuz467 vuz466) (Pos vuz3190 * Neg (Succ vuz31700)))",fontsize=16,color="black",shape="box"];8346 -> 8432[label="",style="solid", color="black", weight=3];
67.71/34.80	8347[label="primQuotInt (primMinusNat Zero Zero) (reduce2D (primMinusNat vuz467 vuz466) (Pos vuz3190 * Neg (Succ vuz31700)))",fontsize=16,color="black",shape="box"];8347 -> 8433[label="",style="solid", color="black", weight=3];
67.71/34.80	8348[label="primQuotInt (Neg (Succ vuz4700)) (reduce2D (Neg (Succ vuz4700)) (Pos vuz3190 * Neg Zero))",fontsize=16,color="black",shape="box"];8348 -> 8434[label="",style="solid", color="black", weight=3];
67.71/34.80	8349[label="primQuotInt (Pos Zero) (reduce2D (Pos Zero) (Pos vuz3190 * Neg Zero))",fontsize=16,color="black",shape="box"];8349 -> 8435[label="",style="solid", color="black", weight=3];
67.71/34.80	9996[label="Pos vuz361",fontsize=16,color="green",shape="box"];8354[label="primQuotInt (Pos vuz360) (gcd2 False (Pos vuz361) (Neg vuz3190 * Neg vuz3170))",fontsize=16,color="black",shape="box"];8354 -> 8436[label="",style="solid", color="black", weight=3];
67.71/34.80	8355[label="primQuotInt (Pos vuz360) (gcd2 True (Pos vuz361) (Neg vuz3190 * Neg vuz3170))",fontsize=16,color="black",shape="box"];8355 -> 8437[label="",style="solid", color="black", weight=3];
67.71/34.80	8356 -> 8438[label="",style="dashed", color="red", weight=0];
67.71/34.80	8356[label="primQuotInt (Pos vuz366) (gcd2 (primEqInt (primPlusInt (Pos vuz369) (Pos (primMulNat vuz3180 vuz3190))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz368) (Pos (primMulNat vuz3180 vuz3190))) (Pos vuz367))",fontsize=16,color="magenta"];8356 -> 8439[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8356 -> 8440[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8357 -> 8447[label="",style="dashed", color="red", weight=0];
67.71/34.80	8357[label="primQuotInt (Pos vuz366) (gcd2 (primEqInt (primPlusInt (Pos vuz369) (Neg (primMulNat vuz3180 vuz3190))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz368) (Neg (primMulNat vuz3180 vuz3190))) (Pos vuz367))",fontsize=16,color="magenta"];8357 -> 8448[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8357 -> 8449[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8358 -> 8456[label="",style="dashed", color="red", weight=0];
67.71/34.80	8358[label="primQuotInt (Pos vuz370) (gcd2 (primEqInt (primPlusInt (Neg vuz373) (Pos (primMulNat vuz3180 vuz3190))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz372) (Pos (primMulNat vuz3180 vuz3190))) (Pos vuz371))",fontsize=16,color="magenta"];8358 -> 8457[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8358 -> 8458[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8359 -> 8465[label="",style="dashed", color="red", weight=0];
67.71/34.80	8359[label="primQuotInt (Pos vuz370) (gcd2 (primEqInt (primPlusInt (Neg vuz373) (Neg (primMulNat vuz3180 vuz3190))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz372) (Neg (primMulNat vuz3180 vuz3190))) (Pos vuz371))",fontsize=16,color="magenta"];8359 -> 8466[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8359 -> 8467[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8360 -> 8474[label="",style="dashed", color="red", weight=0];
67.71/34.80	8360[label="primQuotInt (Neg vuz374) (gcd2 (primEqInt (primPlusInt (Neg vuz377) (Pos (primMulNat vuz3180 vuz3190))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz376) (Pos (primMulNat vuz3180 vuz3190))) (Neg vuz375))",fontsize=16,color="magenta"];8360 -> 8475[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8360 -> 8476[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8361 -> 8483[label="",style="dashed", color="red", weight=0];
67.71/34.80	8361[label="primQuotInt (Neg vuz374) (gcd2 (primEqInt (primPlusInt (Neg vuz377) (Neg (primMulNat vuz3180 vuz3190))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz376) (Neg (primMulNat vuz3180 vuz3190))) (Neg vuz375))",fontsize=16,color="magenta"];8361 -> 8484[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8361 -> 8485[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8362 -> 8492[label="",style="dashed", color="red", weight=0];
67.71/34.80	8362[label="primQuotInt (Neg vuz378) (gcd2 (primEqInt (primPlusInt (Pos vuz381) (Pos (primMulNat vuz3180 vuz3190))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz380) (Pos (primMulNat vuz3180 vuz3190))) (Neg vuz379))",fontsize=16,color="magenta"];8362 -> 8493[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8362 -> 8494[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8363 -> 8501[label="",style="dashed", color="red", weight=0];
67.71/34.80	8363[label="primQuotInt (Neg vuz378) (gcd2 (primEqInt (primPlusInt (Pos vuz381) (Neg (primMulNat vuz3180 vuz3190))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz380) (Neg (primMulNat vuz3180 vuz3190))) (Neg vuz379))",fontsize=16,color="magenta"];8363 -> 8502[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8363 -> 8503[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8364 -> 8501[label="",style="dashed", color="red", weight=0];
67.71/34.80	8364[label="primQuotInt (Neg vuz382) (gcd2 (primEqInt (primPlusInt (Pos vuz385) (Neg (primMulNat vuz3180 vuz3190))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz384) (Neg (primMulNat vuz3180 vuz3190))) (Neg vuz383))",fontsize=16,color="magenta"];8364 -> 8504[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8364 -> 8505[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8364 -> 8506[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8364 -> 8507[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8364 -> 8508[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8364 -> 8509[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8365 -> 8492[label="",style="dashed", color="red", weight=0];
67.71/34.80	8365[label="primQuotInt (Neg vuz382) (gcd2 (primEqInt (primPlusInt (Pos vuz385) (Pos (primMulNat vuz3180 vuz3190))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz384) (Pos (primMulNat vuz3180 vuz3190))) (Neg vuz383))",fontsize=16,color="magenta"];8365 -> 8495[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8365 -> 8496[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8365 -> 8497[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8365 -> 8498[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8365 -> 8499[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8365 -> 8500[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8366 -> 8483[label="",style="dashed", color="red", weight=0];
67.71/34.80	8366[label="primQuotInt (Neg vuz386) (gcd2 (primEqInt (primPlusInt (Neg vuz389) (Neg (primMulNat vuz3180 vuz3190))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz388) (Neg (primMulNat vuz3180 vuz3190))) (Neg vuz387))",fontsize=16,color="magenta"];8366 -> 8486[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8366 -> 8487[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8366 -> 8488[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8366 -> 8489[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8366 -> 8490[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8366 -> 8491[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8367 -> 8474[label="",style="dashed", color="red", weight=0];
67.71/34.80	8367[label="primQuotInt (Neg vuz386) (gcd2 (primEqInt (primPlusInt (Neg vuz389) (Pos (primMulNat vuz3180 vuz3190))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz388) (Pos (primMulNat vuz3180 vuz3190))) (Neg vuz387))",fontsize=16,color="magenta"];8367 -> 8477[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8367 -> 8478[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8367 -> 8479[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8367 -> 8480[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8367 -> 8481[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8367 -> 8482[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8368 -> 8465[label="",style="dashed", color="red", weight=0];
67.71/34.80	8368[label="primQuotInt (Pos vuz390) (gcd2 (primEqInt (primPlusInt (Neg vuz393) (Neg (primMulNat vuz3180 vuz3190))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz392) (Neg (primMulNat vuz3180 vuz3190))) (Pos vuz391))",fontsize=16,color="magenta"];8368 -> 8468[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8368 -> 8469[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8368 -> 8470[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8368 -> 8471[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8368 -> 8472[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8368 -> 8473[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8369 -> 8456[label="",style="dashed", color="red", weight=0];
67.71/34.80	8369[label="primQuotInt (Pos vuz390) (gcd2 (primEqInt (primPlusInt (Neg vuz393) (Pos (primMulNat vuz3180 vuz3190))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz392) (Pos (primMulNat vuz3180 vuz3190))) (Pos vuz391))",fontsize=16,color="magenta"];8369 -> 8459[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8369 -> 8460[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8369 -> 8461[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8369 -> 8462[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8369 -> 8463[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8369 -> 8464[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8370 -> 8447[label="",style="dashed", color="red", weight=0];
67.71/34.80	8370[label="primQuotInt (Pos vuz394) (gcd2 (primEqInt (primPlusInt (Pos vuz397) (Neg (primMulNat vuz3180 vuz3190))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz396) (Neg (primMulNat vuz3180 vuz3190))) (Pos vuz395))",fontsize=16,color="magenta"];8370 -> 8450[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8370 -> 8451[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8370 -> 8452[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8370 -> 8453[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8370 -> 8454[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8370 -> 8455[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8371 -> 8438[label="",style="dashed", color="red", weight=0];
67.71/34.80	8371[label="primQuotInt (Pos vuz394) (gcd2 (primEqInt (primPlusInt (Pos vuz397) (Pos (primMulNat vuz3180 vuz3190))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz396) (Pos (primMulNat vuz3180 vuz3190))) (Pos vuz395))",fontsize=16,color="magenta"];8371 -> 8441[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8371 -> 8442[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8371 -> 8443[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8371 -> 8444[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8371 -> 8445[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8371 -> 8446[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8373[label="primQuotInt (Pos vuz398) (gcd0 (Pos vuz399) (Pos vuz3190 * Pos vuz3170))",fontsize=16,color="black",shape="triangle"];8373 -> 8510[label="",style="solid", color="black", weight=3];
67.71/34.80	8374 -> 8511[label="",style="dashed", color="red", weight=0];
67.71/34.80	8374[label="primQuotInt (Pos vuz398) (gcd1 (Pos vuz3190 * Pos vuz3170 == fromInt (Pos Zero)) (Pos vuz399) (Pos vuz3190 * Pos vuz3170))",fontsize=16,color="magenta"];8374 -> 8512[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8375 -> 7677[label="",style="dashed", color="red", weight=0];
67.71/34.80	8375[label="primQuotInt (primMinusNat vuz4010 vuz4000) (reduce2D (primMinusNat vuz4010 vuz4000) (Neg vuz3190 * Pos (Succ vuz31700)))",fontsize=16,color="magenta"];8375 -> 8513[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8375 -> 8514[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8375 -> 8515[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8375 -> 8516[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8376[label="primQuotInt (Pos (Succ vuz4010)) (reduce2D (Pos (Succ vuz4010)) (Neg vuz3190 * Pos (Succ vuz31700)))",fontsize=16,color="black",shape="box"];8376 -> 8517[label="",style="solid", color="black", weight=3];
67.71/34.80	8377[label="primQuotInt (Neg (Succ vuz4000)) (reduce2D (Neg (Succ vuz4000)) (Neg vuz3190 * Pos (Succ vuz31700)))",fontsize=16,color="black",shape="box"];8377 -> 8518[label="",style="solid", color="black", weight=3];
67.71/34.80	8378[label="primQuotInt (Pos Zero) (reduce2D (Pos Zero) (Neg vuz3190 * Pos (Succ vuz31700)))",fontsize=16,color="black",shape="box"];8378 -> 8519[label="",style="solid", color="black", weight=3];
67.71/34.80	8379[label="primQuotInt (Neg (Succ vuz4060)) (gcd (Neg (Succ vuz4060)) (Neg vuz3190 * Pos Zero))",fontsize=16,color="black",shape="box"];8379 -> 8520[label="",style="solid", color="black", weight=3];
67.71/34.80	8380[label="primQuotInt (Pos Zero) (gcd (Pos Zero) (Neg vuz3190 * Pos Zero))",fontsize=16,color="black",shape="box"];8380 -> 8521[label="",style="solid", color="black", weight=3];
67.71/34.80	8381 -> 7691[label="",style="dashed", color="red", weight=0];
67.71/34.80	8381[label="primQuotInt (primMinusNat vuz4090 vuz4080) (reduce2D (primMinusNat vuz4090 vuz4080) (Pos vuz3190 * Pos (Succ vuz31700)))",fontsize=16,color="magenta"];8381 -> 8522[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8381 -> 8523[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8381 -> 8524[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8381 -> 8525[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8382[label="primQuotInt (Pos (Succ vuz4090)) (reduce2D (Pos (Succ vuz4090)) (Pos vuz3190 * Pos (Succ vuz31700)))",fontsize=16,color="black",shape="box"];8382 -> 8526[label="",style="solid", color="black", weight=3];
67.71/34.80	8383[label="primQuotInt (Neg (Succ vuz4080)) (reduce2D (Neg (Succ vuz4080)) (Pos vuz3190 * Pos (Succ vuz31700)))",fontsize=16,color="black",shape="box"];8383 -> 8527[label="",style="solid", color="black", weight=3];
67.71/34.80	8384[label="primQuotInt (Pos Zero) (reduce2D (Pos Zero) (Pos vuz3190 * Pos (Succ vuz31700)))",fontsize=16,color="black",shape="box"];8384 -> 8528[label="",style="solid", color="black", weight=3];
67.71/34.80	8385[label="primQuotInt (Neg (Succ vuz4140)) (gcd (Neg (Succ vuz4140)) (Pos vuz3190 * Pos Zero))",fontsize=16,color="black",shape="box"];8385 -> 8529[label="",style="solid", color="black", weight=3];
67.71/34.80	8386[label="primQuotInt (Pos Zero) (gcd (Pos Zero) (Pos vuz3190 * Pos Zero))",fontsize=16,color="black",shape="box"];8386 -> 8530[label="",style="solid", color="black", weight=3];
67.71/34.80	8387[label="primQuotInt (Pos vuz416) (gcd0 (Pos vuz417) (Neg vuz3190 * Pos vuz3170))",fontsize=16,color="black",shape="triangle"];8387 -> 8531[label="",style="solid", color="black", weight=3];
67.71/34.80	8388 -> 8532[label="",style="dashed", color="red", weight=0];
67.71/34.80	8388[label="primQuotInt (Pos vuz416) (gcd1 (Neg vuz3190 * Pos vuz3170 == fromInt (Pos Zero)) (Pos vuz417) (Neg vuz3190 * Pos vuz3170))",fontsize=16,color="magenta"];8388 -> 8533[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8389 -> 7723[label="",style="dashed", color="red", weight=0];
67.71/34.80	8389[label="primQuotInt (primMinusNat vuz4190 vuz4180) (reduce2D (primMinusNat vuz4190 vuz4180) (Pos (Succ vuz31900) * Neg vuz3170))",fontsize=16,color="magenta"];8389 -> 8534[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8389 -> 8535[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8389 -> 8536[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8389 -> 8537[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8390[label="primQuotInt (Pos (Succ vuz4190)) (reduce2D (Pos (Succ vuz4190)) (Pos (Succ vuz31900) * Neg vuz3170))",fontsize=16,color="black",shape="box"];8390 -> 8538[label="",style="solid", color="black", weight=3];
67.71/34.80	8391[label="primQuotInt (Neg (Succ vuz4180)) (reduce2D (Neg (Succ vuz4180)) (Pos (Succ vuz31900) * Neg vuz3170))",fontsize=16,color="black",shape="box"];8391 -> 8539[label="",style="solid", color="black", weight=3];
67.71/34.80	8392[label="primQuotInt (Pos Zero) (reduce2D (Pos Zero) (Pos (Succ vuz31900) * Neg vuz3170))",fontsize=16,color="black",shape="box"];8392 -> 8540[label="",style="solid", color="black", weight=3];
67.71/34.80	8393[label="primQuotInt (Neg (Succ vuz4240)) (gcd (Neg (Succ vuz4240)) (Pos Zero * Neg vuz3170))",fontsize=16,color="black",shape="box"];8393 -> 8541[label="",style="solid", color="black", weight=3];
67.71/34.80	8394[label="primQuotInt (Pos Zero) (gcd (Pos Zero) (Pos Zero * Neg vuz3170))",fontsize=16,color="black",shape="box"];8394 -> 8542[label="",style="solid", color="black", weight=3];
67.71/34.80	8396[label="primQuotInt (Neg vuz426) (gcd0 (Neg vuz427) (Neg vuz3190 * Neg vuz3170))",fontsize=16,color="black",shape="triangle"];8396 -> 8543[label="",style="solid", color="black", weight=3];
67.71/34.80	8397 -> 8544[label="",style="dashed", color="red", weight=0];
67.71/34.80	8397[label="primQuotInt (Neg vuz426) (gcd1 (Neg vuz3190 * Neg vuz3170 == fromInt (Pos Zero)) (Neg vuz427) (Neg vuz3190 * Neg vuz3170))",fontsize=16,color="magenta"];8397 -> 8545[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8398[label="primQuotInt (Neg vuz428) (gcd0 (Neg vuz429) (Pos vuz3190 * Neg vuz3170))",fontsize=16,color="black",shape="triangle"];8398 -> 8546[label="",style="solid", color="black", weight=3];
67.71/34.80	8399 -> 8547[label="",style="dashed", color="red", weight=0];
67.71/34.80	8399[label="primQuotInt (Neg vuz428) (gcd1 (Pos vuz3190 * Neg vuz3170 == fromInt (Pos Zero)) (Neg vuz429) (Pos vuz3190 * Neg vuz3170))",fontsize=16,color="magenta"];8399 -> 8548[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8400 -> 7773[label="",style="dashed", color="red", weight=0];
67.71/34.80	8400[label="primQuotInt (primMinusNat vuz4310 vuz4300) (reduce2D (primMinusNat vuz4310 vuz4300) (Neg (Succ vuz31900) * Neg vuz3170))",fontsize=16,color="magenta"];8400 -> 8549[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8400 -> 8550[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8400 -> 8551[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8400 -> 8552[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8401[label="primQuotInt (Pos (Succ vuz4310)) (reduce2D (Pos (Succ vuz4310)) (Neg (Succ vuz31900) * Neg vuz3170))",fontsize=16,color="black",shape="box"];8401 -> 8553[label="",style="solid", color="black", weight=3];
67.71/34.80	8402[label="primQuotInt (Neg (Succ vuz4300)) (reduce2D (Neg (Succ vuz4300)) (Neg (Succ vuz31900) * Neg vuz3170))",fontsize=16,color="black",shape="box"];8402 -> 8554[label="",style="solid", color="black", weight=3];
67.71/34.80	8403[label="primQuotInt (Pos Zero) (reduce2D (Pos Zero) (Neg (Succ vuz31900) * Neg vuz3170))",fontsize=16,color="black",shape="box"];8403 -> 8555[label="",style="solid", color="black", weight=3];
67.71/34.80	8404[label="primQuotInt (Neg (Succ vuz4360)) (gcd (Neg (Succ vuz4360)) (Neg Zero * Neg vuz3170))",fontsize=16,color="black",shape="box"];8404 -> 8556[label="",style="solid", color="black", weight=3];
67.71/34.80	8405[label="primQuotInt (Pos Zero) (gcd (Pos Zero) (Neg Zero * Neg vuz3170))",fontsize=16,color="black",shape="box"];8405 -> 8557[label="",style="solid", color="black", weight=3];
67.71/34.80	8406 -> 7787[label="",style="dashed", color="red", weight=0];
67.71/34.80	8406[label="primQuotInt (primMinusNat vuz4390 vuz4380) (reduce2D (primMinusNat vuz4390 vuz4380) (Pos (Succ vuz31900) * Pos vuz3170))",fontsize=16,color="magenta"];8406 -> 8558[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8406 -> 8559[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8406 -> 8560[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8406 -> 8561[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8407[label="primQuotInt (Pos (Succ vuz4390)) (reduce2D (Pos (Succ vuz4390)) (Pos (Succ vuz31900) * Pos vuz3170))",fontsize=16,color="black",shape="box"];8407 -> 8562[label="",style="solid", color="black", weight=3];
67.71/34.80	8408[label="primQuotInt (Neg (Succ vuz4380)) (reduce2D (Neg (Succ vuz4380)) (Pos (Succ vuz31900) * Pos vuz3170))",fontsize=16,color="black",shape="box"];8408 -> 8563[label="",style="solid", color="black", weight=3];
67.71/34.80	8409[label="primQuotInt (Pos Zero) (reduce2D (Pos Zero) (Pos (Succ vuz31900) * Pos vuz3170))",fontsize=16,color="black",shape="box"];8409 -> 8564[label="",style="solid", color="black", weight=3];
67.71/34.80	8410[label="primQuotInt (Neg (Succ vuz4440)) (gcd (Neg (Succ vuz4440)) (Pos Zero * Pos vuz3170))",fontsize=16,color="black",shape="box"];8410 -> 8565[label="",style="solid", color="black", weight=3];
67.71/34.80	8411[label="primQuotInt (Pos Zero) (gcd (Pos Zero) (Pos Zero * Pos vuz3170))",fontsize=16,color="black",shape="box"];8411 -> 8566[label="",style="solid", color="black", weight=3];
67.71/34.80	8412[label="primQuotInt (Neg vuz446) (gcd0 (Neg vuz447) (Neg vuz3190 * Pos vuz3170))",fontsize=16,color="black",shape="triangle"];8412 -> 8567[label="",style="solid", color="black", weight=3];
67.71/34.80	8413 -> 8568[label="",style="dashed", color="red", weight=0];
67.71/34.80	8413[label="primQuotInt (Neg vuz446) (gcd1 (Neg vuz3190 * Pos vuz3170 == fromInt (Pos Zero)) (Neg vuz447) (Neg vuz3190 * Pos vuz3170))",fontsize=16,color="magenta"];8413 -> 8569[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8414[label="primQuotInt (Neg vuz348) (gcd0 (Neg vuz349) (Pos vuz3190 * Pos vuz3170))",fontsize=16,color="black",shape="triangle"];8414 -> 8570[label="",style="solid", color="black", weight=3];
67.71/34.80	8415 -> 8571[label="",style="dashed", color="red", weight=0];
67.71/34.80	8415[label="primQuotInt (Neg vuz348) (gcd1 (Pos vuz3190 * Pos vuz3170 == fromInt (Pos Zero)) (Neg vuz349) (Pos vuz3190 * Pos vuz3170))",fontsize=16,color="magenta"];8415 -> 8572[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8416 -> 7824[label="",style="dashed", color="red", weight=0];
67.71/34.80	8416[label="primQuotInt (primMinusNat vuz4490 vuz4480) (reduce2D (primMinusNat vuz4490 vuz4480) (Neg (Succ vuz31900) * Pos vuz3170))",fontsize=16,color="magenta"];8416 -> 8573[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8416 -> 8574[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8416 -> 8575[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8416 -> 8576[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8417[label="primQuotInt (Pos (Succ vuz4490)) (reduce2D (Pos (Succ vuz4490)) (Neg (Succ vuz31900) * Pos vuz3170))",fontsize=16,color="black",shape="box"];8417 -> 8577[label="",style="solid", color="black", weight=3];
67.71/34.80	8418[label="primQuotInt (Neg (Succ vuz4480)) (reduce2D (Neg (Succ vuz4480)) (Neg (Succ vuz31900) * Pos vuz3170))",fontsize=16,color="black",shape="box"];8418 -> 8578[label="",style="solid", color="black", weight=3];
67.71/34.80	8419[label="primQuotInt (Pos Zero) (reduce2D (Pos Zero) (Neg (Succ vuz31900) * Pos vuz3170))",fontsize=16,color="black",shape="box"];8419 -> 8579[label="",style="solid", color="black", weight=3];
67.71/34.80	8420[label="primQuotInt (Neg (Succ vuz4540)) (gcd (Neg (Succ vuz4540)) (Neg Zero * Pos vuz3170))",fontsize=16,color="black",shape="box"];8420 -> 8580[label="",style="solid", color="black", weight=3];
67.71/34.80	8421[label="primQuotInt (Pos Zero) (gcd (Pos Zero) (Neg Zero * Pos vuz3170))",fontsize=16,color="black",shape="box"];8421 -> 8581[label="",style="solid", color="black", weight=3];
67.71/34.80	8422[label="primQuotInt (Pos vuz354) (gcd0 (Pos vuz355) (Pos vuz3190 * Neg vuz3170))",fontsize=16,color="black",shape="triangle"];8422 -> 8582[label="",style="solid", color="black", weight=3];
67.71/34.80	8423 -> 8583[label="",style="dashed", color="red", weight=0];
67.71/34.80	8423[label="primQuotInt (Pos vuz354) (gcd1 (Pos vuz3190 * Neg vuz3170 == fromInt (Pos Zero)) (Pos vuz355) (Pos vuz3190 * Neg vuz3170))",fontsize=16,color="magenta"];8423 -> 8584[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8424 -> 7843[label="",style="dashed", color="red", weight=0];
67.71/34.80	8424[label="primQuotInt (primMinusNat vuz4570 vuz4560) (reduce2D (primMinusNat vuz4570 vuz4560) (Neg vuz3190 * Neg (Succ vuz31700)))",fontsize=16,color="magenta"];8424 -> 8585[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8424 -> 8586[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8424 -> 8587[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8424 -> 8588[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8425[label="primQuotInt (Pos (Succ vuz4570)) (reduce2D (Pos (Succ vuz4570)) (Neg vuz3190 * Neg (Succ vuz31700)))",fontsize=16,color="black",shape="box"];8425 -> 8589[label="",style="solid", color="black", weight=3];
67.71/34.80	8426[label="primQuotInt (Neg (Succ vuz4560)) (reduce2D (Neg (Succ vuz4560)) (Neg vuz3190 * Neg (Succ vuz31700)))",fontsize=16,color="black",shape="box"];8426 -> 8590[label="",style="solid", color="black", weight=3];
67.71/34.80	8427[label="primQuotInt (Pos Zero) (reduce2D (Pos Zero) (Neg vuz3190 * Neg (Succ vuz31700)))",fontsize=16,color="black",shape="box"];8427 -> 8591[label="",style="solid", color="black", weight=3];
67.71/34.80	8428[label="primQuotInt (Neg (Succ vuz4620)) (gcd (Neg (Succ vuz4620)) (Neg vuz3190 * Neg Zero))",fontsize=16,color="black",shape="box"];8428 -> 8592[label="",style="solid", color="black", weight=3];
67.71/34.80	8429[label="primQuotInt (Pos Zero) (gcd (Pos Zero) (Neg vuz3190 * Neg Zero))",fontsize=16,color="black",shape="box"];8429 -> 8593[label="",style="solid", color="black", weight=3];
67.71/34.80	8430 -> 7857[label="",style="dashed", color="red", weight=0];
67.71/34.80	8430[label="primQuotInt (primMinusNat vuz4650 vuz4640) (reduce2D (primMinusNat vuz4650 vuz4640) (Pos vuz3190 * Neg (Succ vuz31700)))",fontsize=16,color="magenta"];8430 -> 8594[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8430 -> 8595[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8430 -> 8596[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8430 -> 8597[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8431[label="primQuotInt (Pos (Succ vuz4650)) (reduce2D (Pos (Succ vuz4650)) (Pos vuz3190 * Neg (Succ vuz31700)))",fontsize=16,color="black",shape="box"];8431 -> 8598[label="",style="solid", color="black", weight=3];
67.71/34.80	8432[label="primQuotInt (Neg (Succ vuz4640)) (reduce2D (Neg (Succ vuz4640)) (Pos vuz3190 * Neg (Succ vuz31700)))",fontsize=16,color="black",shape="box"];8432 -> 8599[label="",style="solid", color="black", weight=3];
67.71/34.80	8433[label="primQuotInt (Pos Zero) (reduce2D (Pos Zero) (Pos vuz3190 * Neg (Succ vuz31700)))",fontsize=16,color="black",shape="box"];8433 -> 8600[label="",style="solid", color="black", weight=3];
67.71/34.80	8434[label="primQuotInt (Neg (Succ vuz4700)) (gcd (Neg (Succ vuz4700)) (Pos vuz3190 * Neg Zero))",fontsize=16,color="black",shape="box"];8434 -> 8601[label="",style="solid", color="black", weight=3];
67.71/34.80	8435[label="primQuotInt (Pos Zero) (gcd (Pos Zero) (Pos vuz3190 * Neg Zero))",fontsize=16,color="black",shape="box"];8435 -> 8602[label="",style="solid", color="black", weight=3];
67.71/34.80	8436[label="primQuotInt (Pos vuz360) (gcd0 (Pos vuz361) (Neg vuz3190 * Neg vuz3170))",fontsize=16,color="black",shape="triangle"];8436 -> 8603[label="",style="solid", color="black", weight=3];
67.71/34.80	8437 -> 8604[label="",style="dashed", color="red", weight=0];
67.71/34.80	8437[label="primQuotInt (Pos vuz360) (gcd1 (Neg vuz3190 * Neg vuz3170 == fromInt (Pos Zero)) (Pos vuz361) (Neg vuz3190 * Neg vuz3170))",fontsize=16,color="magenta"];8437 -> 8605[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8439 -> 7480[label="",style="dashed", color="red", weight=0];
67.71/34.80	8439[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];8439 -> 8606[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8439 -> 8607[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8440 -> 7480[label="",style="dashed", color="red", weight=0];
67.71/34.80	8440[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];8440 -> 8608[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8440 -> 8609[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8438[label="primQuotInt (Pos vuz366) (gcd2 (primEqInt (primPlusInt (Pos vuz369) (Pos vuz481)) (fromInt (Pos Zero))) (primPlusInt (Pos vuz368) (Pos vuz480)) (Pos vuz367))",fontsize=16,color="black",shape="triangle"];8438 -> 8610[label="",style="solid", color="black", weight=3];
67.71/34.80	8448 -> 7480[label="",style="dashed", color="red", weight=0];
67.71/34.80	8448[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];8448 -> 8611[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8448 -> 8612[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8449 -> 7480[label="",style="dashed", color="red", weight=0];
67.71/34.80	8449[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];8449 -> 8613[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8449 -> 8614[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8447[label="primQuotInt (Pos vuz366) (gcd2 (primEqInt (primPlusInt (Pos vuz369) (Neg vuz483)) (fromInt (Pos Zero))) (primPlusInt (Pos vuz368) (Neg vuz482)) (Pos vuz367))",fontsize=16,color="black",shape="triangle"];8447 -> 8615[label="",style="solid", color="black", weight=3];
67.71/34.80	8457 -> 7480[label="",style="dashed", color="red", weight=0];
67.71/34.80	8457[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];8457 -> 8616[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8457 -> 8617[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8458 -> 7480[label="",style="dashed", color="red", weight=0];
67.71/34.80	8458[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];8458 -> 8618[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8458 -> 8619[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8456[label="primQuotInt (Pos vuz370) (gcd2 (primEqInt (primPlusInt (Neg vuz373) (Pos vuz485)) (fromInt (Pos Zero))) (primPlusInt (Neg vuz372) (Pos vuz484)) (Pos vuz371))",fontsize=16,color="black",shape="triangle"];8456 -> 8620[label="",style="solid", color="black", weight=3];
67.71/34.80	8466 -> 7480[label="",style="dashed", color="red", weight=0];
67.71/34.80	8466[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];8466 -> 8621[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8466 -> 8622[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8467 -> 7480[label="",style="dashed", color="red", weight=0];
67.71/34.80	8467[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];8467 -> 8623[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8467 -> 8624[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8465[label="primQuotInt (Pos vuz370) (gcd2 (primEqInt (primPlusInt (Neg vuz373) (Neg vuz487)) (fromInt (Pos Zero))) (primPlusInt (Neg vuz372) (Neg vuz486)) (Pos vuz371))",fontsize=16,color="black",shape="triangle"];8465 -> 8625[label="",style="solid", color="black", weight=3];
67.71/34.80	8475 -> 7480[label="",style="dashed", color="red", weight=0];
67.71/34.80	8475[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];8475 -> 8626[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8475 -> 8627[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8476 -> 7480[label="",style="dashed", color="red", weight=0];
67.71/34.80	8476[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];8476 -> 8628[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8476 -> 8629[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8474[label="primQuotInt (Neg vuz374) (gcd2 (primEqInt (primPlusInt (Neg vuz377) (Pos vuz489)) (fromInt (Pos Zero))) (primPlusInt (Neg vuz376) (Pos vuz488)) (Neg vuz375))",fontsize=16,color="black",shape="triangle"];8474 -> 8630[label="",style="solid", color="black", weight=3];
67.71/34.80	8484 -> 7480[label="",style="dashed", color="red", weight=0];
67.71/34.80	8484[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];8484 -> 8631[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8484 -> 8632[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8485 -> 7480[label="",style="dashed", color="red", weight=0];
67.71/34.80	8485[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];8485 -> 8633[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8485 -> 8634[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8483[label="primQuotInt (Neg vuz374) (gcd2 (primEqInt (primPlusInt (Neg vuz377) (Neg vuz491)) (fromInt (Pos Zero))) (primPlusInt (Neg vuz376) (Neg vuz490)) (Neg vuz375))",fontsize=16,color="black",shape="triangle"];8483 -> 8635[label="",style="solid", color="black", weight=3];
67.71/34.80	8493 -> 7480[label="",style="dashed", color="red", weight=0];
67.71/34.80	8493[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];8493 -> 8636[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8493 -> 8637[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8494 -> 7480[label="",style="dashed", color="red", weight=0];
67.71/34.80	8494[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];8494 -> 8638[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8494 -> 8639[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8492[label="primQuotInt (Neg vuz378) (gcd2 (primEqInt (primPlusInt (Pos vuz381) (Pos vuz493)) (fromInt (Pos Zero))) (primPlusInt (Pos vuz380) (Pos vuz492)) (Neg vuz379))",fontsize=16,color="black",shape="triangle"];8492 -> 8640[label="",style="solid", color="black", weight=3];
67.71/34.80	8502 -> 7480[label="",style="dashed", color="red", weight=0];
67.71/34.80	8502[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];8502 -> 8641[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8502 -> 8642[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8503 -> 7480[label="",style="dashed", color="red", weight=0];
67.71/34.80	8503[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];8503 -> 8643[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8503 -> 8644[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8501[label="primQuotInt (Neg vuz378) (gcd2 (primEqInt (primPlusInt (Pos vuz381) (Neg vuz495)) (fromInt (Pos Zero))) (primPlusInt (Pos vuz380) (Neg vuz494)) (Neg vuz379))",fontsize=16,color="black",shape="triangle"];8501 -> 8645[label="",style="solid", color="black", weight=3];
67.71/34.80	8504[label="vuz383",fontsize=16,color="green",shape="box"];8505[label="vuz384",fontsize=16,color="green",shape="box"];8506 -> 7480[label="",style="dashed", color="red", weight=0];
67.71/34.80	8506[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];8506 -> 8646[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8506 -> 8647[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8507[label="vuz385",fontsize=16,color="green",shape="box"];8508 -> 7480[label="",style="dashed", color="red", weight=0];
67.71/34.80	8508[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];8508 -> 8648[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8508 -> 8649[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8509[label="vuz382",fontsize=16,color="green",shape="box"];8495[label="vuz383",fontsize=16,color="green",shape="box"];8496[label="vuz384",fontsize=16,color="green",shape="box"];8497[label="vuz385",fontsize=16,color="green",shape="box"];8498 -> 7480[label="",style="dashed", color="red", weight=0];
67.71/34.80	8498[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];8498 -> 8650[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8498 -> 8651[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8499[label="vuz382",fontsize=16,color="green",shape="box"];8500 -> 7480[label="",style="dashed", color="red", weight=0];
67.71/34.80	8500[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];8500 -> 8652[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8500 -> 8653[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8486 -> 7480[label="",style="dashed", color="red", weight=0];
67.71/34.80	8486[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];8486 -> 8654[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8486 -> 8655[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8487[label="vuz387",fontsize=16,color="green",shape="box"];8488[label="vuz388",fontsize=16,color="green",shape="box"];8489[label="vuz386",fontsize=16,color="green",shape="box"];8490[label="vuz389",fontsize=16,color="green",shape="box"];8491 -> 7480[label="",style="dashed", color="red", weight=0];
67.71/34.80	8491[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];8491 -> 8656[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8491 -> 8657[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8477 -> 7480[label="",style="dashed", color="red", weight=0];
67.71/34.80	8477[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];8477 -> 8658[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8477 -> 8659[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8478[label="vuz387",fontsize=16,color="green",shape="box"];8479[label="vuz388",fontsize=16,color="green",shape="box"];8480 -> 7480[label="",style="dashed", color="red", weight=0];
67.71/34.80	8480[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];8480 -> 8660[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8480 -> 8661[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8481[label="vuz386",fontsize=16,color="green",shape="box"];8482[label="vuz389",fontsize=16,color="green",shape="box"];8468[label="vuz392",fontsize=16,color="green",shape="box"];8469 -> 7480[label="",style="dashed", color="red", weight=0];
67.71/34.80	8469[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];8469 -> 8662[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8469 -> 8663[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8470[label="vuz393",fontsize=16,color="green",shape="box"];8471[label="vuz390",fontsize=16,color="green",shape="box"];8472[label="vuz391",fontsize=16,color="green",shape="box"];8473 -> 7480[label="",style="dashed", color="red", weight=0];
67.71/34.80	8473[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];8473 -> 8664[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8473 -> 8665[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8459[label="vuz392",fontsize=16,color="green",shape="box"];8460 -> 7480[label="",style="dashed", color="red", weight=0];
67.71/34.80	8460[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];8460 -> 8666[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8460 -> 8667[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8461[label="vuz393",fontsize=16,color="green",shape="box"];8462[label="vuz390",fontsize=16,color="green",shape="box"];8463[label="vuz391",fontsize=16,color="green",shape="box"];8464 -> 7480[label="",style="dashed", color="red", weight=0];
67.71/34.80	8464[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];8464 -> 8668[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8464 -> 8669[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8450[label="vuz395",fontsize=16,color="green",shape="box"];8451[label="vuz397",fontsize=16,color="green",shape="box"];8452[label="vuz396",fontsize=16,color="green",shape="box"];8453 -> 7480[label="",style="dashed", color="red", weight=0];
67.71/34.80	8453[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];8453 -> 8670[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8453 -> 8671[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8454 -> 7480[label="",style="dashed", color="red", weight=0];
67.71/34.80	8454[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];8454 -> 8672[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8454 -> 8673[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8455[label="vuz394",fontsize=16,color="green",shape="box"];8441 -> 7480[label="",style="dashed", color="red", weight=0];
67.71/34.80	8441[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];8441 -> 8674[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8441 -> 8675[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8442[label="vuz395",fontsize=16,color="green",shape="box"];8443[label="vuz397",fontsize=16,color="green",shape="box"];8444 -> 7480[label="",style="dashed", color="red", weight=0];
67.71/34.80	8444[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];8444 -> 8676[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8444 -> 8677[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8445[label="vuz396",fontsize=16,color="green",shape="box"];8446[label="vuz394",fontsize=16,color="green",shape="box"];8510[label="primQuotInt (Pos vuz398) (gcd0Gcd' (abs (Pos vuz399)) (abs (Pos vuz3190 * Pos vuz3170)))",fontsize=16,color="black",shape="box"];8510 -> 8678[label="",style="solid", color="black", weight=3];
67.71/34.80	8512 -> 9987[label="",style="dashed", color="red", weight=0];
67.71/34.80	8512[label="Pos vuz3190 * Pos vuz3170 == fromInt (Pos Zero)",fontsize=16,color="magenta"];8512 -> 9997[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8511[label="primQuotInt (Pos vuz398) (gcd1 vuz496 (Pos vuz399) (Pos vuz3190 * Pos vuz3170))",fontsize=16,color="burlywood",shape="triangle"];11047[label="vuz496/False",fontsize=10,color="white",style="solid",shape="box"];8511 -> 11047[label="",style="solid", color="burlywood", weight=9];
67.71/34.80	11047 -> 8681[label="",style="solid", color="burlywood", weight=3];
67.71/34.80	11048[label="vuz496/True",fontsize=10,color="white",style="solid",shape="box"];8511 -> 11048[label="",style="solid", color="burlywood", weight=9];
67.71/34.80	11048 -> 8682[label="",style="solid", color="burlywood", weight=3];
67.71/34.80	8513[label="vuz4000",fontsize=16,color="green",shape="box"];8514[label="vuz4010",fontsize=16,color="green",shape="box"];8515[label="vuz4010",fontsize=16,color="green",shape="box"];8516[label="vuz4000",fontsize=16,color="green",shape="box"];8517[label="primQuotInt (Pos (Succ vuz4010)) (gcd (Pos (Succ vuz4010)) (Neg vuz3190 * Pos (Succ vuz31700)))",fontsize=16,color="black",shape="box"];8517 -> 8683[label="",style="solid", color="black", weight=3];
67.71/34.80	8518[label="primQuotInt (Neg (Succ vuz4000)) (gcd (Neg (Succ vuz4000)) (Neg vuz3190 * Pos (Succ vuz31700)))",fontsize=16,color="black",shape="box"];8518 -> 8684[label="",style="solid", color="black", weight=3];
67.71/34.80	8519[label="primQuotInt (Pos Zero) (gcd (Pos Zero) (Neg vuz3190 * Pos (Succ vuz31700)))",fontsize=16,color="black",shape="box"];8519 -> 8685[label="",style="solid", color="black", weight=3];
67.71/34.80	8520 -> 7809[label="",style="dashed", color="red", weight=0];
67.71/34.80	8520[label="primQuotInt (Neg (Succ vuz4060)) (gcd3 (Neg (Succ vuz4060)) (Neg vuz3190 * Pos Zero))",fontsize=16,color="magenta"];8520 -> 8686[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8520 -> 8687[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8520 -> 8688[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8521 -> 7713[label="",style="dashed", color="red", weight=0];
67.71/34.80	8521[label="primQuotInt (Pos Zero) (gcd3 (Pos Zero) (Neg vuz3190 * Pos Zero))",fontsize=16,color="magenta"];8521 -> 8689[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8521 -> 8690[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8521 -> 8691[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8522[label="vuz4090",fontsize=16,color="green",shape="box"];8523[label="vuz4080",fontsize=16,color="green",shape="box"];8524[label="vuz4090",fontsize=16,color="green",shape="box"];8525[label="vuz4080",fontsize=16,color="green",shape="box"];8526[label="primQuotInt (Pos (Succ vuz4090)) (gcd (Pos (Succ vuz4090)) (Pos vuz3190 * Pos (Succ vuz31700)))",fontsize=16,color="black",shape="box"];8526 -> 8692[label="",style="solid", color="black", weight=3];
67.71/34.80	8527[label="primQuotInt (Neg (Succ vuz4080)) (gcd (Neg (Succ vuz4080)) (Pos vuz3190 * Pos (Succ vuz31700)))",fontsize=16,color="black",shape="box"];8527 -> 8693[label="",style="solid", color="black", weight=3];
67.71/34.80	8528[label="primQuotInt (Pos Zero) (gcd (Pos Zero) (Pos vuz3190 * Pos (Succ vuz31700)))",fontsize=16,color="black",shape="box"];8528 -> 8694[label="",style="solid", color="black", weight=3];
67.71/34.80	8529 -> 7587[label="",style="dashed", color="red", weight=0];
67.71/34.80	8529[label="primQuotInt (Neg (Succ vuz4140)) (gcd3 (Neg (Succ vuz4140)) (Pos vuz3190 * Pos Zero))",fontsize=16,color="magenta"];8529 -> 8695[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8529 -> 8696[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8529 -> 8697[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8530 -> 7667[label="",style="dashed", color="red", weight=0];
67.71/34.80	8530[label="primQuotInt (Pos Zero) (gcd3 (Pos Zero) (Pos vuz3190 * Pos Zero))",fontsize=16,color="magenta"];8530 -> 8698[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8530 -> 8699[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8530 -> 8700[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8531[label="primQuotInt (Pos vuz416) (gcd0Gcd' (abs (Pos vuz417)) (abs (Neg vuz3190 * Pos vuz3170)))",fontsize=16,color="black",shape="box"];8531 -> 8701[label="",style="solid", color="black", weight=3];
67.71/34.80	8533 -> 9987[label="",style="dashed", color="red", weight=0];
67.71/34.80	8533[label="Neg vuz3190 * Pos vuz3170 == fromInt (Pos Zero)",fontsize=16,color="magenta"];8533 -> 9998[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8532[label="primQuotInt (Pos vuz416) (gcd1 vuz497 (Pos vuz417) (Neg vuz3190 * Pos vuz3170))",fontsize=16,color="burlywood",shape="triangle"];11049[label="vuz497/False",fontsize=10,color="white",style="solid",shape="box"];8532 -> 11049[label="",style="solid", color="burlywood", weight=9];
67.71/34.80	11049 -> 8704[label="",style="solid", color="burlywood", weight=3];
67.71/34.80	11050[label="vuz497/True",fontsize=10,color="white",style="solid",shape="box"];8532 -> 11050[label="",style="solid", color="burlywood", weight=9];
67.71/34.80	11050 -> 8705[label="",style="solid", color="burlywood", weight=3];
67.71/34.80	8534[label="vuz4180",fontsize=16,color="green",shape="box"];8535[label="vuz4190",fontsize=16,color="green",shape="box"];8536[label="vuz4180",fontsize=16,color="green",shape="box"];8537[label="vuz4190",fontsize=16,color="green",shape="box"];8538[label="primQuotInt (Pos (Succ vuz4190)) (gcd (Pos (Succ vuz4190)) (Pos (Succ vuz31900) * Neg vuz3170))",fontsize=16,color="black",shape="box"];8538 -> 8706[label="",style="solid", color="black", weight=3];
67.71/34.80	8539[label="primQuotInt (Neg (Succ vuz4180)) (gcd (Neg (Succ vuz4180)) (Pos (Succ vuz31900) * Neg vuz3170))",fontsize=16,color="black",shape="box"];8539 -> 8707[label="",style="solid", color="black", weight=3];
67.71/34.80	8540[label="primQuotInt (Pos Zero) (gcd (Pos Zero) (Pos (Succ vuz31900) * Neg vuz3170))",fontsize=16,color="black",shape="box"];8540 -> 8708[label="",style="solid", color="black", weight=3];
67.71/34.80	8541 -> 7763[label="",style="dashed", color="red", weight=0];
67.71/34.80	8541[label="primQuotInt (Neg (Succ vuz4240)) (gcd3 (Neg (Succ vuz4240)) (Pos Zero * Neg vuz3170))",fontsize=16,color="magenta"];8541 -> 8709[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8541 -> 8710[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8541 -> 8711[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8542 -> 7598[label="",style="dashed", color="red", weight=0];
67.71/34.80	8542[label="primQuotInt (Pos Zero) (gcd3 (Pos Zero) (Pos Zero * Neg vuz3170))",fontsize=16,color="magenta"];8542 -> 8712[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8542 -> 8713[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8542 -> 8714[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8543[label="primQuotInt (Neg vuz426) (gcd0Gcd' (abs (Neg vuz427)) (abs (Neg vuz3190 * Neg vuz3170)))",fontsize=16,color="black",shape="box"];8543 -> 8715[label="",style="solid", color="black", weight=3];
67.71/34.80	8545 -> 9987[label="",style="dashed", color="red", weight=0];
67.71/34.80	8545[label="Neg vuz3190 * Neg vuz3170 == fromInt (Pos Zero)",fontsize=16,color="magenta"];8545 -> 9999[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8544[label="primQuotInt (Neg vuz426) (gcd1 vuz498 (Neg vuz427) (Neg vuz3190 * Neg vuz3170))",fontsize=16,color="burlywood",shape="triangle"];11051[label="vuz498/False",fontsize=10,color="white",style="solid",shape="box"];8544 -> 11051[label="",style="solid", color="burlywood", weight=9];
67.71/34.80	11051 -> 8718[label="",style="solid", color="burlywood", weight=3];
67.71/34.80	11052[label="vuz498/True",fontsize=10,color="white",style="solid",shape="box"];8544 -> 11052[label="",style="solid", color="burlywood", weight=9];
67.71/34.80	11052 -> 8719[label="",style="solid", color="burlywood", weight=3];
67.71/34.80	8546[label="primQuotInt (Neg vuz428) (gcd0Gcd' (abs (Neg vuz429)) (abs (Pos vuz3190 * Neg vuz3170)))",fontsize=16,color="black",shape="box"];8546 -> 8720[label="",style="solid", color="black", weight=3];
67.71/34.80	8548 -> 9987[label="",style="dashed", color="red", weight=0];
67.71/34.80	8548[label="Pos vuz3190 * Neg vuz3170 == fromInt (Pos Zero)",fontsize=16,color="magenta"];8548 -> 10000[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8547[label="primQuotInt (Neg vuz428) (gcd1 vuz499 (Neg vuz429) (Pos vuz3190 * Neg vuz3170))",fontsize=16,color="burlywood",shape="triangle"];11053[label="vuz499/False",fontsize=10,color="white",style="solid",shape="box"];8547 -> 11053[label="",style="solid", color="burlywood", weight=9];
67.71/34.80	11053 -> 8723[label="",style="solid", color="burlywood", weight=3];
67.71/34.80	11054[label="vuz499/True",fontsize=10,color="white",style="solid",shape="box"];8547 -> 11054[label="",style="solid", color="burlywood", weight=9];
67.71/34.80	11054 -> 8724[label="",style="solid", color="burlywood", weight=3];
67.71/34.80	8549[label="vuz4310",fontsize=16,color="green",shape="box"];8550[label="vuz4300",fontsize=16,color="green",shape="box"];8551[label="vuz4300",fontsize=16,color="green",shape="box"];8552[label="vuz4310",fontsize=16,color="green",shape="box"];8553[label="primQuotInt (Pos (Succ vuz4310)) (gcd (Pos (Succ vuz4310)) (Neg (Succ vuz31900) * Neg vuz3170))",fontsize=16,color="black",shape="box"];8553 -> 8725[label="",style="solid", color="black", weight=3];
67.71/34.80	8554[label="primQuotInt (Neg (Succ vuz4300)) (gcd (Neg (Succ vuz4300)) (Neg (Succ vuz31900) * Neg vuz3170))",fontsize=16,color="black",shape="box"];8554 -> 8726[label="",style="solid", color="black", weight=3];
67.71/34.80	8555[label="primQuotInt (Pos Zero) (gcd (Pos Zero) (Neg (Succ vuz31900) * Neg vuz3170))",fontsize=16,color="black",shape="box"];8555 -> 8727[label="",style="solid", color="black", weight=3];
67.71/34.80	8556 -> 7745[label="",style="dashed", color="red", weight=0];
67.71/34.80	8556[label="primQuotInt (Neg (Succ vuz4360)) (gcd3 (Neg (Succ vuz4360)) (Neg Zero * Neg vuz3170))",fontsize=16,color="magenta"];8556 -> 8728[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8556 -> 8729[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8556 -> 8730[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8557 -> 7613[label="",style="dashed", color="red", weight=0];
67.71/34.80	8557[label="primQuotInt (Pos Zero) (gcd3 (Pos Zero) (Neg Zero * Neg vuz3170))",fontsize=16,color="magenta"];8557 -> 8731[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8557 -> 8732[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8557 -> 8733[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8558[label="vuz4390",fontsize=16,color="green",shape="box"];8559[label="vuz4380",fontsize=16,color="green",shape="box"];8560[label="vuz4380",fontsize=16,color="green",shape="box"];8561[label="vuz4390",fontsize=16,color="green",shape="box"];8562[label="primQuotInt (Pos (Succ vuz4390)) (gcd (Pos (Succ vuz4390)) (Pos (Succ vuz31900) * Pos vuz3170))",fontsize=16,color="black",shape="box"];8562 -> 8734[label="",style="solid", color="black", weight=3];
67.71/34.80	8563[label="primQuotInt (Neg (Succ vuz4380)) (gcd (Neg (Succ vuz4380)) (Pos (Succ vuz31900) * Pos vuz3170))",fontsize=16,color="black",shape="box"];8563 -> 8735[label="",style="solid", color="black", weight=3];
67.71/34.80	8564[label="primQuotInt (Pos Zero) (gcd (Pos Zero) (Pos (Succ vuz31900) * Pos vuz3170))",fontsize=16,color="black",shape="box"];8564 -> 8736[label="",style="solid", color="black", weight=3];
67.71/34.80	8565 -> 7587[label="",style="dashed", color="red", weight=0];
67.71/34.80	8565[label="primQuotInt (Neg (Succ vuz4440)) (gcd3 (Neg (Succ vuz4440)) (Pos Zero * Pos vuz3170))",fontsize=16,color="magenta"];8565 -> 8737[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8565 -> 8738[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8565 -> 8739[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8566 -> 7667[label="",style="dashed", color="red", weight=0];
67.71/34.80	8566[label="primQuotInt (Pos Zero) (gcd3 (Pos Zero) (Pos Zero * Pos vuz3170))",fontsize=16,color="magenta"];8566 -> 8740[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8566 -> 8741[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8566 -> 8742[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8567[label="primQuotInt (Neg vuz446) (gcd0Gcd' (abs (Neg vuz447)) (abs (Neg vuz3190 * Pos vuz3170)))",fontsize=16,color="black",shape="box"];8567 -> 8743[label="",style="solid", color="black", weight=3];
67.71/34.80	8569 -> 9987[label="",style="dashed", color="red", weight=0];
67.71/34.80	8569[label="Neg vuz3190 * Pos vuz3170 == fromInt (Pos Zero)",fontsize=16,color="magenta"];8569 -> 10001[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8568[label="primQuotInt (Neg vuz446) (gcd1 vuz500 (Neg vuz447) (Neg vuz3190 * Pos vuz3170))",fontsize=16,color="burlywood",shape="triangle"];11055[label="vuz500/False",fontsize=10,color="white",style="solid",shape="box"];8568 -> 11055[label="",style="solid", color="burlywood", weight=9];
67.71/34.80	11055 -> 8746[label="",style="solid", color="burlywood", weight=3];
67.71/34.80	11056[label="vuz500/True",fontsize=10,color="white",style="solid",shape="box"];8568 -> 11056[label="",style="solid", color="burlywood", weight=9];
67.71/34.80	11056 -> 8747[label="",style="solid", color="burlywood", weight=3];
67.71/34.80	8570[label="primQuotInt (Neg vuz348) (gcd0Gcd' (abs (Neg vuz349)) (abs (Pos vuz3190 * Pos vuz3170)))",fontsize=16,color="black",shape="box"];8570 -> 8748[label="",style="solid", color="black", weight=3];
67.71/34.80	8572 -> 9987[label="",style="dashed", color="red", weight=0];
67.71/34.80	8572[label="Pos vuz3190 * Pos vuz3170 == fromInt (Pos Zero)",fontsize=16,color="magenta"];8572 -> 10002[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8571[label="primQuotInt (Neg vuz348) (gcd1 vuz501 (Neg vuz349) (Pos vuz3190 * Pos vuz3170))",fontsize=16,color="burlywood",shape="triangle"];11057[label="vuz501/False",fontsize=10,color="white",style="solid",shape="box"];8571 -> 11057[label="",style="solid", color="burlywood", weight=9];
67.71/34.80	11057 -> 8751[label="",style="solid", color="burlywood", weight=3];
67.71/34.80	11058[label="vuz501/True",fontsize=10,color="white",style="solid",shape="box"];8571 -> 11058[label="",style="solid", color="burlywood", weight=9];
67.71/34.80	11058 -> 8752[label="",style="solid", color="burlywood", weight=3];
67.71/34.80	8573[label="vuz4490",fontsize=16,color="green",shape="box"];8574[label="vuz4490",fontsize=16,color="green",shape="box"];8575[label="vuz4480",fontsize=16,color="green",shape="box"];8576[label="vuz4480",fontsize=16,color="green",shape="box"];8577[label="primQuotInt (Pos (Succ vuz4490)) (gcd (Pos (Succ vuz4490)) (Neg (Succ vuz31900) * Pos vuz3170))",fontsize=16,color="black",shape="box"];8577 -> 8753[label="",style="solid", color="black", weight=3];
67.71/34.80	8578[label="primQuotInt (Neg (Succ vuz4480)) (gcd (Neg (Succ vuz4480)) (Neg (Succ vuz31900) * Pos vuz3170))",fontsize=16,color="black",shape="box"];8578 -> 8754[label="",style="solid", color="black", weight=3];
67.71/34.80	8579[label="primQuotInt (Pos Zero) (gcd (Pos Zero) (Neg (Succ vuz31900) * Pos vuz3170))",fontsize=16,color="black",shape="box"];8579 -> 8755[label="",style="solid", color="black", weight=3];
67.71/34.80	8580 -> 7809[label="",style="dashed", color="red", weight=0];
67.71/34.80	8580[label="primQuotInt (Neg (Succ vuz4540)) (gcd3 (Neg (Succ vuz4540)) (Neg Zero * Pos vuz3170))",fontsize=16,color="magenta"];8580 -> 8756[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8580 -> 8757[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8580 -> 8758[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8581 -> 7713[label="",style="dashed", color="red", weight=0];
67.71/34.80	8581[label="primQuotInt (Pos Zero) (gcd3 (Pos Zero) (Neg Zero * Pos vuz3170))",fontsize=16,color="magenta"];8581 -> 8759[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8581 -> 8760[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8581 -> 8761[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8582[label="primQuotInt (Pos vuz354) (gcd0Gcd' (abs (Pos vuz355)) (abs (Pos vuz3190 * Neg vuz3170)))",fontsize=16,color="black",shape="box"];8582 -> 8762[label="",style="solid", color="black", weight=3];
67.71/34.80	8584 -> 9987[label="",style="dashed", color="red", weight=0];
67.71/34.80	8584[label="Pos vuz3190 * Neg vuz3170 == fromInt (Pos Zero)",fontsize=16,color="magenta"];8584 -> 10003[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8583[label="primQuotInt (Pos vuz354) (gcd1 vuz502 (Pos vuz355) (Pos vuz3190 * Neg vuz3170))",fontsize=16,color="burlywood",shape="triangle"];11059[label="vuz502/False",fontsize=10,color="white",style="solid",shape="box"];8583 -> 11059[label="",style="solid", color="burlywood", weight=9];
67.71/34.80	11059 -> 8765[label="",style="solid", color="burlywood", weight=3];
67.71/34.80	11060[label="vuz502/True",fontsize=10,color="white",style="solid",shape="box"];8583 -> 11060[label="",style="solid", color="burlywood", weight=9];
67.71/34.80	11060 -> 8766[label="",style="solid", color="burlywood", weight=3];
67.71/34.80	8585[label="vuz4570",fontsize=16,color="green",shape="box"];8586[label="vuz4560",fontsize=16,color="green",shape="box"];8587[label="vuz4560",fontsize=16,color="green",shape="box"];8588[label="vuz4570",fontsize=16,color="green",shape="box"];8589[label="primQuotInt (Pos (Succ vuz4570)) (gcd (Pos (Succ vuz4570)) (Neg vuz3190 * Neg (Succ vuz31700)))",fontsize=16,color="black",shape="box"];8589 -> 8767[label="",style="solid", color="black", weight=3];
67.71/34.80	8590[label="primQuotInt (Neg (Succ vuz4560)) (gcd (Neg (Succ vuz4560)) (Neg vuz3190 * Neg (Succ vuz31700)))",fontsize=16,color="black",shape="box"];8590 -> 8768[label="",style="solid", color="black", weight=3];
67.71/34.80	8591[label="primQuotInt (Pos Zero) (gcd (Pos Zero) (Neg vuz3190 * Neg (Succ vuz31700)))",fontsize=16,color="black",shape="box"];8591 -> 8769[label="",style="solid", color="black", weight=3];
67.71/34.80	8592 -> 7745[label="",style="dashed", color="red", weight=0];
67.71/34.80	8592[label="primQuotInt (Neg (Succ vuz4620)) (gcd3 (Neg (Succ vuz4620)) (Neg vuz3190 * Neg Zero))",fontsize=16,color="magenta"];8592 -> 8770[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8592 -> 8771[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8592 -> 8772[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8593 -> 7613[label="",style="dashed", color="red", weight=0];
67.71/34.80	8593[label="primQuotInt (Pos Zero) (gcd3 (Pos Zero) (Neg vuz3190 * Neg Zero))",fontsize=16,color="magenta"];8593 -> 8773[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8593 -> 8774[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8593 -> 8775[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8594[label="vuz4650",fontsize=16,color="green",shape="box"];8595[label="vuz4640",fontsize=16,color="green",shape="box"];8596[label="vuz4640",fontsize=16,color="green",shape="box"];8597[label="vuz4650",fontsize=16,color="green",shape="box"];8598[label="primQuotInt (Pos (Succ vuz4650)) (gcd (Pos (Succ vuz4650)) (Pos vuz3190 * Neg (Succ vuz31700)))",fontsize=16,color="black",shape="box"];8598 -> 8776[label="",style="solid", color="black", weight=3];
67.71/34.80	8599[label="primQuotInt (Neg (Succ vuz4640)) (gcd (Neg (Succ vuz4640)) (Pos vuz3190 * Neg (Succ vuz31700)))",fontsize=16,color="black",shape="box"];8599 -> 8777[label="",style="solid", color="black", weight=3];
67.71/34.80	8600[label="primQuotInt (Pos Zero) (gcd (Pos Zero) (Pos vuz3190 * Neg (Succ vuz31700)))",fontsize=16,color="black",shape="box"];8600 -> 8778[label="",style="solid", color="black", weight=3];
67.71/34.80	8601 -> 7763[label="",style="dashed", color="red", weight=0];
67.71/34.80	8601[label="primQuotInt (Neg (Succ vuz4700)) (gcd3 (Neg (Succ vuz4700)) (Pos vuz3190 * Neg Zero))",fontsize=16,color="magenta"];8601 -> 8779[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8601 -> 8780[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8601 -> 8781[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8602 -> 7598[label="",style="dashed", color="red", weight=0];
67.71/34.80	8602[label="primQuotInt (Pos Zero) (gcd3 (Pos Zero) (Pos vuz3190 * Neg Zero))",fontsize=16,color="magenta"];8602 -> 8782[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8602 -> 8783[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8602 -> 8784[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8603[label="primQuotInt (Pos vuz360) (gcd0Gcd' (abs (Pos vuz361)) (abs (Neg vuz3190 * Neg vuz3170)))",fontsize=16,color="black",shape="box"];8603 -> 8785[label="",style="solid", color="black", weight=3];
67.71/34.80	8605 -> 9987[label="",style="dashed", color="red", weight=0];
67.71/34.80	8605[label="Neg vuz3190 * Neg vuz3170 == fromInt (Pos Zero)",fontsize=16,color="magenta"];8605 -> 10004[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8604[label="primQuotInt (Pos vuz360) (gcd1 vuz503 (Pos vuz361) (Neg vuz3190 * Neg vuz3170))",fontsize=16,color="burlywood",shape="triangle"];11061[label="vuz503/False",fontsize=10,color="white",style="solid",shape="box"];8604 -> 11061[label="",style="solid", color="burlywood", weight=9];
67.71/34.80	11061 -> 8788[label="",style="solid", color="burlywood", weight=3];
67.71/34.80	11062[label="vuz503/True",fontsize=10,color="white",style="solid",shape="box"];8604 -> 11062[label="",style="solid", color="burlywood", weight=9];
67.71/34.80	11062 -> 8789[label="",style="solid", color="burlywood", weight=3];
67.71/34.80	8606[label="vuz3180",fontsize=16,color="green",shape="box"];8607[label="vuz3190",fontsize=16,color="green",shape="box"];8608[label="vuz3180",fontsize=16,color="green",shape="box"];8609[label="vuz3190",fontsize=16,color="green",shape="box"];8610 -> 8790[label="",style="dashed", color="red", weight=0];
67.71/34.80	8610[label="primQuotInt (Pos vuz366) (gcd2 (primEqInt (Pos (primPlusNat vuz369 vuz481)) (fromInt (Pos Zero))) (Pos (primPlusNat vuz369 vuz481)) (Pos vuz367))",fontsize=16,color="magenta"];8610 -> 8791[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8610 -> 8792[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8611[label="vuz3180",fontsize=16,color="green",shape="box"];8612[label="vuz3190",fontsize=16,color="green",shape="box"];8613[label="vuz3180",fontsize=16,color="green",shape="box"];8614[label="vuz3190",fontsize=16,color="green",shape="box"];8615[label="primQuotInt (Pos vuz366) (gcd2 (primEqInt (primMinusNat vuz369 vuz483) (fromInt (Pos Zero))) (primMinusNat vuz369 vuz483) (Pos vuz367))",fontsize=16,color="burlywood",shape="triangle"];11063[label="vuz369/Succ vuz3690",fontsize=10,color="white",style="solid",shape="box"];8615 -> 11063[label="",style="solid", color="burlywood", weight=9];
67.71/34.80	11063 -> 8793[label="",style="solid", color="burlywood", weight=3];
67.71/34.80	11064[label="vuz369/Zero",fontsize=10,color="white",style="solid",shape="box"];8615 -> 11064[label="",style="solid", color="burlywood", weight=9];
67.71/34.80	11064 -> 8794[label="",style="solid", color="burlywood", weight=3];
67.71/34.80	8616[label="vuz3180",fontsize=16,color="green",shape="box"];8617[label="vuz3190",fontsize=16,color="green",shape="box"];8618[label="vuz3180",fontsize=16,color="green",shape="box"];8619[label="vuz3190",fontsize=16,color="green",shape="box"];8620 -> 8615[label="",style="dashed", color="red", weight=0];
67.71/34.80	8620[label="primQuotInt (Pos vuz370) (gcd2 (primEqInt (primMinusNat vuz485 vuz373) (fromInt (Pos Zero))) (primMinusNat vuz485 vuz373) (Pos vuz371))",fontsize=16,color="magenta"];8620 -> 8795[label="",style="dashed", color="magenta", weight=3];
67.71/34.80	8620 -> 8796[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8620 -> 8797[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8620 -> 8798[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8621[label="vuz3180",fontsize=16,color="green",shape="box"];8622[label="vuz3190",fontsize=16,color="green",shape="box"];8623[label="vuz3180",fontsize=16,color="green",shape="box"];8624[label="vuz3190",fontsize=16,color="green",shape="box"];8625 -> 8799[label="",style="dashed", color="red", weight=0];
67.72/34.80	8625[label="primQuotInt (Pos vuz370) (gcd2 (primEqInt (Neg (primPlusNat vuz373 vuz487)) (fromInt (Pos Zero))) (Neg (primPlusNat vuz373 vuz487)) (Pos vuz371))",fontsize=16,color="magenta"];8625 -> 8800[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8625 -> 8801[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8626[label="vuz3180",fontsize=16,color="green",shape="box"];8627[label="vuz3190",fontsize=16,color="green",shape="box"];8628[label="vuz3180",fontsize=16,color="green",shape="box"];8629[label="vuz3190",fontsize=16,color="green",shape="box"];8630[label="primQuotInt (Neg vuz374) (gcd2 (primEqInt (primMinusNat vuz489 vuz377) (fromInt (Pos Zero))) (primMinusNat vuz489 vuz377) (Neg vuz375))",fontsize=16,color="burlywood",shape="triangle"];11065[label="vuz489/Succ vuz4890",fontsize=10,color="white",style="solid",shape="box"];8630 -> 11065[label="",style="solid", color="burlywood", weight=9];
67.72/34.80	11065 -> 8802[label="",style="solid", color="burlywood", weight=3];
67.72/34.80	11066[label="vuz489/Zero",fontsize=10,color="white",style="solid",shape="box"];8630 -> 11066[label="",style="solid", color="burlywood", weight=9];
67.72/34.80	11066 -> 8803[label="",style="solid", color="burlywood", weight=3];
67.72/34.80	8631[label="vuz3180",fontsize=16,color="green",shape="box"];8632[label="vuz3190",fontsize=16,color="green",shape="box"];8633[label="vuz3180",fontsize=16,color="green",shape="box"];8634[label="vuz3190",fontsize=16,color="green",shape="box"];8635 -> 8804[label="",style="dashed", color="red", weight=0];
67.72/34.80	8635[label="primQuotInt (Neg vuz374) (gcd2 (primEqInt (Neg (primPlusNat vuz377 vuz491)) (fromInt (Pos Zero))) (Neg (primPlusNat vuz377 vuz491)) (Neg vuz375))",fontsize=16,color="magenta"];8635 -> 8805[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8635 -> 8806[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8636[label="vuz3180",fontsize=16,color="green",shape="box"];8637[label="vuz3190",fontsize=16,color="green",shape="box"];8638[label="vuz3180",fontsize=16,color="green",shape="box"];8639[label="vuz3190",fontsize=16,color="green",shape="box"];8640 -> 8807[label="",style="dashed", color="red", weight=0];
67.72/34.80	8640[label="primQuotInt (Neg vuz378) (gcd2 (primEqInt (Pos (primPlusNat vuz381 vuz493)) (fromInt (Pos Zero))) (Pos (primPlusNat vuz381 vuz493)) (Neg vuz379))",fontsize=16,color="magenta"];8640 -> 8808[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8640 -> 8809[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8641[label="vuz3180",fontsize=16,color="green",shape="box"];8642[label="vuz3190",fontsize=16,color="green",shape="box"];8643[label="vuz3180",fontsize=16,color="green",shape="box"];8644[label="vuz3190",fontsize=16,color="green",shape="box"];8645 -> 8630[label="",style="dashed", color="red", weight=0];
67.72/34.80	8645[label="primQuotInt (Neg vuz378) (gcd2 (primEqInt (primMinusNat vuz381 vuz495) (fromInt (Pos Zero))) (primMinusNat vuz381 vuz495) (Neg vuz379))",fontsize=16,color="magenta"];8645 -> 8810[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8645 -> 8811[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8645 -> 8812[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8645 -> 8813[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8646[label="vuz3180",fontsize=16,color="green",shape="box"];8647[label="vuz3190",fontsize=16,color="green",shape="box"];8648[label="vuz3180",fontsize=16,color="green",shape="box"];8649[label="vuz3190",fontsize=16,color="green",shape="box"];8650[label="vuz3180",fontsize=16,color="green",shape="box"];8651[label="vuz3190",fontsize=16,color="green",shape="box"];8652[label="vuz3180",fontsize=16,color="green",shape="box"];8653[label="vuz3190",fontsize=16,color="green",shape="box"];8654[label="vuz3180",fontsize=16,color="green",shape="box"];8655[label="vuz3190",fontsize=16,color="green",shape="box"];8656[label="vuz3180",fontsize=16,color="green",shape="box"];8657[label="vuz3190",fontsize=16,color="green",shape="box"];8658[label="vuz3180",fontsize=16,color="green",shape="box"];8659[label="vuz3190",fontsize=16,color="green",shape="box"];8660[label="vuz3180",fontsize=16,color="green",shape="box"];8661[label="vuz3190",fontsize=16,color="green",shape="box"];8662[label="vuz3180",fontsize=16,color="green",shape="box"];8663[label="vuz3190",fontsize=16,color="green",shape="box"];8664[label="vuz3180",fontsize=16,color="green",shape="box"];8665[label="vuz3190",fontsize=16,color="green",shape="box"];8666[label="vuz3180",fontsize=16,color="green",shape="box"];8667[label="vuz3190",fontsize=16,color="green",shape="box"];8668[label="vuz3180",fontsize=16,color="green",shape="box"];8669[label="vuz3190",fontsize=16,color="green",shape="box"];8670[label="vuz3180",fontsize=16,color="green",shape="box"];8671[label="vuz3190",fontsize=16,color="green",shape="box"];8672[label="vuz3180",fontsize=16,color="green",shape="box"];8673[label="vuz3190",fontsize=16,color="green",shape="box"];8674[label="vuz3180",fontsize=16,color="green",shape="box"];8675[label="vuz3190",fontsize=16,color="green",shape="box"];8676[label="vuz3180",fontsize=16,color="green",shape="box"];8677[label="vuz3190",fontsize=16,color="green",shape="box"];8678[label="primQuotInt (Pos vuz398) (gcd0Gcd'2 (abs (Pos vuz399)) (abs (Pos vuz3190 * Pos vuz3170)))",fontsize=16,color="black",shape="box"];8678 -> 8814[label="",style="solid", color="black", weight=3];
67.72/34.80	9997 -> 9988[label="",style="dashed", color="red", weight=0];
67.72/34.80	9997[label="Pos vuz3190 * Pos vuz3170",fontsize=16,color="magenta"];9997 -> 10017[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	9997 -> 10018[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8681[label="primQuotInt (Pos vuz398) (gcd1 False (Pos vuz399) (Pos vuz3190 * Pos vuz3170))",fontsize=16,color="black",shape="box"];8681 -> 8815[label="",style="solid", color="black", weight=3];
67.72/34.80	8682[label="primQuotInt (Pos vuz398) (gcd1 True (Pos vuz399) (Pos vuz3190 * Pos vuz3170))",fontsize=16,color="black",shape="box"];8682 -> 8816[label="",style="solid", color="black", weight=3];
67.72/34.80	8683 -> 7713[label="",style="dashed", color="red", weight=0];
67.72/34.80	8683[label="primQuotInt (Pos (Succ vuz4010)) (gcd3 (Pos (Succ vuz4010)) (Neg vuz3190 * Pos (Succ vuz31700)))",fontsize=16,color="magenta"];8683 -> 8817[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8683 -> 8818[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8683 -> 8819[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8684 -> 7809[label="",style="dashed", color="red", weight=0];
67.72/34.80	8684[label="primQuotInt (Neg (Succ vuz4000)) (gcd3 (Neg (Succ vuz4000)) (Neg vuz3190 * Pos (Succ vuz31700)))",fontsize=16,color="magenta"];8684 -> 8820[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8684 -> 8821[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8684 -> 8822[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8685 -> 7713[label="",style="dashed", color="red", weight=0];
67.72/34.80	8685[label="primQuotInt (Pos Zero) (gcd3 (Pos Zero) (Neg vuz3190 * Pos (Succ vuz31700)))",fontsize=16,color="magenta"];8685 -> 8823[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8685 -> 8824[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8685 -> 8825[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8686[label="Succ vuz4060",fontsize=16,color="green",shape="box"];8687[label="Zero",fontsize=16,color="green",shape="box"];8688[label="Succ vuz4060",fontsize=16,color="green",shape="box"];8689[label="Zero",fontsize=16,color="green",shape="box"];8690[label="Zero",fontsize=16,color="green",shape="box"];8691[label="Zero",fontsize=16,color="green",shape="box"];8692 -> 7667[label="",style="dashed", color="red", weight=0];
67.72/34.80	8692[label="primQuotInt (Pos (Succ vuz4090)) (gcd3 (Pos (Succ vuz4090)) (Pos vuz3190 * Pos (Succ vuz31700)))",fontsize=16,color="magenta"];8692 -> 8826[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8692 -> 8827[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8692 -> 8828[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8693 -> 7587[label="",style="dashed", color="red", weight=0];
67.72/34.80	8693[label="primQuotInt (Neg (Succ vuz4080)) (gcd3 (Neg (Succ vuz4080)) (Pos vuz3190 * Pos (Succ vuz31700)))",fontsize=16,color="magenta"];8693 -> 8829[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8693 -> 8830[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8693 -> 8831[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8694 -> 7667[label="",style="dashed", color="red", weight=0];
67.72/34.80	8694[label="primQuotInt (Pos Zero) (gcd3 (Pos Zero) (Pos vuz3190 * Pos (Succ vuz31700)))",fontsize=16,color="magenta"];8694 -> 8832[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8694 -> 8833[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8694 -> 8834[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8695[label="Succ vuz4140",fontsize=16,color="green",shape="box"];8696[label="Zero",fontsize=16,color="green",shape="box"];8697[label="Succ vuz4140",fontsize=16,color="green",shape="box"];8698[label="Zero",fontsize=16,color="green",shape="box"];8699[label="Zero",fontsize=16,color="green",shape="box"];8700[label="Zero",fontsize=16,color="green",shape="box"];8701[label="primQuotInt (Pos vuz416) (gcd0Gcd'2 (abs (Pos vuz417)) (abs (Neg vuz3190 * Pos vuz3170)))",fontsize=16,color="black",shape="box"];8701 -> 8835[label="",style="solid", color="black", weight=3];
67.72/34.80	9998 -> 9988[label="",style="dashed", color="red", weight=0];
67.72/34.80	9998[label="Neg vuz3190 * Pos vuz3170",fontsize=16,color="magenta"];9998 -> 10019[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	9998 -> 10020[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8704[label="primQuotInt (Pos vuz416) (gcd1 False (Pos vuz417) (Neg vuz3190 * Pos vuz3170))",fontsize=16,color="black",shape="box"];8704 -> 8836[label="",style="solid", color="black", weight=3];
67.72/34.80	8705[label="primQuotInt (Pos vuz416) (gcd1 True (Pos vuz417) (Neg vuz3190 * Pos vuz3170))",fontsize=16,color="black",shape="box"];8705 -> 8837[label="",style="solid", color="black", weight=3];
67.72/34.80	8706 -> 7598[label="",style="dashed", color="red", weight=0];
67.72/34.80	8706[label="primQuotInt (Pos (Succ vuz4190)) (gcd3 (Pos (Succ vuz4190)) (Pos (Succ vuz31900) * Neg vuz3170))",fontsize=16,color="magenta"];8706 -> 8838[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8706 -> 8839[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8706 -> 8840[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8707 -> 7763[label="",style="dashed", color="red", weight=0];
67.72/34.80	8707[label="primQuotInt (Neg (Succ vuz4180)) (gcd3 (Neg (Succ vuz4180)) (Pos (Succ vuz31900) * Neg vuz3170))",fontsize=16,color="magenta"];8707 -> 8841[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8707 -> 8842[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8707 -> 8843[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8708 -> 7598[label="",style="dashed", color="red", weight=0];
67.72/34.80	8708[label="primQuotInt (Pos Zero) (gcd3 (Pos Zero) (Pos (Succ vuz31900) * Neg vuz3170))",fontsize=16,color="magenta"];8708 -> 8844[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8708 -> 8845[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8708 -> 8846[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8709[label="Succ vuz4240",fontsize=16,color="green",shape="box"];8710[label="Succ vuz4240",fontsize=16,color="green",shape="box"];8711[label="Zero",fontsize=16,color="green",shape="box"];8712[label="Zero",fontsize=16,color="green",shape="box"];8713[label="Zero",fontsize=16,color="green",shape="box"];8714[label="Zero",fontsize=16,color="green",shape="box"];8715[label="primQuotInt (Neg vuz426) (gcd0Gcd'2 (abs (Neg vuz427)) (abs (Neg vuz3190 * Neg vuz3170)))",fontsize=16,color="black",shape="box"];8715 -> 8847[label="",style="solid", color="black", weight=3];
67.72/34.80	9999 -> 9988[label="",style="dashed", color="red", weight=0];
67.72/34.80	9999[label="Neg vuz3190 * Neg vuz3170",fontsize=16,color="magenta"];9999 -> 10021[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	9999 -> 10022[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8718[label="primQuotInt (Neg vuz426) (gcd1 False (Neg vuz427) (Neg vuz3190 * Neg vuz3170))",fontsize=16,color="black",shape="box"];8718 -> 8848[label="",style="solid", color="black", weight=3];
67.72/34.80	8719[label="primQuotInt (Neg vuz426) (gcd1 True (Neg vuz427) (Neg vuz3190 * Neg vuz3170))",fontsize=16,color="black",shape="box"];8719 -> 8849[label="",style="solid", color="black", weight=3];
67.72/34.80	8720[label="primQuotInt (Neg vuz428) (gcd0Gcd'2 (abs (Neg vuz429)) (abs (Pos vuz3190 * Neg vuz3170)))",fontsize=16,color="black",shape="box"];8720 -> 8850[label="",style="solid", color="black", weight=3];
67.72/34.80	10000 -> 9988[label="",style="dashed", color="red", weight=0];
67.72/34.80	10000[label="Pos vuz3190 * Neg vuz3170",fontsize=16,color="magenta"];10000 -> 10023[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	10000 -> 10024[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8723[label="primQuotInt (Neg vuz428) (gcd1 False (Neg vuz429) (Pos vuz3190 * Neg vuz3170))",fontsize=16,color="black",shape="box"];8723 -> 8851[label="",style="solid", color="black", weight=3];
67.72/34.80	8724[label="primQuotInt (Neg vuz428) (gcd1 True (Neg vuz429) (Pos vuz3190 * Neg vuz3170))",fontsize=16,color="black",shape="box"];8724 -> 8852[label="",style="solid", color="black", weight=3];
67.72/34.80	8725 -> 7613[label="",style="dashed", color="red", weight=0];
67.72/34.80	8725[label="primQuotInt (Pos (Succ vuz4310)) (gcd3 (Pos (Succ vuz4310)) (Neg (Succ vuz31900) * Neg vuz3170))",fontsize=16,color="magenta"];8725 -> 8853[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8725 -> 8854[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8725 -> 8855[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8726 -> 7745[label="",style="dashed", color="red", weight=0];
67.72/34.80	8726[label="primQuotInt (Neg (Succ vuz4300)) (gcd3 (Neg (Succ vuz4300)) (Neg (Succ vuz31900) * Neg vuz3170))",fontsize=16,color="magenta"];8726 -> 8856[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8726 -> 8857[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8726 -> 8858[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8727 -> 7613[label="",style="dashed", color="red", weight=0];
67.72/34.80	8727[label="primQuotInt (Pos Zero) (gcd3 (Pos Zero) (Neg (Succ vuz31900) * Neg vuz3170))",fontsize=16,color="magenta"];8727 -> 8859[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8727 -> 8860[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8727 -> 8861[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8728[label="Succ vuz4360",fontsize=16,color="green",shape="box"];8729[label="Zero",fontsize=16,color="green",shape="box"];8730[label="Succ vuz4360",fontsize=16,color="green",shape="box"];8731[label="Zero",fontsize=16,color="green",shape="box"];8732[label="Zero",fontsize=16,color="green",shape="box"];8733[label="Zero",fontsize=16,color="green",shape="box"];8734 -> 7667[label="",style="dashed", color="red", weight=0];
67.72/34.80	8734[label="primQuotInt (Pos (Succ vuz4390)) (gcd3 (Pos (Succ vuz4390)) (Pos (Succ vuz31900) * Pos vuz3170))",fontsize=16,color="magenta"];8734 -> 8862[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8734 -> 8863[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8734 -> 8864[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8735 -> 7587[label="",style="dashed", color="red", weight=0];
67.72/34.80	8735[label="primQuotInt (Neg (Succ vuz4380)) (gcd3 (Neg (Succ vuz4380)) (Pos (Succ vuz31900) * Pos vuz3170))",fontsize=16,color="magenta"];8735 -> 8865[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8735 -> 8866[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8735 -> 8867[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8736 -> 7667[label="",style="dashed", color="red", weight=0];
67.72/34.80	8736[label="primQuotInt (Pos Zero) (gcd3 (Pos Zero) (Pos (Succ vuz31900) * Pos vuz3170))",fontsize=16,color="magenta"];8736 -> 8868[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8736 -> 8869[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8736 -> 8870[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8737[label="Succ vuz4440",fontsize=16,color="green",shape="box"];8738[label="Zero",fontsize=16,color="green",shape="box"];8739[label="Succ vuz4440",fontsize=16,color="green",shape="box"];8740[label="Zero",fontsize=16,color="green",shape="box"];8741[label="Zero",fontsize=16,color="green",shape="box"];8742[label="Zero",fontsize=16,color="green",shape="box"];8743[label="primQuotInt (Neg vuz446) (gcd0Gcd'2 (abs (Neg vuz447)) (abs (Neg vuz3190 * Pos vuz3170)))",fontsize=16,color="black",shape="box"];8743 -> 8871[label="",style="solid", color="black", weight=3];
67.72/34.80	10001 -> 9988[label="",style="dashed", color="red", weight=0];
67.72/34.80	10001[label="Neg vuz3190 * Pos vuz3170",fontsize=16,color="magenta"];10001 -> 10025[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	10001 -> 10026[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8746[label="primQuotInt (Neg vuz446) (gcd1 False (Neg vuz447) (Neg vuz3190 * Pos vuz3170))",fontsize=16,color="black",shape="box"];8746 -> 8872[label="",style="solid", color="black", weight=3];
67.72/34.80	8747[label="primQuotInt (Neg vuz446) (gcd1 True (Neg vuz447) (Neg vuz3190 * Pos vuz3170))",fontsize=16,color="black",shape="box"];8747 -> 8873[label="",style="solid", color="black", weight=3];
67.72/34.80	8748[label="primQuotInt (Neg vuz348) (gcd0Gcd'2 (abs (Neg vuz349)) (abs (Pos vuz3190 * Pos vuz3170)))",fontsize=16,color="black",shape="box"];8748 -> 8874[label="",style="solid", color="black", weight=3];
67.72/34.80	10002 -> 9988[label="",style="dashed", color="red", weight=0];
67.72/34.80	10002[label="Pos vuz3190 * Pos vuz3170",fontsize=16,color="magenta"];10002 -> 10027[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	10002 -> 10028[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8751[label="primQuotInt (Neg vuz348) (gcd1 False (Neg vuz349) (Pos vuz3190 * Pos vuz3170))",fontsize=16,color="black",shape="box"];8751 -> 8875[label="",style="solid", color="black", weight=3];
67.72/34.80	8752[label="primQuotInt (Neg vuz348) (gcd1 True (Neg vuz349) (Pos vuz3190 * Pos vuz3170))",fontsize=16,color="black",shape="box"];8752 -> 8876[label="",style="solid", color="black", weight=3];
67.72/34.80	8753 -> 7713[label="",style="dashed", color="red", weight=0];
67.72/34.80	8753[label="primQuotInt (Pos (Succ vuz4490)) (gcd3 (Pos (Succ vuz4490)) (Neg (Succ vuz31900) * Pos vuz3170))",fontsize=16,color="magenta"];8753 -> 8877[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8753 -> 8878[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8753 -> 8879[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8754 -> 7809[label="",style="dashed", color="red", weight=0];
67.72/34.80	8754[label="primQuotInt (Neg (Succ vuz4480)) (gcd3 (Neg (Succ vuz4480)) (Neg (Succ vuz31900) * Pos vuz3170))",fontsize=16,color="magenta"];8754 -> 8880[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8754 -> 8881[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8754 -> 8882[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8755 -> 7713[label="",style="dashed", color="red", weight=0];
67.72/34.80	8755[label="primQuotInt (Pos Zero) (gcd3 (Pos Zero) (Neg (Succ vuz31900) * Pos vuz3170))",fontsize=16,color="magenta"];8755 -> 8883[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8755 -> 8884[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8755 -> 8885[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8756[label="Succ vuz4540",fontsize=16,color="green",shape="box"];8757[label="Zero",fontsize=16,color="green",shape="box"];8758[label="Succ vuz4540",fontsize=16,color="green",shape="box"];8759[label="Zero",fontsize=16,color="green",shape="box"];8760[label="Zero",fontsize=16,color="green",shape="box"];8761[label="Zero",fontsize=16,color="green",shape="box"];8762[label="primQuotInt (Pos vuz354) (gcd0Gcd'2 (abs (Pos vuz355)) (abs (Pos vuz3190 * Neg vuz3170)))",fontsize=16,color="black",shape="box"];8762 -> 8886[label="",style="solid", color="black", weight=3];
67.72/34.80	10003 -> 9988[label="",style="dashed", color="red", weight=0];
67.72/34.80	10003[label="Pos vuz3190 * Neg vuz3170",fontsize=16,color="magenta"];10003 -> 10029[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	10003 -> 10030[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8765[label="primQuotInt (Pos vuz354) (gcd1 False (Pos vuz355) (Pos vuz3190 * Neg vuz3170))",fontsize=16,color="black",shape="box"];8765 -> 8887[label="",style="solid", color="black", weight=3];
67.72/34.80	8766[label="primQuotInt (Pos vuz354) (gcd1 True (Pos vuz355) (Pos vuz3190 * Neg vuz3170))",fontsize=16,color="black",shape="box"];8766 -> 8888[label="",style="solid", color="black", weight=3];
67.72/34.80	8767 -> 7613[label="",style="dashed", color="red", weight=0];
67.72/34.80	8767[label="primQuotInt (Pos (Succ vuz4570)) (gcd3 (Pos (Succ vuz4570)) (Neg vuz3190 * Neg (Succ vuz31700)))",fontsize=16,color="magenta"];8767 -> 8889[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8767 -> 8890[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8767 -> 8891[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8768 -> 7745[label="",style="dashed", color="red", weight=0];
67.72/34.80	8768[label="primQuotInt (Neg (Succ vuz4560)) (gcd3 (Neg (Succ vuz4560)) (Neg vuz3190 * Neg (Succ vuz31700)))",fontsize=16,color="magenta"];8768 -> 8892[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8768 -> 8893[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8768 -> 8894[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8769 -> 7613[label="",style="dashed", color="red", weight=0];
67.72/34.80	8769[label="primQuotInt (Pos Zero) (gcd3 (Pos Zero) (Neg vuz3190 * Neg (Succ vuz31700)))",fontsize=16,color="magenta"];8769 -> 8895[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8769 -> 8896[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8769 -> 8897[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8770[label="Succ vuz4620",fontsize=16,color="green",shape="box"];8771[label="Zero",fontsize=16,color="green",shape="box"];8772[label="Succ vuz4620",fontsize=16,color="green",shape="box"];8773[label="Zero",fontsize=16,color="green",shape="box"];8774[label="Zero",fontsize=16,color="green",shape="box"];8775[label="Zero",fontsize=16,color="green",shape="box"];8776 -> 7598[label="",style="dashed", color="red", weight=0];
67.72/34.80	8776[label="primQuotInt (Pos (Succ vuz4650)) (gcd3 (Pos (Succ vuz4650)) (Pos vuz3190 * Neg (Succ vuz31700)))",fontsize=16,color="magenta"];8776 -> 8898[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8776 -> 8899[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8776 -> 8900[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8777 -> 7763[label="",style="dashed", color="red", weight=0];
67.72/34.80	8777[label="primQuotInt (Neg (Succ vuz4640)) (gcd3 (Neg (Succ vuz4640)) (Pos vuz3190 * Neg (Succ vuz31700)))",fontsize=16,color="magenta"];8777 -> 8901[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8777 -> 8902[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8777 -> 8903[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8778 -> 7598[label="",style="dashed", color="red", weight=0];
67.72/34.80	8778[label="primQuotInt (Pos Zero) (gcd3 (Pos Zero) (Pos vuz3190 * Neg (Succ vuz31700)))",fontsize=16,color="magenta"];8778 -> 8904[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8778 -> 8905[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8778 -> 8906[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8779[label="Succ vuz4700",fontsize=16,color="green",shape="box"];8780[label="Succ vuz4700",fontsize=16,color="green",shape="box"];8781[label="Zero",fontsize=16,color="green",shape="box"];8782[label="Zero",fontsize=16,color="green",shape="box"];8783[label="Zero",fontsize=16,color="green",shape="box"];8784[label="Zero",fontsize=16,color="green",shape="box"];8785[label="primQuotInt (Pos vuz360) (gcd0Gcd'2 (abs (Pos vuz361)) (abs (Neg vuz3190 * Neg vuz3170)))",fontsize=16,color="black",shape="box"];8785 -> 8907[label="",style="solid", color="black", weight=3];
67.72/34.80	10004 -> 9988[label="",style="dashed", color="red", weight=0];
67.72/34.80	10004[label="Neg vuz3190 * Neg vuz3170",fontsize=16,color="magenta"];10004 -> 10031[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	10004 -> 10032[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8788[label="primQuotInt (Pos vuz360) (gcd1 False (Pos vuz361) (Neg vuz3190 * Neg vuz3170))",fontsize=16,color="black",shape="box"];8788 -> 8908[label="",style="solid", color="black", weight=3];
67.72/34.80	8789[label="primQuotInt (Pos vuz360) (gcd1 True (Pos vuz361) (Neg vuz3190 * Neg vuz3170))",fontsize=16,color="black",shape="box"];8789 -> 8909[label="",style="solid", color="black", weight=3];
67.72/34.80	8791 -> 7571[label="",style="dashed", color="red", weight=0];
67.72/34.80	8791[label="primPlusNat vuz369 vuz481",fontsize=16,color="magenta"];8791 -> 8910[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8791 -> 8911[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8792 -> 7479[label="",style="dashed", color="red", weight=0];
67.72/34.80	8792[label="primEqInt (Pos (primPlusNat vuz369 vuz481)) (fromInt (Pos Zero))",fontsize=16,color="magenta"];8792 -> 8912[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8790[label="primQuotInt (Pos vuz366) (gcd2 vuz504 (Pos vuz505) (Pos vuz367))",fontsize=16,color="burlywood",shape="triangle"];11067[label="vuz504/False",fontsize=10,color="white",style="solid",shape="box"];8790 -> 11067[label="",style="solid", color="burlywood", weight=9];
67.72/34.80	11067 -> 8913[label="",style="solid", color="burlywood", weight=3];
67.72/34.80	11068[label="vuz504/True",fontsize=10,color="white",style="solid",shape="box"];8790 -> 11068[label="",style="solid", color="burlywood", weight=9];
67.72/34.80	11068 -> 8914[label="",style="solid", color="burlywood", weight=3];
67.72/34.80	8793[label="primQuotInt (Pos vuz366) (gcd2 (primEqInt (primMinusNat (Succ vuz3690) vuz483) (fromInt (Pos Zero))) (primMinusNat (Succ vuz3690) vuz483) (Pos vuz367))",fontsize=16,color="burlywood",shape="box"];11069[label="vuz483/Succ vuz4830",fontsize=10,color="white",style="solid",shape="box"];8793 -> 11069[label="",style="solid", color="burlywood", weight=9];
67.72/34.80	11069 -> 8915[label="",style="solid", color="burlywood", weight=3];
67.72/34.80	11070[label="vuz483/Zero",fontsize=10,color="white",style="solid",shape="box"];8793 -> 11070[label="",style="solid", color="burlywood", weight=9];
67.72/34.80	11070 -> 8916[label="",style="solid", color="burlywood", weight=3];
67.72/34.80	8794[label="primQuotInt (Pos vuz366) (gcd2 (primEqInt (primMinusNat Zero vuz483) (fromInt (Pos Zero))) (primMinusNat Zero vuz483) (Pos vuz367))",fontsize=16,color="burlywood",shape="box"];11071[label="vuz483/Succ vuz4830",fontsize=10,color="white",style="solid",shape="box"];8794 -> 11071[label="",style="solid", color="burlywood", weight=9];
67.72/34.80	11071 -> 8917[label="",style="solid", color="burlywood", weight=3];
67.72/34.80	11072[label="vuz483/Zero",fontsize=10,color="white",style="solid",shape="box"];8794 -> 11072[label="",style="solid", color="burlywood", weight=9];
67.72/34.80	11072 -> 8918[label="",style="solid", color="burlywood", weight=3];
67.72/34.80	8795[label="vuz371",fontsize=16,color="green",shape="box"];8796[label="vuz485",fontsize=16,color="green",shape="box"];8797[label="vuz373",fontsize=16,color="green",shape="box"];8798[label="vuz370",fontsize=16,color="green",shape="box"];8800 -> 7498[label="",style="dashed", color="red", weight=0];
67.72/34.80	8800[label="primEqInt (Neg (primPlusNat vuz373 vuz487)) (fromInt (Pos Zero))",fontsize=16,color="magenta"];8800 -> 8919[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8801 -> 7571[label="",style="dashed", color="red", weight=0];
67.72/34.80	8801[label="primPlusNat vuz373 vuz487",fontsize=16,color="magenta"];8801 -> 8920[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8801 -> 8921[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8799[label="primQuotInt (Pos vuz370) (gcd2 vuz507 (Neg vuz508) (Pos vuz371))",fontsize=16,color="burlywood",shape="triangle"];11073[label="vuz507/False",fontsize=10,color="white",style="solid",shape="box"];8799 -> 11073[label="",style="solid", color="burlywood", weight=9];
67.72/34.80	11073 -> 8922[label="",style="solid", color="burlywood", weight=3];
67.72/34.80	11074[label="vuz507/True",fontsize=10,color="white",style="solid",shape="box"];8799 -> 11074[label="",style="solid", color="burlywood", weight=9];
67.72/34.80	11074 -> 8923[label="",style="solid", color="burlywood", weight=3];
67.72/34.80	8802[label="primQuotInt (Neg vuz374) (gcd2 (primEqInt (primMinusNat (Succ vuz4890) vuz377) (fromInt (Pos Zero))) (primMinusNat (Succ vuz4890) vuz377) (Neg vuz375))",fontsize=16,color="burlywood",shape="box"];11075[label="vuz377/Succ vuz3770",fontsize=10,color="white",style="solid",shape="box"];8802 -> 11075[label="",style="solid", color="burlywood", weight=9];
67.72/34.80	11075 -> 8924[label="",style="solid", color="burlywood", weight=3];
67.72/34.80	11076[label="vuz377/Zero",fontsize=10,color="white",style="solid",shape="box"];8802 -> 11076[label="",style="solid", color="burlywood", weight=9];
67.72/34.80	11076 -> 8925[label="",style="solid", color="burlywood", weight=3];
67.72/34.80	8803[label="primQuotInt (Neg vuz374) (gcd2 (primEqInt (primMinusNat Zero vuz377) (fromInt (Pos Zero))) (primMinusNat Zero vuz377) (Neg vuz375))",fontsize=16,color="burlywood",shape="box"];11077[label="vuz377/Succ vuz3770",fontsize=10,color="white",style="solid",shape="box"];8803 -> 11077[label="",style="solid", color="burlywood", weight=9];
67.72/34.80	11077 -> 8926[label="",style="solid", color="burlywood", weight=3];
67.72/34.80	11078[label="vuz377/Zero",fontsize=10,color="white",style="solid",shape="box"];8803 -> 11078[label="",style="solid", color="burlywood", weight=9];
67.72/34.80	11078 -> 8927[label="",style="solid", color="burlywood", weight=3];
67.72/34.80	8805 -> 7498[label="",style="dashed", color="red", weight=0];
67.72/34.80	8805[label="primEqInt (Neg (primPlusNat vuz377 vuz491)) (fromInt (Pos Zero))",fontsize=16,color="magenta"];8805 -> 8928[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8806 -> 7571[label="",style="dashed", color="red", weight=0];
67.72/34.80	8806[label="primPlusNat vuz377 vuz491",fontsize=16,color="magenta"];8806 -> 8929[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8806 -> 8930[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8804[label="primQuotInt (Neg vuz374) (gcd2 vuz510 (Neg vuz511) (Neg vuz375))",fontsize=16,color="burlywood",shape="triangle"];11079[label="vuz510/False",fontsize=10,color="white",style="solid",shape="box"];8804 -> 11079[label="",style="solid", color="burlywood", weight=9];
67.72/34.80	11079 -> 8931[label="",style="solid", color="burlywood", weight=3];
67.72/34.80	11080[label="vuz510/True",fontsize=10,color="white",style="solid",shape="box"];8804 -> 11080[label="",style="solid", color="burlywood", weight=9];
67.72/34.80	11080 -> 8932[label="",style="solid", color="burlywood", weight=3];
67.72/34.80	8808 -> 7479[label="",style="dashed", color="red", weight=0];
67.72/34.80	8808[label="primEqInt (Pos (primPlusNat vuz381 vuz493)) (fromInt (Pos Zero))",fontsize=16,color="magenta"];8808 -> 8933[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8809 -> 7571[label="",style="dashed", color="red", weight=0];
67.72/34.80	8809[label="primPlusNat vuz381 vuz493",fontsize=16,color="magenta"];8809 -> 8934[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8809 -> 8935[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8807[label="primQuotInt (Neg vuz378) (gcd2 vuz513 (Pos vuz514) (Neg vuz379))",fontsize=16,color="burlywood",shape="triangle"];11081[label="vuz513/False",fontsize=10,color="white",style="solid",shape="box"];8807 -> 11081[label="",style="solid", color="burlywood", weight=9];
67.72/34.80	11081 -> 8936[label="",style="solid", color="burlywood", weight=3];
67.72/34.80	11082[label="vuz513/True",fontsize=10,color="white",style="solid",shape="box"];8807 -> 11082[label="",style="solid", color="burlywood", weight=9];
67.72/34.80	11082 -> 8937[label="",style="solid", color="burlywood", weight=3];
67.72/34.80	8810[label="vuz379",fontsize=16,color="green",shape="box"];8811[label="vuz381",fontsize=16,color="green",shape="box"];8812[label="vuz378",fontsize=16,color="green",shape="box"];8813[label="vuz495",fontsize=16,color="green",shape="box"];8814 -> 9854[label="",style="dashed", color="red", weight=0];
67.72/34.80	8814[label="primQuotInt (Pos vuz398) (gcd0Gcd'1 (abs (Pos vuz3190 * Pos vuz3170) == fromInt (Pos Zero)) (abs (Pos vuz399)) (abs (Pos vuz3190 * Pos vuz3170)))",fontsize=16,color="magenta"];8814 -> 9855[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8814 -> 9856[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8814 -> 9857[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8814 -> 9858[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	10017[label="Pos vuz3170",fontsize=16,color="green",shape="box"];10018[label="Pos vuz3190",fontsize=16,color="green",shape="box"];8815 -> 8373[label="",style="dashed", color="red", weight=0];
67.72/34.80	8815[label="primQuotInt (Pos vuz398) (gcd0 (Pos vuz399) (Pos vuz3190 * Pos vuz3170))",fontsize=16,color="magenta"];8816[label="primQuotInt (Pos vuz398) (error [])",fontsize=16,color="black",shape="triangle"];8816 -> 8939[label="",style="solid", color="black", weight=3];
67.72/34.80	8817[label="Succ vuz4010",fontsize=16,color="green",shape="box"];8818[label="Succ vuz31700",fontsize=16,color="green",shape="box"];8819[label="Succ vuz4010",fontsize=16,color="green",shape="box"];8820[label="Succ vuz4000",fontsize=16,color="green",shape="box"];8821[label="Succ vuz31700",fontsize=16,color="green",shape="box"];8822[label="Succ vuz4000",fontsize=16,color="green",shape="box"];8823[label="Zero",fontsize=16,color="green",shape="box"];8824[label="Succ vuz31700",fontsize=16,color="green",shape="box"];8825[label="Zero",fontsize=16,color="green",shape="box"];8826[label="Succ vuz4090",fontsize=16,color="green",shape="box"];8827[label="Succ vuz4090",fontsize=16,color="green",shape="box"];8828[label="Succ vuz31700",fontsize=16,color="green",shape="box"];8829[label="Succ vuz4080",fontsize=16,color="green",shape="box"];8830[label="Succ vuz31700",fontsize=16,color="green",shape="box"];8831[label="Succ vuz4080",fontsize=16,color="green",shape="box"];8832[label="Zero",fontsize=16,color="green",shape="box"];8833[label="Zero",fontsize=16,color="green",shape="box"];8834[label="Succ vuz31700",fontsize=16,color="green",shape="box"];8835 -> 9854[label="",style="dashed", color="red", weight=0];
67.72/34.80	8835[label="primQuotInt (Pos vuz416) (gcd0Gcd'1 (abs (Neg vuz3190 * Pos vuz3170) == fromInt (Pos Zero)) (abs (Pos vuz417)) (abs (Neg vuz3190 * Pos vuz3170)))",fontsize=16,color="magenta"];8835 -> 9859[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8835 -> 9860[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8835 -> 9861[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	10019[label="Pos vuz3170",fontsize=16,color="green",shape="box"];10020[label="Neg vuz3190",fontsize=16,color="green",shape="box"];8836 -> 8387[label="",style="dashed", color="red", weight=0];
67.72/34.80	8836[label="primQuotInt (Pos vuz416) (gcd0 (Pos vuz417) (Neg vuz3190 * Pos vuz3170))",fontsize=16,color="magenta"];8837 -> 8816[label="",style="dashed", color="red", weight=0];
67.72/34.80	8837[label="primQuotInt (Pos vuz416) (error [])",fontsize=16,color="magenta"];8837 -> 8941[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8838[label="Succ vuz4190",fontsize=16,color="green",shape="box"];8839[label="Succ vuz4190",fontsize=16,color="green",shape="box"];8840[label="Succ vuz31900",fontsize=16,color="green",shape="box"];8841[label="Succ vuz4180",fontsize=16,color="green",shape="box"];8842[label="Succ vuz4180",fontsize=16,color="green",shape="box"];8843[label="Succ vuz31900",fontsize=16,color="green",shape="box"];8844[label="Zero",fontsize=16,color="green",shape="box"];8845[label="Zero",fontsize=16,color="green",shape="box"];8846[label="Succ vuz31900",fontsize=16,color="green",shape="box"];8847 -> 10039[label="",style="dashed", color="red", weight=0];
67.72/34.80	8847[label="primQuotInt (Neg vuz426) (gcd0Gcd'1 (abs (Neg vuz3190 * Neg vuz3170) == fromInt (Pos Zero)) (abs (Neg vuz427)) (abs (Neg vuz3190 * Neg vuz3170)))",fontsize=16,color="magenta"];8847 -> 10040[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8847 -> 10041[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8847 -> 10042[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8847 -> 10043[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	10021[label="Neg vuz3170",fontsize=16,color="green",shape="box"];10022[label="Neg vuz3190",fontsize=16,color="green",shape="box"];8848 -> 8396[label="",style="dashed", color="red", weight=0];
67.72/34.80	8848[label="primQuotInt (Neg vuz426) (gcd0 (Neg vuz427) (Neg vuz3190 * Neg vuz3170))",fontsize=16,color="magenta"];8849[label="primQuotInt (Neg vuz426) (error [])",fontsize=16,color="black",shape="triangle"];8849 -> 8943[label="",style="solid", color="black", weight=3];
67.72/34.80	8850 -> 10039[label="",style="dashed", color="red", weight=0];
67.72/34.80	8850[label="primQuotInt (Neg vuz428) (gcd0Gcd'1 (abs (Pos vuz3190 * Neg vuz3170) == fromInt (Pos Zero)) (abs (Neg vuz429)) (abs (Pos vuz3190 * Neg vuz3170)))",fontsize=16,color="magenta"];8850 -> 10044[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8850 -> 10045[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8850 -> 10046[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	10023[label="Neg vuz3170",fontsize=16,color="green",shape="box"];10024[label="Pos vuz3190",fontsize=16,color="green",shape="box"];8851 -> 8398[label="",style="dashed", color="red", weight=0];
67.72/34.80	8851[label="primQuotInt (Neg vuz428) (gcd0 (Neg vuz429) (Pos vuz3190 * Neg vuz3170))",fontsize=16,color="magenta"];8852 -> 8849[label="",style="dashed", color="red", weight=0];
67.72/34.80	8852[label="primQuotInt (Neg vuz428) (error [])",fontsize=16,color="magenta"];8852 -> 8945[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8853[label="Succ vuz4310",fontsize=16,color="green",shape="box"];8854[label="Succ vuz31900",fontsize=16,color="green",shape="box"];8855[label="Succ vuz4310",fontsize=16,color="green",shape="box"];8856[label="Succ vuz4300",fontsize=16,color="green",shape="box"];8857[label="Succ vuz31900",fontsize=16,color="green",shape="box"];8858[label="Succ vuz4300",fontsize=16,color="green",shape="box"];8859[label="Zero",fontsize=16,color="green",shape="box"];8860[label="Succ vuz31900",fontsize=16,color="green",shape="box"];8861[label="Zero",fontsize=16,color="green",shape="box"];8862[label="Succ vuz4390",fontsize=16,color="green",shape="box"];8863[label="Succ vuz4390",fontsize=16,color="green",shape="box"];8864[label="Succ vuz31900",fontsize=16,color="green",shape="box"];8865[label="Succ vuz4380",fontsize=16,color="green",shape="box"];8866[label="Succ vuz31900",fontsize=16,color="green",shape="box"];8867[label="Succ vuz4380",fontsize=16,color="green",shape="box"];8868[label="Zero",fontsize=16,color="green",shape="box"];8869[label="Zero",fontsize=16,color="green",shape="box"];8870[label="Succ vuz31900",fontsize=16,color="green",shape="box"];8871 -> 10039[label="",style="dashed", color="red", weight=0];
67.72/34.80	8871[label="primQuotInt (Neg vuz446) (gcd0Gcd'1 (abs (Neg vuz3190 * Pos vuz3170) == fromInt (Pos Zero)) (abs (Neg vuz447)) (abs (Neg vuz3190 * Pos vuz3170)))",fontsize=16,color="magenta"];8871 -> 10047[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8871 -> 10048[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8871 -> 10049[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8871 -> 10050[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	10025[label="Pos vuz3170",fontsize=16,color="green",shape="box"];10026[label="Neg vuz3190",fontsize=16,color="green",shape="box"];8872 -> 8412[label="",style="dashed", color="red", weight=0];
67.72/34.80	8872[label="primQuotInt (Neg vuz446) (gcd0 (Neg vuz447) (Neg vuz3190 * Pos vuz3170))",fontsize=16,color="magenta"];8873 -> 8849[label="",style="dashed", color="red", weight=0];
67.72/34.80	8873[label="primQuotInt (Neg vuz446) (error [])",fontsize=16,color="magenta"];8873 -> 8947[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8874 -> 10039[label="",style="dashed", color="red", weight=0];
67.72/34.80	8874[label="primQuotInt (Neg vuz348) (gcd0Gcd'1 (abs (Pos vuz3190 * Pos vuz3170) == fromInt (Pos Zero)) (abs (Neg vuz349)) (abs (Pos vuz3190 * Pos vuz3170)))",fontsize=16,color="magenta"];8874 -> 10051[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8874 -> 10052[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8874 -> 10053[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8874 -> 10054[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	10027[label="Pos vuz3170",fontsize=16,color="green",shape="box"];10028[label="Pos vuz3190",fontsize=16,color="green",shape="box"];8875 -> 8414[label="",style="dashed", color="red", weight=0];
67.72/34.80	8875[label="primQuotInt (Neg vuz348) (gcd0 (Neg vuz349) (Pos vuz3190 * Pos vuz3170))",fontsize=16,color="magenta"];8876 -> 8849[label="",style="dashed", color="red", weight=0];
67.72/34.80	8876[label="primQuotInt (Neg vuz348) (error [])",fontsize=16,color="magenta"];8876 -> 8949[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8877[label="Succ vuz31900",fontsize=16,color="green",shape="box"];8878[label="Succ vuz4490",fontsize=16,color="green",shape="box"];8879[label="Succ vuz4490",fontsize=16,color="green",shape="box"];8880[label="Succ vuz4480",fontsize=16,color="green",shape="box"];8881[label="Succ vuz31900",fontsize=16,color="green",shape="box"];8882[label="Succ vuz4480",fontsize=16,color="green",shape="box"];8883[label="Succ vuz31900",fontsize=16,color="green",shape="box"];8884[label="Zero",fontsize=16,color="green",shape="box"];8885[label="Zero",fontsize=16,color="green",shape="box"];8886 -> 9854[label="",style="dashed", color="red", weight=0];
67.72/34.80	8886[label="primQuotInt (Pos vuz354) (gcd0Gcd'1 (abs (Pos vuz3190 * Neg vuz3170) == fromInt (Pos Zero)) (abs (Pos vuz355)) (abs (Pos vuz3190 * Neg vuz3170)))",fontsize=16,color="magenta"];8886 -> 9862[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8886 -> 9863[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8886 -> 9864[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8886 -> 9865[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	10029[label="Neg vuz3170",fontsize=16,color="green",shape="box"];10030[label="Pos vuz3190",fontsize=16,color="green",shape="box"];8887 -> 8422[label="",style="dashed", color="red", weight=0];
67.72/34.80	8887[label="primQuotInt (Pos vuz354) (gcd0 (Pos vuz355) (Pos vuz3190 * Neg vuz3170))",fontsize=16,color="magenta"];8888 -> 8816[label="",style="dashed", color="red", weight=0];
67.72/34.80	8888[label="primQuotInt (Pos vuz354) (error [])",fontsize=16,color="magenta"];8888 -> 8951[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8889[label="Succ vuz4570",fontsize=16,color="green",shape="box"];8890[label="Succ vuz4570",fontsize=16,color="green",shape="box"];8891[label="Succ vuz31700",fontsize=16,color="green",shape="box"];8892[label="Succ vuz4560",fontsize=16,color="green",shape="box"];8893[label="Succ vuz31700",fontsize=16,color="green",shape="box"];8894[label="Succ vuz4560",fontsize=16,color="green",shape="box"];8895[label="Zero",fontsize=16,color="green",shape="box"];8896[label="Zero",fontsize=16,color="green",shape="box"];8897[label="Succ vuz31700",fontsize=16,color="green",shape="box"];8898[label="Succ vuz4650",fontsize=16,color="green",shape="box"];8899[label="Succ vuz4650",fontsize=16,color="green",shape="box"];8900[label="Succ vuz31700",fontsize=16,color="green",shape="box"];8901[label="Succ vuz4640",fontsize=16,color="green",shape="box"];8902[label="Succ vuz4640",fontsize=16,color="green",shape="box"];8903[label="Succ vuz31700",fontsize=16,color="green",shape="box"];8904[label="Zero",fontsize=16,color="green",shape="box"];8905[label="Zero",fontsize=16,color="green",shape="box"];8906[label="Succ vuz31700",fontsize=16,color="green",shape="box"];8907 -> 9854[label="",style="dashed", color="red", weight=0];
67.72/34.80	8907[label="primQuotInt (Pos vuz360) (gcd0Gcd'1 (abs (Neg vuz3190 * Neg vuz3170) == fromInt (Pos Zero)) (abs (Pos vuz361)) (abs (Neg vuz3190 * Neg vuz3170)))",fontsize=16,color="magenta"];8907 -> 9866[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8907 -> 9867[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8907 -> 9868[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8907 -> 9869[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	10031[label="Neg vuz3170",fontsize=16,color="green",shape="box"];10032[label="Neg vuz3190",fontsize=16,color="green",shape="box"];8908 -> 8436[label="",style="dashed", color="red", weight=0];
67.72/34.80	8908[label="primQuotInt (Pos vuz360) (gcd0 (Pos vuz361) (Neg vuz3190 * Neg vuz3170))",fontsize=16,color="magenta"];8909 -> 8816[label="",style="dashed", color="red", weight=0];
67.72/34.80	8909[label="primQuotInt (Pos vuz360) (error [])",fontsize=16,color="magenta"];8909 -> 8953[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8910[label="vuz369",fontsize=16,color="green",shape="box"];8911[label="vuz481",fontsize=16,color="green",shape="box"];8912 -> 7571[label="",style="dashed", color="red", weight=0];
67.72/34.80	8912[label="primPlusNat vuz369 vuz481",fontsize=16,color="magenta"];8912 -> 8954[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8912 -> 8955[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	7479[label="primEqInt (Pos vuz325) (fromInt (Pos Zero))",fontsize=16,color="burlywood",shape="triangle"];11083[label="vuz325/Succ vuz3250",fontsize=10,color="white",style="solid",shape="box"];7479 -> 11083[label="",style="solid", color="burlywood", weight=9];
67.72/34.80	11083 -> 7494[label="",style="solid", color="burlywood", weight=3];
67.72/34.80	11084[label="vuz325/Zero",fontsize=10,color="white",style="solid",shape="box"];7479 -> 11084[label="",style="solid", color="burlywood", weight=9];
67.72/34.80	11084 -> 7495[label="",style="solid", color="burlywood", weight=3];
67.72/34.80	8913[label="primQuotInt (Pos vuz366) (gcd2 False (Pos vuz505) (Pos vuz367))",fontsize=16,color="black",shape="box"];8913 -> 8956[label="",style="solid", color="black", weight=3];
67.72/34.80	8914[label="primQuotInt (Pos vuz366) (gcd2 True (Pos vuz505) (Pos vuz367))",fontsize=16,color="black",shape="box"];8914 -> 8957[label="",style="solid", color="black", weight=3];
67.72/34.80	8915[label="primQuotInt (Pos vuz366) (gcd2 (primEqInt (primMinusNat (Succ vuz3690) (Succ vuz4830)) (fromInt (Pos Zero))) (primMinusNat (Succ vuz3690) (Succ vuz4830)) (Pos vuz367))",fontsize=16,color="black",shape="box"];8915 -> 8958[label="",style="solid", color="black", weight=3];
67.72/34.80	8916[label="primQuotInt (Pos vuz366) (gcd2 (primEqInt (primMinusNat (Succ vuz3690) Zero) (fromInt (Pos Zero))) (primMinusNat (Succ vuz3690) Zero) (Pos vuz367))",fontsize=16,color="black",shape="box"];8916 -> 8959[label="",style="solid", color="black", weight=3];
67.72/34.80	8917[label="primQuotInt (Pos vuz366) (gcd2 (primEqInt (primMinusNat Zero (Succ vuz4830)) (fromInt (Pos Zero))) (primMinusNat Zero (Succ vuz4830)) (Pos vuz367))",fontsize=16,color="black",shape="box"];8917 -> 8960[label="",style="solid", color="black", weight=3];
67.72/34.80	8918[label="primQuotInt (Pos vuz366) (gcd2 (primEqInt (primMinusNat Zero Zero) (fromInt (Pos Zero))) (primMinusNat Zero Zero) (Pos vuz367))",fontsize=16,color="black",shape="box"];8918 -> 8961[label="",style="solid", color="black", weight=3];
67.72/34.80	8919 -> 7571[label="",style="dashed", color="red", weight=0];
67.72/34.80	8919[label="primPlusNat vuz373 vuz487",fontsize=16,color="magenta"];8919 -> 8962[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8919 -> 8963[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	7498[label="primEqInt (Neg vuz326) (fromInt (Pos Zero))",fontsize=16,color="burlywood",shape="triangle"];11085[label="vuz326/Succ vuz3260",fontsize=10,color="white",style="solid",shape="box"];7498 -> 11085[label="",style="solid", color="burlywood", weight=9];
67.72/34.80	11085 -> 7512[label="",style="solid", color="burlywood", weight=3];
67.72/34.80	11086[label="vuz326/Zero",fontsize=10,color="white",style="solid",shape="box"];7498 -> 11086[label="",style="solid", color="burlywood", weight=9];
67.72/34.80	11086 -> 7513[label="",style="solid", color="burlywood", weight=3];
67.72/34.80	8920[label="vuz373",fontsize=16,color="green",shape="box"];8921[label="vuz487",fontsize=16,color="green",shape="box"];8922[label="primQuotInt (Pos vuz370) (gcd2 False (Neg vuz508) (Pos vuz371))",fontsize=16,color="black",shape="box"];8922 -> 8964[label="",style="solid", color="black", weight=3];
67.72/34.80	8923[label="primQuotInt (Pos vuz370) (gcd2 True (Neg vuz508) (Pos vuz371))",fontsize=16,color="black",shape="box"];8923 -> 8965[label="",style="solid", color="black", weight=3];
67.72/34.80	8924[label="primQuotInt (Neg vuz374) (gcd2 (primEqInt (primMinusNat (Succ vuz4890) (Succ vuz3770)) (fromInt (Pos Zero))) (primMinusNat (Succ vuz4890) (Succ vuz3770)) (Neg vuz375))",fontsize=16,color="black",shape="box"];8924 -> 8966[label="",style="solid", color="black", weight=3];
67.72/34.80	8925[label="primQuotInt (Neg vuz374) (gcd2 (primEqInt (primMinusNat (Succ vuz4890) Zero) (fromInt (Pos Zero))) (primMinusNat (Succ vuz4890) Zero) (Neg vuz375))",fontsize=16,color="black",shape="box"];8925 -> 8967[label="",style="solid", color="black", weight=3];
67.72/34.80	8926[label="primQuotInt (Neg vuz374) (gcd2 (primEqInt (primMinusNat Zero (Succ vuz3770)) (fromInt (Pos Zero))) (primMinusNat Zero (Succ vuz3770)) (Neg vuz375))",fontsize=16,color="black",shape="box"];8926 -> 8968[label="",style="solid", color="black", weight=3];
67.72/34.80	8927[label="primQuotInt (Neg vuz374) (gcd2 (primEqInt (primMinusNat Zero Zero) (fromInt (Pos Zero))) (primMinusNat Zero Zero) (Neg vuz375))",fontsize=16,color="black",shape="box"];8927 -> 8969[label="",style="solid", color="black", weight=3];
67.72/34.80	8928 -> 7571[label="",style="dashed", color="red", weight=0];
67.72/34.80	8928[label="primPlusNat vuz377 vuz491",fontsize=16,color="magenta"];8928 -> 8970[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8928 -> 8971[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8929[label="vuz377",fontsize=16,color="green",shape="box"];8930[label="vuz491",fontsize=16,color="green",shape="box"];8931[label="primQuotInt (Neg vuz374) (gcd2 False (Neg vuz511) (Neg vuz375))",fontsize=16,color="black",shape="box"];8931 -> 8972[label="",style="solid", color="black", weight=3];
67.72/34.80	8932[label="primQuotInt (Neg vuz374) (gcd2 True (Neg vuz511) (Neg vuz375))",fontsize=16,color="black",shape="box"];8932 -> 8973[label="",style="solid", color="black", weight=3];
67.72/34.80	8933 -> 7571[label="",style="dashed", color="red", weight=0];
67.72/34.80	8933[label="primPlusNat vuz381 vuz493",fontsize=16,color="magenta"];8933 -> 8974[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8933 -> 8975[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8934[label="vuz381",fontsize=16,color="green",shape="box"];8935[label="vuz493",fontsize=16,color="green",shape="box"];8936[label="primQuotInt (Neg vuz378) (gcd2 False (Pos vuz514) (Neg vuz379))",fontsize=16,color="black",shape="box"];8936 -> 8976[label="",style="solid", color="black", weight=3];
67.72/34.80	8937[label="primQuotInt (Neg vuz378) (gcd2 True (Pos vuz514) (Neg vuz379))",fontsize=16,color="black",shape="box"];8937 -> 8977[label="",style="solid", color="black", weight=3];
67.72/34.80	9855 -> 9987[label="",style="dashed", color="red", weight=0];
67.72/34.80	9855[label="abs (Pos vuz3190 * Pos vuz3170) == fromInt (Pos Zero)",fontsize=16,color="magenta"];9855 -> 10005[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	9856[label="vuz398",fontsize=16,color="green",shape="box"];9857[label="abs (Pos vuz399)",fontsize=16,color="black",shape="triangle"];9857 -> 10033[label="",style="solid", color="black", weight=3];
67.72/34.80	9858 -> 9366[label="",style="dashed", color="red", weight=0];
67.72/34.80	9858[label="abs (Pos vuz3190 * Pos vuz3170)",fontsize=16,color="magenta"];9854[label="primQuotInt (Pos vuz416) (gcd0Gcd'1 vuz550 vuz549 vuz542)",fontsize=16,color="burlywood",shape="triangle"];11087[label="vuz550/False",fontsize=10,color="white",style="solid",shape="box"];9854 -> 11087[label="",style="solid", color="burlywood", weight=9];
67.72/34.80	11087 -> 10034[label="",style="solid", color="burlywood", weight=3];
67.72/34.80	11088[label="vuz550/True",fontsize=10,color="white",style="solid",shape="box"];9854 -> 11088[label="",style="solid", color="burlywood", weight=9];
67.72/34.80	11088 -> 10035[label="",style="solid", color="burlywood", weight=3];
67.72/34.80	8939[label="error []",fontsize=16,color="red",shape="box"];9859 -> 9987[label="",style="dashed", color="red", weight=0];
67.72/34.80	9859[label="abs (Neg vuz3190 * Pos vuz3170) == fromInt (Pos Zero)",fontsize=16,color="magenta"];9859 -> 10006[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	9860 -> 9857[label="",style="dashed", color="red", weight=0];
67.72/34.80	9860[label="abs (Pos vuz417)",fontsize=16,color="magenta"];9860 -> 10036[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	9861 -> 9369[label="",style="dashed", color="red", weight=0];
67.72/34.80	9861[label="abs (Neg vuz3190 * Pos vuz3170)",fontsize=16,color="magenta"];8941[label="vuz416",fontsize=16,color="green",shape="box"];10040[label="vuz426",fontsize=16,color="green",shape="box"];10041 -> 9376[label="",style="dashed", color="red", weight=0];
67.72/34.80	10041[label="abs (Neg vuz3190 * Neg vuz3170)",fontsize=16,color="magenta"];10042[label="abs (Neg vuz427)",fontsize=16,color="black",shape="triangle"];10042 -> 10172[label="",style="solid", color="black", weight=3];
67.72/34.80	10043 -> 9987[label="",style="dashed", color="red", weight=0];
67.72/34.80	10043[label="abs (Neg vuz3190 * Neg vuz3170) == fromInt (Pos Zero)",fontsize=16,color="magenta"];10043 -> 10173[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	10039[label="primQuotInt (Neg vuz428) (gcd0Gcd'1 vuz553 vuz552 vuz544)",fontsize=16,color="burlywood",shape="triangle"];11089[label="vuz553/False",fontsize=10,color="white",style="solid",shape="box"];10039 -> 11089[label="",style="solid", color="burlywood", weight=9];
67.72/34.80	11089 -> 10174[label="",style="solid", color="burlywood", weight=3];
67.72/34.80	11090[label="vuz553/True",fontsize=10,color="white",style="solid",shape="box"];10039 -> 11090[label="",style="solid", color="burlywood", weight=9];
67.72/34.80	11090 -> 10175[label="",style="solid", color="burlywood", weight=3];
67.72/34.80	8943[label="error []",fontsize=16,color="red",shape="box"];10044 -> 9372[label="",style="dashed", color="red", weight=0];
67.72/34.80	10044[label="abs (Pos vuz3190 * Neg vuz3170)",fontsize=16,color="magenta"];10045 -> 10042[label="",style="dashed", color="red", weight=0];
67.72/34.80	10045[label="abs (Neg vuz429)",fontsize=16,color="magenta"];10045 -> 10176[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	10046 -> 9987[label="",style="dashed", color="red", weight=0];
67.72/34.80	10046[label="abs (Pos vuz3190 * Neg vuz3170) == fromInt (Pos Zero)",fontsize=16,color="magenta"];10046 -> 10177[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8945[label="vuz428",fontsize=16,color="green",shape="box"];10047[label="vuz446",fontsize=16,color="green",shape="box"];10048 -> 9369[label="",style="dashed", color="red", weight=0];
67.72/34.80	10048[label="abs (Neg vuz3190 * Pos vuz3170)",fontsize=16,color="magenta"];10049 -> 10042[label="",style="dashed", color="red", weight=0];
67.72/34.80	10049[label="abs (Neg vuz447)",fontsize=16,color="magenta"];10049 -> 10178[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	10050 -> 9987[label="",style="dashed", color="red", weight=0];
67.72/34.80	10050[label="abs (Neg vuz3190 * Pos vuz3170) == fromInt (Pos Zero)",fontsize=16,color="magenta"];10050 -> 10179[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8947[label="vuz446",fontsize=16,color="green",shape="box"];10051[label="vuz348",fontsize=16,color="green",shape="box"];10052 -> 9366[label="",style="dashed", color="red", weight=0];
67.72/34.80	10052[label="abs (Pos vuz3190 * Pos vuz3170)",fontsize=16,color="magenta"];10053 -> 10042[label="",style="dashed", color="red", weight=0];
67.72/34.80	10053[label="abs (Neg vuz349)",fontsize=16,color="magenta"];10053 -> 10180[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	10054 -> 9987[label="",style="dashed", color="red", weight=0];
67.72/34.80	10054[label="abs (Pos vuz3190 * Pos vuz3170) == fromInt (Pos Zero)",fontsize=16,color="magenta"];10054 -> 10181[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8949[label="vuz348",fontsize=16,color="green",shape="box"];9862 -> 9987[label="",style="dashed", color="red", weight=0];
67.72/34.80	9862[label="abs (Pos vuz3190 * Neg vuz3170) == fromInt (Pos Zero)",fontsize=16,color="magenta"];9862 -> 10007[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	9863[label="vuz354",fontsize=16,color="green",shape="box"];9864 -> 9857[label="",style="dashed", color="red", weight=0];
67.72/34.80	9864[label="abs (Pos vuz355)",fontsize=16,color="magenta"];9864 -> 10037[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	9865 -> 9372[label="",style="dashed", color="red", weight=0];
67.72/34.80	9865[label="abs (Pos vuz3190 * Neg vuz3170)",fontsize=16,color="magenta"];8951[label="vuz354",fontsize=16,color="green",shape="box"];9866 -> 9987[label="",style="dashed", color="red", weight=0];
67.72/34.80	9866[label="abs (Neg vuz3190 * Neg vuz3170) == fromInt (Pos Zero)",fontsize=16,color="magenta"];9866 -> 10008[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	9867[label="vuz360",fontsize=16,color="green",shape="box"];9868 -> 9857[label="",style="dashed", color="red", weight=0];
67.72/34.80	9868[label="abs (Pos vuz361)",fontsize=16,color="magenta"];9868 -> 10038[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	9869 -> 9376[label="",style="dashed", color="red", weight=0];
67.72/34.80	9869[label="abs (Neg vuz3190 * Neg vuz3170)",fontsize=16,color="magenta"];8953[label="vuz360",fontsize=16,color="green",shape="box"];8954[label="vuz369",fontsize=16,color="green",shape="box"];8955[label="vuz481",fontsize=16,color="green",shape="box"];7494[label="primEqInt (Pos (Succ vuz3250)) (fromInt (Pos Zero))",fontsize=16,color="black",shape="box"];7494 -> 7519[label="",style="solid", color="black", weight=3];
67.72/34.80	7495[label="primEqInt (Pos Zero) (fromInt (Pos Zero))",fontsize=16,color="black",shape="box"];7495 -> 7520[label="",style="solid", color="black", weight=3];
67.72/34.80	8956[label="primQuotInt (Pos vuz366) (gcd0 (Pos vuz505) (Pos vuz367))",fontsize=16,color="black",shape="triangle"];8956 -> 8986[label="",style="solid", color="black", weight=3];
67.72/34.80	8957 -> 8987[label="",style="dashed", color="red", weight=0];
67.72/34.80	8957[label="primQuotInt (Pos vuz366) (gcd1 (Pos vuz367 == fromInt (Pos Zero)) (Pos vuz505) (Pos vuz367))",fontsize=16,color="magenta"];8957 -> 8988[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8958 -> 8615[label="",style="dashed", color="red", weight=0];
67.72/34.80	8958[label="primQuotInt (Pos vuz366) (gcd2 (primEqInt (primMinusNat vuz3690 vuz4830) (fromInt (Pos Zero))) (primMinusNat vuz3690 vuz4830) (Pos vuz367))",fontsize=16,color="magenta"];8958 -> 8989[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8958 -> 8990[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8959 -> 8790[label="",style="dashed", color="red", weight=0];
67.72/34.80	8959[label="primQuotInt (Pos vuz366) (gcd2 (primEqInt (Pos (Succ vuz3690)) (fromInt (Pos Zero))) (Pos (Succ vuz3690)) (Pos vuz367))",fontsize=16,color="magenta"];8959 -> 8991[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8959 -> 8992[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8960 -> 8799[label="",style="dashed", color="red", weight=0];
67.72/34.80	8960[label="primQuotInt (Pos vuz366) (gcd2 (primEqInt (Neg (Succ vuz4830)) (fromInt (Pos Zero))) (Neg (Succ vuz4830)) (Pos vuz367))",fontsize=16,color="magenta"];8960 -> 8993[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8960 -> 8994[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8960 -> 8995[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8960 -> 8996[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8961 -> 8790[label="",style="dashed", color="red", weight=0];
67.72/34.80	8961[label="primQuotInt (Pos vuz366) (gcd2 (primEqInt (Pos Zero) (fromInt (Pos Zero))) (Pos Zero) (Pos vuz367))",fontsize=16,color="magenta"];8961 -> 8997[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8961 -> 8998[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8962[label="vuz373",fontsize=16,color="green",shape="box"];8963[label="vuz487",fontsize=16,color="green",shape="box"];7512[label="primEqInt (Neg (Succ vuz3260)) (fromInt (Pos Zero))",fontsize=16,color="black",shape="box"];7512 -> 7526[label="",style="solid", color="black", weight=3];
67.72/34.80	7513[label="primEqInt (Neg Zero) (fromInt (Pos Zero))",fontsize=16,color="black",shape="box"];7513 -> 7527[label="",style="solid", color="black", weight=3];
67.72/34.80	8964[label="primQuotInt (Pos vuz370) (gcd0 (Neg vuz508) (Pos vuz371))",fontsize=16,color="black",shape="triangle"];8964 -> 8999[label="",style="solid", color="black", weight=3];
67.72/34.80	8965 -> 9000[label="",style="dashed", color="red", weight=0];
67.72/34.80	8965[label="primQuotInt (Pos vuz370) (gcd1 (Pos vuz371 == fromInt (Pos Zero)) (Neg vuz508) (Pos vuz371))",fontsize=16,color="magenta"];8965 -> 9001[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8966 -> 8630[label="",style="dashed", color="red", weight=0];
67.72/34.80	8966[label="primQuotInt (Neg vuz374) (gcd2 (primEqInt (primMinusNat vuz4890 vuz3770) (fromInt (Pos Zero))) (primMinusNat vuz4890 vuz3770) (Neg vuz375))",fontsize=16,color="magenta"];8966 -> 9002[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8966 -> 9003[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8967 -> 8807[label="",style="dashed", color="red", weight=0];
67.72/34.80	8967[label="primQuotInt (Neg vuz374) (gcd2 (primEqInt (Pos (Succ vuz4890)) (fromInt (Pos Zero))) (Pos (Succ vuz4890)) (Neg vuz375))",fontsize=16,color="magenta"];8967 -> 9004[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8967 -> 9005[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8967 -> 9006[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8967 -> 9007[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8968 -> 8804[label="",style="dashed", color="red", weight=0];
67.72/34.80	8968[label="primQuotInt (Neg vuz374) (gcd2 (primEqInt (Neg (Succ vuz3770)) (fromInt (Pos Zero))) (Neg (Succ vuz3770)) (Neg vuz375))",fontsize=16,color="magenta"];8968 -> 9008[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8968 -> 9009[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8969 -> 8807[label="",style="dashed", color="red", weight=0];
67.72/34.80	8969[label="primQuotInt (Neg vuz374) (gcd2 (primEqInt (Pos Zero) (fromInt (Pos Zero))) (Pos Zero) (Neg vuz375))",fontsize=16,color="magenta"];8969 -> 9010[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8969 -> 9011[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8969 -> 9012[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8969 -> 9013[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8970[label="vuz377",fontsize=16,color="green",shape="box"];8971[label="vuz491",fontsize=16,color="green",shape="box"];8972[label="primQuotInt (Neg vuz374) (gcd0 (Neg vuz511) (Neg vuz375))",fontsize=16,color="black",shape="triangle"];8972 -> 9014[label="",style="solid", color="black", weight=3];
67.72/34.80	8973 -> 9015[label="",style="dashed", color="red", weight=0];
67.72/34.80	8973[label="primQuotInt (Neg vuz374) (gcd1 (Neg vuz375 == fromInt (Pos Zero)) (Neg vuz511) (Neg vuz375))",fontsize=16,color="magenta"];8973 -> 9016[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8974[label="vuz381",fontsize=16,color="green",shape="box"];8975[label="vuz493",fontsize=16,color="green",shape="box"];8976[label="primQuotInt (Neg vuz378) (gcd0 (Pos vuz514) (Neg vuz379))",fontsize=16,color="black",shape="triangle"];8976 -> 9017[label="",style="solid", color="black", weight=3];
67.72/34.80	8977 -> 9018[label="",style="dashed", color="red", weight=0];
67.72/34.80	8977[label="primQuotInt (Neg vuz378) (gcd1 (Neg vuz379 == fromInt (Pos Zero)) (Pos vuz514) (Neg vuz379))",fontsize=16,color="magenta"];8977 -> 9019[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	10005 -> 9366[label="",style="dashed", color="red", weight=0];
67.72/34.80	10005[label="abs (Pos vuz3190 * Pos vuz3170)",fontsize=16,color="magenta"];10033[label="absReal (Pos vuz399)",fontsize=16,color="black",shape="box"];10033 -> 10182[label="",style="solid", color="black", weight=3];
67.72/34.80	9366[label="abs (Pos vuz3190 * Pos vuz3170)",fontsize=16,color="black",shape="triangle"];9366 -> 9585[label="",style="solid", color="black", weight=3];
67.72/34.80	10034[label="primQuotInt (Pos vuz416) (gcd0Gcd'1 False vuz549 vuz542)",fontsize=16,color="black",shape="box"];10034 -> 10183[label="",style="solid", color="black", weight=3];
67.72/34.80	10035[label="primQuotInt (Pos vuz416) (gcd0Gcd'1 True vuz549 vuz542)",fontsize=16,color="black",shape="box"];10035 -> 10184[label="",style="solid", color="black", weight=3];
67.72/34.80	10006 -> 9369[label="",style="dashed", color="red", weight=0];
67.72/34.80	10006[label="abs (Neg vuz3190 * Pos vuz3170)",fontsize=16,color="magenta"];10036[label="vuz417",fontsize=16,color="green",shape="box"];9369[label="abs (Neg vuz3190 * Pos vuz3170)",fontsize=16,color="black",shape="triangle"];9369 -> 9588[label="",style="solid", color="black", weight=3];
67.72/34.80	9376[label="abs (Neg vuz3190 * Neg vuz3170)",fontsize=16,color="black",shape="triangle"];9376 -> 9590[label="",style="solid", color="black", weight=3];
67.72/34.80	10172[label="absReal (Neg vuz427)",fontsize=16,color="black",shape="box"];10172 -> 10202[label="",style="solid", color="black", weight=3];
67.72/34.80	10173 -> 9376[label="",style="dashed", color="red", weight=0];
67.72/34.80	10173[label="abs (Neg vuz3190 * Neg vuz3170)",fontsize=16,color="magenta"];10174[label="primQuotInt (Neg vuz428) (gcd0Gcd'1 False vuz552 vuz544)",fontsize=16,color="black",shape="box"];10174 -> 10203[label="",style="solid", color="black", weight=3];
67.72/34.80	10175[label="primQuotInt (Neg vuz428) (gcd0Gcd'1 True vuz552 vuz544)",fontsize=16,color="black",shape="box"];10175 -> 10204[label="",style="solid", color="black", weight=3];
67.72/34.80	9372[label="abs (Pos vuz3190 * Neg vuz3170)",fontsize=16,color="black",shape="triangle"];9372 -> 9589[label="",style="solid", color="black", weight=3];
67.72/34.80	10176[label="vuz429",fontsize=16,color="green",shape="box"];10177 -> 9372[label="",style="dashed", color="red", weight=0];
67.72/34.80	10177[label="abs (Pos vuz3190 * Neg vuz3170)",fontsize=16,color="magenta"];10178[label="vuz447",fontsize=16,color="green",shape="box"];10179 -> 9369[label="",style="dashed", color="red", weight=0];
67.72/34.80	10179[label="abs (Neg vuz3190 * Pos vuz3170)",fontsize=16,color="magenta"];10180[label="vuz349",fontsize=16,color="green",shape="box"];10181 -> 9366[label="",style="dashed", color="red", weight=0];
67.72/34.80	10181[label="abs (Pos vuz3190 * Pos vuz3170)",fontsize=16,color="magenta"];10007 -> 9372[label="",style="dashed", color="red", weight=0];
67.72/34.80	10007[label="abs (Pos vuz3190 * Neg vuz3170)",fontsize=16,color="magenta"];10037[label="vuz355",fontsize=16,color="green",shape="box"];10008 -> 9376[label="",style="dashed", color="red", weight=0];
67.72/34.80	10008[label="abs (Neg vuz3190 * Neg vuz3170)",fontsize=16,color="magenta"];10038[label="vuz361",fontsize=16,color="green",shape="box"];8986[label="primQuotInt (Pos vuz366) (gcd0Gcd' (abs (Pos vuz505)) (abs (Pos vuz367)))",fontsize=16,color="black",shape="box"];8986 -> 9028[label="",style="solid", color="black", weight=3];
67.72/34.80	8988 -> 9987[label="",style="dashed", color="red", weight=0];
67.72/34.80	8988[label="Pos vuz367 == fromInt (Pos Zero)",fontsize=16,color="magenta"];8988 -> 10009[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8987[label="primQuotInt (Pos vuz366) (gcd1 vuz516 (Pos vuz505) (Pos vuz367))",fontsize=16,color="burlywood",shape="triangle"];11091[label="vuz516/False",fontsize=10,color="white",style="solid",shape="box"];8987 -> 11091[label="",style="solid", color="burlywood", weight=9];
67.72/34.80	11091 -> 9030[label="",style="solid", color="burlywood", weight=3];
67.72/34.80	11092[label="vuz516/True",fontsize=10,color="white",style="solid",shape="box"];8987 -> 11092[label="",style="solid", color="burlywood", weight=9];
67.72/34.80	11092 -> 9031[label="",style="solid", color="burlywood", weight=3];
67.72/34.80	8989[label="vuz3690",fontsize=16,color="green",shape="box"];8990[label="vuz4830",fontsize=16,color="green",shape="box"];8991[label="Succ vuz3690",fontsize=16,color="green",shape="box"];8992 -> 7479[label="",style="dashed", color="red", weight=0];
67.72/34.80	8992[label="primEqInt (Pos (Succ vuz3690)) (fromInt (Pos Zero))",fontsize=16,color="magenta"];8992 -> 9032[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8993 -> 7498[label="",style="dashed", color="red", weight=0];
67.72/34.80	8993[label="primEqInt (Neg (Succ vuz4830)) (fromInt (Pos Zero))",fontsize=16,color="magenta"];8993 -> 9033[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8994[label="Succ vuz4830",fontsize=16,color="green",shape="box"];8995[label="vuz366",fontsize=16,color="green",shape="box"];8996[label="vuz367",fontsize=16,color="green",shape="box"];8997[label="Zero",fontsize=16,color="green",shape="box"];8998 -> 7479[label="",style="dashed", color="red", weight=0];
67.72/34.80	8998[label="primEqInt (Pos Zero) (fromInt (Pos Zero))",fontsize=16,color="magenta"];8998 -> 9034[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	8999[label="primQuotInt (Pos vuz370) (gcd0Gcd' (abs (Neg vuz508)) (abs (Pos vuz371)))",fontsize=16,color="black",shape="box"];8999 -> 9035[label="",style="solid", color="black", weight=3];
67.72/34.80	9001 -> 9987[label="",style="dashed", color="red", weight=0];
67.72/34.80	9001[label="Pos vuz371 == fromInt (Pos Zero)",fontsize=16,color="magenta"];9001 -> 10010[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	9000[label="primQuotInt (Pos vuz370) (gcd1 vuz517 (Neg vuz508) (Pos vuz371))",fontsize=16,color="burlywood",shape="triangle"];11093[label="vuz517/False",fontsize=10,color="white",style="solid",shape="box"];9000 -> 11093[label="",style="solid", color="burlywood", weight=9];
67.72/34.80	11093 -> 9037[label="",style="solid", color="burlywood", weight=3];
67.72/34.80	11094[label="vuz517/True",fontsize=10,color="white",style="solid",shape="box"];9000 -> 11094[label="",style="solid", color="burlywood", weight=9];
67.72/34.80	11094 -> 9038[label="",style="solid", color="burlywood", weight=3];
67.72/34.80	9002[label="vuz4890",fontsize=16,color="green",shape="box"];9003[label="vuz3770",fontsize=16,color="green",shape="box"];9004[label="vuz375",fontsize=16,color="green",shape="box"];9005 -> 7479[label="",style="dashed", color="red", weight=0];
67.72/34.80	9005[label="primEqInt (Pos (Succ vuz4890)) (fromInt (Pos Zero))",fontsize=16,color="magenta"];9005 -> 9039[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	9006[label="Succ vuz4890",fontsize=16,color="green",shape="box"];9007[label="vuz374",fontsize=16,color="green",shape="box"];9008 -> 7498[label="",style="dashed", color="red", weight=0];
67.72/34.80	9008[label="primEqInt (Neg (Succ vuz3770)) (fromInt (Pos Zero))",fontsize=16,color="magenta"];9008 -> 9040[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	9009[label="Succ vuz3770",fontsize=16,color="green",shape="box"];9010[label="vuz375",fontsize=16,color="green",shape="box"];9011 -> 7479[label="",style="dashed", color="red", weight=0];
67.72/34.80	9011[label="primEqInt (Pos Zero) (fromInt (Pos Zero))",fontsize=16,color="magenta"];9011 -> 9041[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	9012[label="Zero",fontsize=16,color="green",shape="box"];9013[label="vuz374",fontsize=16,color="green",shape="box"];9014[label="primQuotInt (Neg vuz374) (gcd0Gcd' (abs (Neg vuz511)) (abs (Neg vuz375)))",fontsize=16,color="black",shape="box"];9014 -> 9042[label="",style="solid", color="black", weight=3];
67.72/34.80	9016 -> 9987[label="",style="dashed", color="red", weight=0];
67.72/34.80	9016[label="Neg vuz375 == fromInt (Pos Zero)",fontsize=16,color="magenta"];9016 -> 10011[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	9015[label="primQuotInt (Neg vuz374) (gcd1 vuz518 (Neg vuz511) (Neg vuz375))",fontsize=16,color="burlywood",shape="triangle"];11095[label="vuz518/False",fontsize=10,color="white",style="solid",shape="box"];9015 -> 11095[label="",style="solid", color="burlywood", weight=9];
67.72/34.80	11095 -> 9044[label="",style="solid", color="burlywood", weight=3];
67.72/34.80	11096[label="vuz518/True",fontsize=10,color="white",style="solid",shape="box"];9015 -> 11096[label="",style="solid", color="burlywood", weight=9];
67.72/34.80	11096 -> 9045[label="",style="solid", color="burlywood", weight=3];
67.72/34.80	9017[label="primQuotInt (Neg vuz378) (gcd0Gcd' (abs (Pos vuz514)) (abs (Neg vuz379)))",fontsize=16,color="black",shape="box"];9017 -> 9046[label="",style="solid", color="black", weight=3];
67.72/34.80	9019 -> 9987[label="",style="dashed", color="red", weight=0];
67.72/34.80	9019[label="Neg vuz379 == fromInt (Pos Zero)",fontsize=16,color="magenta"];9019 -> 10012[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	9018[label="primQuotInt (Neg vuz378) (gcd1 vuz519 (Pos vuz514) (Neg vuz379))",fontsize=16,color="burlywood",shape="triangle"];11097[label="vuz519/False",fontsize=10,color="white",style="solid",shape="box"];9018 -> 11097[label="",style="solid", color="burlywood", weight=9];
67.72/34.80	11097 -> 9048[label="",style="solid", color="burlywood", weight=3];
67.72/34.80	11098[label="vuz519/True",fontsize=10,color="white",style="solid",shape="box"];9018 -> 11098[label="",style="solid", color="burlywood", weight=9];
67.72/34.80	11098 -> 9049[label="",style="solid", color="burlywood", weight=3];
67.72/34.80	10182[label="absReal2 (Pos vuz399)",fontsize=16,color="black",shape="box"];10182 -> 10205[label="",style="solid", color="black", weight=3];
67.72/34.80	9585[label="absReal (Pos vuz3190 * Pos vuz3170)",fontsize=16,color="black",shape="box"];9585 -> 9817[label="",style="solid", color="black", weight=3];
67.72/34.80	10183[label="primQuotInt (Pos vuz416) (gcd0Gcd'0 vuz549 vuz542)",fontsize=16,color="black",shape="box"];10183 -> 10206[label="",style="solid", color="black", weight=3];
67.72/34.80	10184[label="primQuotInt (Pos vuz416) vuz549",fontsize=16,color="burlywood",shape="triangle"];11099[label="vuz549/Pos vuz5490",fontsize=10,color="white",style="solid",shape="box"];10184 -> 11099[label="",style="solid", color="burlywood", weight=9];
67.72/34.80	11099 -> 10207[label="",style="solid", color="burlywood", weight=3];
67.72/34.80	11100[label="vuz549/Neg vuz5490",fontsize=10,color="white",style="solid",shape="box"];10184 -> 11100[label="",style="solid", color="burlywood", weight=9];
67.72/34.80	11100 -> 10208[label="",style="solid", color="burlywood", weight=3];
67.72/34.80	9588[label="absReal (Neg vuz3190 * Pos vuz3170)",fontsize=16,color="black",shape="box"];9588 -> 9822[label="",style="solid", color="black", weight=3];
67.72/34.80	9590[label="absReal (Neg vuz3190 * Neg vuz3170)",fontsize=16,color="black",shape="box"];9590 -> 9824[label="",style="solid", color="black", weight=3];
67.72/34.80	10202[label="absReal2 (Neg vuz427)",fontsize=16,color="black",shape="box"];10202 -> 10246[label="",style="solid", color="black", weight=3];
67.72/34.80	10203[label="primQuotInt (Neg vuz428) (gcd0Gcd'0 vuz552 vuz544)",fontsize=16,color="black",shape="box"];10203 -> 10247[label="",style="solid", color="black", weight=3];
67.72/34.80	10204[label="primQuotInt (Neg vuz428) vuz552",fontsize=16,color="burlywood",shape="triangle"];11101[label="vuz552/Pos vuz5520",fontsize=10,color="white",style="solid",shape="box"];10204 -> 11101[label="",style="solid", color="burlywood", weight=9];
67.72/34.80	11101 -> 10248[label="",style="solid", color="burlywood", weight=3];
67.72/34.80	11102[label="vuz552/Neg vuz5520",fontsize=10,color="white",style="solid",shape="box"];10204 -> 11102[label="",style="solid", color="burlywood", weight=9];
67.72/34.80	11102 -> 10249[label="",style="solid", color="burlywood", weight=3];
67.72/34.80	9589[label="absReal (Pos vuz3190 * Neg vuz3170)",fontsize=16,color="black",shape="box"];9589 -> 9823[label="",style="solid", color="black", weight=3];
67.72/34.80	9028[label="primQuotInt (Pos vuz366) (gcd0Gcd'2 (abs (Pos vuz505)) (abs (Pos vuz367)))",fontsize=16,color="black",shape="box"];9028 -> 9058[label="",style="solid", color="black", weight=3];
67.72/34.80	10009[label="Pos vuz367",fontsize=16,color="green",shape="box"];9030[label="primQuotInt (Pos vuz366) (gcd1 False (Pos vuz505) (Pos vuz367))",fontsize=16,color="black",shape="box"];9030 -> 9059[label="",style="solid", color="black", weight=3];
67.72/34.80	9031[label="primQuotInt (Pos vuz366) (gcd1 True (Pos vuz505) (Pos vuz367))",fontsize=16,color="black",shape="box"];9031 -> 9060[label="",style="solid", color="black", weight=3];
67.72/34.80	9032[label="Succ vuz3690",fontsize=16,color="green",shape="box"];9033[label="Succ vuz4830",fontsize=16,color="green",shape="box"];9034[label="Zero",fontsize=16,color="green",shape="box"];9035[label="primQuotInt (Pos vuz370) (gcd0Gcd'2 (abs (Neg vuz508)) (abs (Pos vuz371)))",fontsize=16,color="black",shape="box"];9035 -> 9061[label="",style="solid", color="black", weight=3];
67.72/34.80	10010[label="Pos vuz371",fontsize=16,color="green",shape="box"];9037[label="primQuotInt (Pos vuz370) (gcd1 False (Neg vuz508) (Pos vuz371))",fontsize=16,color="black",shape="box"];9037 -> 9062[label="",style="solid", color="black", weight=3];
67.72/34.80	9038[label="primQuotInt (Pos vuz370) (gcd1 True (Neg vuz508) (Pos vuz371))",fontsize=16,color="black",shape="box"];9038 -> 9063[label="",style="solid", color="black", weight=3];
67.72/34.80	9039[label="Succ vuz4890",fontsize=16,color="green",shape="box"];9040[label="Succ vuz3770",fontsize=16,color="green",shape="box"];9041[label="Zero",fontsize=16,color="green",shape="box"];9042[label="primQuotInt (Neg vuz374) (gcd0Gcd'2 (abs (Neg vuz511)) (abs (Neg vuz375)))",fontsize=16,color="black",shape="box"];9042 -> 9064[label="",style="solid", color="black", weight=3];
67.72/34.80	10011[label="Neg vuz375",fontsize=16,color="green",shape="box"];9044[label="primQuotInt (Neg vuz374) (gcd1 False (Neg vuz511) (Neg vuz375))",fontsize=16,color="black",shape="box"];9044 -> 9065[label="",style="solid", color="black", weight=3];
67.72/34.80	9045[label="primQuotInt (Neg vuz374) (gcd1 True (Neg vuz511) (Neg vuz375))",fontsize=16,color="black",shape="box"];9045 -> 9066[label="",style="solid", color="black", weight=3];
67.72/34.80	9046[label="primQuotInt (Neg vuz378) (gcd0Gcd'2 (abs (Pos vuz514)) (abs (Neg vuz379)))",fontsize=16,color="black",shape="box"];9046 -> 9067[label="",style="solid", color="black", weight=3];
67.72/34.80	10012[label="Neg vuz379",fontsize=16,color="green",shape="box"];9048[label="primQuotInt (Neg vuz378) (gcd1 False (Pos vuz514) (Neg vuz379))",fontsize=16,color="black",shape="box"];9048 -> 9068[label="",style="solid", color="black", weight=3];
67.72/34.80	9049[label="primQuotInt (Neg vuz378) (gcd1 True (Pos vuz514) (Neg vuz379))",fontsize=16,color="black",shape="box"];9049 -> 9069[label="",style="solid", color="black", weight=3];
67.72/34.80	10205 -> 10185[label="",style="dashed", color="red", weight=0];
67.72/34.80	10205[label="absReal1 (Pos vuz399) (Pos vuz399 >= fromInt (Pos Zero))",fontsize=16,color="magenta"];10205 -> 10250[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	10205 -> 10251[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	9817[label="absReal2 (Pos vuz3190 * Pos vuz3170)",fontsize=16,color="black",shape="box"];9817 -> 9834[label="",style="solid", color="black", weight=3];
67.72/34.80	10206 -> 10184[label="",style="dashed", color="red", weight=0];
67.72/34.80	10206[label="primQuotInt (Pos vuz416) (gcd0Gcd' vuz542 (vuz549 `rem` vuz542))",fontsize=16,color="magenta"];10206 -> 10252[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	10207[label="primQuotInt (Pos vuz416) (Pos vuz5490)",fontsize=16,color="burlywood",shape="box"];11103[label="vuz5490/Succ vuz54900",fontsize=10,color="white",style="solid",shape="box"];10207 -> 11103[label="",style="solid", color="burlywood", weight=9];
67.72/34.80	11103 -> 10253[label="",style="solid", color="burlywood", weight=3];
67.72/34.80	11104[label="vuz5490/Zero",fontsize=10,color="white",style="solid",shape="box"];10207 -> 11104[label="",style="solid", color="burlywood", weight=9];
67.72/34.80	11104 -> 10254[label="",style="solid", color="burlywood", weight=3];
67.72/34.80	10208[label="primQuotInt (Pos vuz416) (Neg vuz5490)",fontsize=16,color="burlywood",shape="box"];11105[label="vuz5490/Succ vuz54900",fontsize=10,color="white",style="solid",shape="box"];10208 -> 11105[label="",style="solid", color="burlywood", weight=9];
67.72/34.80	11105 -> 10255[label="",style="solid", color="burlywood", weight=3];
67.72/34.80	11106[label="vuz5490/Zero",fontsize=10,color="white",style="solid",shape="box"];10208 -> 11106[label="",style="solid", color="burlywood", weight=9];
67.72/34.80	11106 -> 10256[label="",style="solid", color="burlywood", weight=3];
67.72/34.80	9822[label="absReal2 (Neg vuz3190 * Pos vuz3170)",fontsize=16,color="black",shape="box"];9822 -> 9839[label="",style="solid", color="black", weight=3];
67.72/34.80	9824[label="absReal2 (Neg vuz3190 * Neg vuz3170)",fontsize=16,color="black",shape="box"];9824 -> 9841[label="",style="solid", color="black", weight=3];
67.72/34.80	10246 -> 10185[label="",style="dashed", color="red", weight=0];
67.72/34.80	10246[label="absReal1 (Neg vuz427) (Neg vuz427 >= fromInt (Pos Zero))",fontsize=16,color="magenta"];10246 -> 10266[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	10246 -> 10267[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	10247 -> 10204[label="",style="dashed", color="red", weight=0];
67.72/34.80	10247[label="primQuotInt (Neg vuz428) (gcd0Gcd' vuz544 (vuz552 `rem` vuz544))",fontsize=16,color="magenta"];10247 -> 10268[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	10248[label="primQuotInt (Neg vuz428) (Pos vuz5520)",fontsize=16,color="burlywood",shape="box"];11107[label="vuz5520/Succ vuz55200",fontsize=10,color="white",style="solid",shape="box"];10248 -> 11107[label="",style="solid", color="burlywood", weight=9];
67.72/34.80	11107 -> 10269[label="",style="solid", color="burlywood", weight=3];
67.72/34.80	11108[label="vuz5520/Zero",fontsize=10,color="white",style="solid",shape="box"];10248 -> 11108[label="",style="solid", color="burlywood", weight=9];
67.72/34.80	11108 -> 10270[label="",style="solid", color="burlywood", weight=3];
67.72/34.80	10249[label="primQuotInt (Neg vuz428) (Neg vuz5520)",fontsize=16,color="burlywood",shape="box"];11109[label="vuz5520/Succ vuz55200",fontsize=10,color="white",style="solid",shape="box"];10249 -> 11109[label="",style="solid", color="burlywood", weight=9];
67.72/34.80	11109 -> 10271[label="",style="solid", color="burlywood", weight=3];
67.72/34.80	11110[label="vuz5520/Zero",fontsize=10,color="white",style="solid",shape="box"];10249 -> 11110[label="",style="solid", color="burlywood", weight=9];
67.72/34.80	11110 -> 10272[label="",style="solid", color="burlywood", weight=3];
67.72/34.80	9823[label="absReal2 (Pos vuz3190 * Neg vuz3170)",fontsize=16,color="black",shape="box"];9823 -> 9840[label="",style="solid", color="black", weight=3];
67.72/34.80	9058 -> 9854[label="",style="dashed", color="red", weight=0];
67.72/34.80	9058[label="primQuotInt (Pos vuz366) (gcd0Gcd'1 (abs (Pos vuz367) == fromInt (Pos Zero)) (abs (Pos vuz505)) (abs (Pos vuz367)))",fontsize=16,color="magenta"];9058 -> 9887[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	9058 -> 9888[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	9058 -> 9889[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	9058 -> 9890[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	9059 -> 8956[label="",style="dashed", color="red", weight=0];
67.72/34.80	9059[label="primQuotInt (Pos vuz366) (gcd0 (Pos vuz505) (Pos vuz367))",fontsize=16,color="magenta"];9060 -> 8816[label="",style="dashed", color="red", weight=0];
67.72/34.80	9060[label="primQuotInt (Pos vuz366) (error [])",fontsize=16,color="magenta"];9060 -> 9079[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	9061 -> 9854[label="",style="dashed", color="red", weight=0];
67.72/34.80	9061[label="primQuotInt (Pos vuz370) (gcd0Gcd'1 (abs (Pos vuz371) == fromInt (Pos Zero)) (abs (Neg vuz508)) (abs (Pos vuz371)))",fontsize=16,color="magenta"];9061 -> 9891[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	9061 -> 9892[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	9061 -> 9893[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	9061 -> 9894[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	9062 -> 8964[label="",style="dashed", color="red", weight=0];
67.72/34.80	9062[label="primQuotInt (Pos vuz370) (gcd0 (Neg vuz508) (Pos vuz371))",fontsize=16,color="magenta"];9063 -> 8816[label="",style="dashed", color="red", weight=0];
67.72/34.80	9063[label="primQuotInt (Pos vuz370) (error [])",fontsize=16,color="magenta"];9063 -> 9081[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	9064 -> 10039[label="",style="dashed", color="red", weight=0];
67.72/34.80	9064[label="primQuotInt (Neg vuz374) (gcd0Gcd'1 (abs (Neg vuz375) == fromInt (Pos Zero)) (abs (Neg vuz511)) (abs (Neg vuz375)))",fontsize=16,color="magenta"];9064 -> 10072[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	9064 -> 10073[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	9064 -> 10074[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	9064 -> 10075[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	9065 -> 8972[label="",style="dashed", color="red", weight=0];
67.72/34.80	9065[label="primQuotInt (Neg vuz374) (gcd0 (Neg vuz511) (Neg vuz375))",fontsize=16,color="magenta"];9066 -> 8849[label="",style="dashed", color="red", weight=0];
67.72/34.80	9066[label="primQuotInt (Neg vuz374) (error [])",fontsize=16,color="magenta"];9066 -> 9083[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	9067 -> 10039[label="",style="dashed", color="red", weight=0];
67.72/34.80	9067[label="primQuotInt (Neg vuz378) (gcd0Gcd'1 (abs (Neg vuz379) == fromInt (Pos Zero)) (abs (Pos vuz514)) (abs (Neg vuz379)))",fontsize=16,color="magenta"];9067 -> 10076[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	9067 -> 10077[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	9067 -> 10078[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	9067 -> 10079[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	9068 -> 8976[label="",style="dashed", color="red", weight=0];
67.72/34.80	9068[label="primQuotInt (Neg vuz378) (gcd0 (Pos vuz514) (Neg vuz379))",fontsize=16,color="magenta"];9069 -> 8849[label="",style="dashed", color="red", weight=0];
67.72/34.80	9069[label="primQuotInt (Neg vuz378) (error [])",fontsize=16,color="magenta"];9069 -> 9085[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	10250[label="Pos vuz399",fontsize=16,color="green",shape="box"];10251[label="Pos vuz399",fontsize=16,color="green",shape="box"];10185[label="absReal1 vuz554 (vuz555 >= fromInt (Pos Zero))",fontsize=16,color="black",shape="triangle"];10185 -> 10223[label="",style="solid", color="black", weight=3];
67.72/34.80	9834 -> 10185[label="",style="dashed", color="red", weight=0];
67.72/34.80	9834[label="absReal1 (Pos vuz3190 * Pos vuz3170) (Pos vuz3190 * Pos vuz3170 >= fromInt (Pos Zero))",fontsize=16,color="magenta"];9834 -> 10186[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	9834 -> 10187[label="",style="dashed", color="magenta", weight=3];
67.72/34.80	10252[label="gcd0Gcd' vuz542 (vuz549 `rem` vuz542)",fontsize=16,color="black",shape="triangle"];10252 -> 10273[label="",style="solid", color="black", weight=3];
67.72/34.80	10253[label="primQuotInt (Pos vuz416) (Pos (Succ vuz54900))",fontsize=16,color="black",shape="box"];10253 -> 10274[label="",style="solid", color="black", weight=3];
67.72/34.80	10254[label="primQuotInt (Pos vuz416) (Pos Zero)",fontsize=16,color="black",shape="box"];10254 -> 10275[label="",style="solid", color="black", weight=3];
67.72/34.80	10255[label="primQuotInt (Pos vuz416) (Neg (Succ vuz54900))",fontsize=16,color="black",shape="box"];10255 -> 10276[label="",style="solid", color="black", weight=3];
67.72/34.80	10256[label="primQuotInt (Pos vuz416) (Neg Zero)",fontsize=16,color="black",shape="box"];10256 -> 10277[label="",style="solid", color="black", weight=3];
67.72/34.80	9839 -> 10185[label="",style="dashed", color="red", weight=0];
67.72/34.81	9839[label="absReal1 (Neg vuz3190 * Pos vuz3170) (Neg vuz3190 * Pos vuz3170 >= fromInt (Pos Zero))",fontsize=16,color="magenta"];9839 -> 10188[label="",style="dashed", color="magenta", weight=3];
67.72/34.81	9839 -> 10189[label="",style="dashed", color="magenta", weight=3];
67.72/34.81	9841 -> 10185[label="",style="dashed", color="red", weight=0];
67.72/34.81	9841[label="absReal1 (Neg vuz3190 * Neg vuz3170) (Neg vuz3190 * Neg vuz3170 >= fromInt (Pos Zero))",fontsize=16,color="magenta"];9841 -> 10190[label="",style="dashed", color="magenta", weight=3];
67.72/34.81	9841 -> 10191[label="",style="dashed", color="magenta", weight=3];
67.72/34.81	10266[label="Neg vuz427",fontsize=16,color="green",shape="box"];10267[label="Neg vuz427",fontsize=16,color="green",shape="box"];10268 -> 10252[label="",style="dashed", color="red", weight=0];
67.72/34.81	10268[label="gcd0Gcd' vuz544 (vuz552 `rem` vuz544)",fontsize=16,color="magenta"];10268 -> 10283[label="",style="dashed", color="magenta", weight=3];
67.72/34.81	10268 -> 10284[label="",style="dashed", color="magenta", weight=3];
67.72/34.81	10269[label="primQuotInt (Neg vuz428) (Pos (Succ vuz55200))",fontsize=16,color="black",shape="box"];10269 -> 10285[label="",style="solid", color="black", weight=3];
67.72/34.81	10270[label="primQuotInt (Neg vuz428) (Pos Zero)",fontsize=16,color="black",shape="box"];10270 -> 10286[label="",style="solid", color="black", weight=3];
67.72/34.81	10271[label="primQuotInt (Neg vuz428) (Neg (Succ vuz55200))",fontsize=16,color="black",shape="box"];10271 -> 10287[label="",style="solid", color="black", weight=3];
67.72/34.81	10272[label="primQuotInt (Neg vuz428) (Neg Zero)",fontsize=16,color="black",shape="box"];10272 -> 10288[label="",style="solid", color="black", weight=3];
67.72/34.81	9840 -> 10185[label="",style="dashed", color="red", weight=0];
67.72/34.81	9840[label="absReal1 (Pos vuz3190 * Neg vuz3170) (Pos vuz3190 * Neg vuz3170 >= fromInt (Pos Zero))",fontsize=16,color="magenta"];9840 -> 10192[label="",style="dashed", color="magenta", weight=3];
67.72/34.81	9840 -> 10193[label="",style="dashed", color="magenta", weight=3];
67.72/34.81	9887 -> 9987[label="",style="dashed", color="red", weight=0];
67.72/34.81	9887[label="abs (Pos vuz367) == fromInt (Pos Zero)",fontsize=16,color="magenta"];9887 -> 10013[label="",style="dashed", color="magenta", weight=3];
67.72/34.81	9888[label="vuz366",fontsize=16,color="green",shape="box"];9889 -> 9857[label="",style="dashed", color="red", weight=0];
67.72/34.81	9889[label="abs (Pos vuz505)",fontsize=16,color="magenta"];9889 -> 10209[label="",style="dashed", color="magenta", weight=3];
67.72/34.81	9890 -> 9857[label="",style="dashed", color="red", weight=0];
67.72/34.81	9890[label="abs (Pos vuz367)",fontsize=16,color="magenta"];9890 -> 10210[label="",style="dashed", color="magenta", weight=3];
67.72/34.81	9079[label="vuz366",fontsize=16,color="green",shape="box"];9891 -> 9987[label="",style="dashed", color="red", weight=0];
67.72/34.81	9891[label="abs (Pos vuz371) == fromInt (Pos Zero)",fontsize=16,color="magenta"];9891 -> 10014[label="",style="dashed", color="magenta", weight=3];
67.72/34.81	9892[label="vuz370",fontsize=16,color="green",shape="box"];9893 -> 10042[label="",style="dashed", color="red", weight=0];
67.72/34.81	9893[label="abs (Neg vuz508)",fontsize=16,color="magenta"];9893 -> 10211[label="",style="dashed", color="magenta", weight=3];
67.72/34.81	9894 -> 9857[label="",style="dashed", color="red", weight=0];
67.72/34.81	9894[label="abs (Pos vuz371)",fontsize=16,color="magenta"];9894 -> 10212[label="",style="dashed", color="magenta", weight=3];
67.72/34.81	9081[label="vuz370",fontsize=16,color="green",shape="box"];10072[label="vuz374",fontsize=16,color="green",shape="box"];10073 -> 10042[label="",style="dashed", color="red", weight=0];
67.72/34.81	10073[label="abs (Neg vuz375)",fontsize=16,color="magenta"];10073 -> 10213[label="",style="dashed", color="magenta", weight=3];
67.72/34.81	10074 -> 10042[label="",style="dashed", color="red", weight=0];
67.72/34.81	10074[label="abs (Neg vuz511)",fontsize=16,color="magenta"];10074 -> 10214[label="",style="dashed", color="magenta", weight=3];
67.72/34.81	10075 -> 9987[label="",style="dashed", color="red", weight=0];
67.72/34.81	10075[label="abs (Neg vuz375) == fromInt (Pos Zero)",fontsize=16,color="magenta"];10075 -> 10215[label="",style="dashed", color="magenta", weight=3];
67.72/34.81	9083[label="vuz374",fontsize=16,color="green",shape="box"];10076[label="vuz378",fontsize=16,color="green",shape="box"];10077 -> 10042[label="",style="dashed", color="red", weight=0];
67.72/34.81	10077[label="abs (Neg vuz379)",fontsize=16,color="magenta"];10077 -> 10216[label="",style="dashed", color="magenta", weight=3];
67.72/34.81	10078 -> 9857[label="",style="dashed", color="red", weight=0];
67.72/34.81	10078[label="abs (Pos vuz514)",fontsize=16,color="magenta"];10078 -> 10217[label="",style="dashed", color="magenta", weight=3];
67.72/34.81	10079 -> 9987[label="",style="dashed", color="red", weight=0];
67.72/34.81	10079[label="abs (Neg vuz379) == fromInt (Pos Zero)",fontsize=16,color="magenta"];10079 -> 10218[label="",style="dashed", color="magenta", weight=3];
67.72/34.81	9085[label="vuz378",fontsize=16,color="green",shape="box"];10223[label="absReal1 vuz554 (compare vuz555 (fromInt (Pos Zero)) /= LT)",fontsize=16,color="black",shape="box"];10223 -> 10259[label="",style="solid", color="black", weight=3];
67.72/34.81	10186 -> 9988[label="",style="dashed", color="red", weight=0];
67.72/34.81	10186[label="Pos vuz3190 * Pos vuz3170",fontsize=16,color="magenta"];10186 -> 10219[label="",style="dashed", color="magenta", weight=3];
67.72/34.81	10186 -> 10220[label="",style="dashed", color="magenta", weight=3];
67.72/34.81	10187 -> 9988[label="",style="dashed", color="red", weight=0];
67.72/34.81	10187[label="Pos vuz3190 * Pos vuz3170",fontsize=16,color="magenta"];10187 -> 10221[label="",style="dashed", color="magenta", weight=3];
67.72/34.81	10187 -> 10222[label="",style="dashed", color="magenta", weight=3];
67.72/34.81	10273[label="gcd0Gcd'2 vuz542 (vuz549 `rem` vuz542)",fontsize=16,color="black",shape="box"];10273 -> 10289[label="",style="solid", color="black", weight=3];
67.72/34.81	10274[label="Pos (primDivNatS vuz416 (Succ vuz54900))",fontsize=16,color="green",shape="box"];10274 -> 10290[label="",style="dashed", color="green", weight=3];
67.72/34.81	10275[label="error []",fontsize=16,color="black",shape="triangle"];10275 -> 10291[label="",style="solid", color="black", weight=3];
67.72/34.81	10276[label="Neg (primDivNatS vuz416 (Succ vuz54900))",fontsize=16,color="green",shape="box"];10276 -> 10292[label="",style="dashed", color="green", weight=3];
67.72/34.81	10277 -> 10275[label="",style="dashed", color="red", weight=0];
67.72/34.81	10277[label="error []",fontsize=16,color="magenta"];10188 -> 9988[label="",style="dashed", color="red", weight=0];
67.72/34.81	10188[label="Neg vuz3190 * Pos vuz3170",fontsize=16,color="magenta"];10188 -> 10224[label="",style="dashed", color="magenta", weight=3];
67.72/34.81	10188 -> 10225[label="",style="dashed", color="magenta", weight=3];
67.72/34.81	10189 -> 9988[label="",style="dashed", color="red", weight=0];
67.72/34.81	10189[label="Neg vuz3190 * Pos vuz3170",fontsize=16,color="magenta"];10189 -> 10226[label="",style="dashed", color="magenta", weight=3];
67.72/34.81	10189 -> 10227[label="",style="dashed", color="magenta", weight=3];
67.72/34.81	10190 -> 9988[label="",style="dashed", color="red", weight=0];
67.72/34.81	10190[label="Neg vuz3190 * Neg vuz3170",fontsize=16,color="magenta"];10190 -> 10228[label="",style="dashed", color="magenta", weight=3];
67.72/34.81	10190 -> 10229[label="",style="dashed", color="magenta", weight=3];
67.72/34.81	10191 -> 9988[label="",style="dashed", color="red", weight=0];
67.72/34.81	10191[label="Neg vuz3190 * Neg vuz3170",fontsize=16,color="magenta"];10191 -> 10230[label="",style="dashed", color="magenta", weight=3];
67.72/34.81	10191 -> 10231[label="",style="dashed", color="magenta", weight=3];
67.72/34.81	10283[label="vuz552",fontsize=16,color="green",shape="box"];10284[label="vuz544",fontsize=16,color="green",shape="box"];10285[label="Neg (primDivNatS vuz428 (Succ vuz55200))",fontsize=16,color="green",shape="box"];10285 -> 10295[label="",style="dashed", color="green", weight=3];
67.72/34.81	10286 -> 10275[label="",style="dashed", color="red", weight=0];
67.72/34.81	10286[label="error []",fontsize=16,color="magenta"];10287[label="Pos (primDivNatS vuz428 (Succ vuz55200))",fontsize=16,color="green",shape="box"];10287 -> 10296[label="",style="dashed", color="green", weight=3];
67.72/34.81	10288 -> 10275[label="",style="dashed", color="red", weight=0];
67.72/34.81	10288[label="error []",fontsize=16,color="magenta"];10192 -> 9988[label="",style="dashed", color="red", weight=0];
67.72/34.81	10192[label="Pos vuz3190 * Neg vuz3170",fontsize=16,color="magenta"];10192 -> 10232[label="",style="dashed", color="magenta", weight=3];
67.72/34.81	10192 -> 10233[label="",style="dashed", color="magenta", weight=3];
67.72/34.81	10193 -> 9988[label="",style="dashed", color="red", weight=0];
67.72/34.81	10193[label="Pos vuz3190 * Neg vuz3170",fontsize=16,color="magenta"];10193 -> 10234[label="",style="dashed", color="magenta", weight=3];
67.72/34.81	10193 -> 10235[label="",style="dashed", color="magenta", weight=3];
67.72/34.81	10013 -> 9857[label="",style="dashed", color="red", weight=0];
67.72/34.81	10013[label="abs (Pos vuz367)",fontsize=16,color="magenta"];10013 -> 10236[label="",style="dashed", color="magenta", weight=3];
67.72/34.81	10209[label="vuz505",fontsize=16,color="green",shape="box"];10210[label="vuz367",fontsize=16,color="green",shape="box"];10014 -> 9857[label="",style="dashed", color="red", weight=0];
67.72/34.81	10014[label="abs (Pos vuz371)",fontsize=16,color="magenta"];10014 -> 10237[label="",style="dashed", color="magenta", weight=3];
67.72/34.81	10211[label="vuz508",fontsize=16,color="green",shape="box"];10212[label="vuz371",fontsize=16,color="green",shape="box"];10213[label="vuz375",fontsize=16,color="green",shape="box"];10214[label="vuz511",fontsize=16,color="green",shape="box"];10215 -> 10042[label="",style="dashed", color="red", weight=0];
67.72/34.81	10215[label="abs (Neg vuz375)",fontsize=16,color="magenta"];10215 -> 10257[label="",style="dashed", color="magenta", weight=3];
67.72/34.81	10216[label="vuz379",fontsize=16,color="green",shape="box"];10217[label="vuz514",fontsize=16,color="green",shape="box"];10218 -> 10042[label="",style="dashed", color="red", weight=0];
67.72/34.81	10218[label="abs (Neg vuz379)",fontsize=16,color="magenta"];10218 -> 10258[label="",style="dashed", color="magenta", weight=3];
67.72/34.81	10259[label="absReal1 vuz554 (not (compare vuz555 (fromInt (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];10259 -> 10278[label="",style="solid", color="black", weight=3];
67.72/34.81	10219[label="Pos vuz3170",fontsize=16,color="green",shape="box"];10220[label="Pos vuz3190",fontsize=16,color="green",shape="box"];10221[label="Pos vuz3170",fontsize=16,color="green",shape="box"];10222[label="Pos vuz3190",fontsize=16,color="green",shape="box"];10289 -> 10297[label="",style="dashed", color="red", weight=0];
67.72/34.81	10289[label="gcd0Gcd'1 (vuz549 `rem` vuz542 == fromInt (Pos Zero)) vuz542 (vuz549 `rem` vuz542)",fontsize=16,color="magenta"];10289 -> 10298[label="",style="dashed", color="magenta", weight=3];
67.72/34.81	10290[label="primDivNatS vuz416 (Succ vuz54900)",fontsize=16,color="burlywood",shape="triangle"];11111[label="vuz416/Succ vuz4160",fontsize=10,color="white",style="solid",shape="box"];10290 -> 11111[label="",style="solid", color="burlywood", weight=9];
67.72/34.81	11111 -> 10299[label="",style="solid", color="burlywood", weight=3];
67.72/34.81	11112[label="vuz416/Zero",fontsize=10,color="white",style="solid",shape="box"];10290 -> 11112[label="",style="solid", color="burlywood", weight=9];
67.72/34.81	11112 -> 10300[label="",style="solid", color="burlywood", weight=3];
67.72/34.81	10291[label="error []",fontsize=16,color="red",shape="box"];10292 -> 10290[label="",style="dashed", color="red", weight=0];
67.72/34.81	10292[label="primDivNatS vuz416 (Succ vuz54900)",fontsize=16,color="magenta"];10292 -> 10301[label="",style="dashed", color="magenta", weight=3];
67.72/34.81	10224[label="Pos vuz3170",fontsize=16,color="green",shape="box"];10225[label="Neg vuz3190",fontsize=16,color="green",shape="box"];10226[label="Pos vuz3170",fontsize=16,color="green",shape="box"];10227[label="Neg vuz3190",fontsize=16,color="green",shape="box"];10228[label="Neg vuz3170",fontsize=16,color="green",shape="box"];10229[label="Neg vuz3190",fontsize=16,color="green",shape="box"];10230[label="Neg vuz3170",fontsize=16,color="green",shape="box"];10231[label="Neg vuz3190",fontsize=16,color="green",shape="box"];10295 -> 10290[label="",style="dashed", color="red", weight=0];
67.72/34.81	10295[label="primDivNatS vuz428 (Succ vuz55200)",fontsize=16,color="magenta"];10295 -> 10302[label="",style="dashed", color="magenta", weight=3];
67.72/34.81	10295 -> 10303[label="",style="dashed", color="magenta", weight=3];
67.72/34.81	10296 -> 10290[label="",style="dashed", color="red", weight=0];
67.72/34.81	10296[label="primDivNatS vuz428 (Succ vuz55200)",fontsize=16,color="magenta"];10296 -> 10304[label="",style="dashed", color="magenta", weight=3];
67.72/34.81	10296 -> 10305[label="",style="dashed", color="magenta", weight=3];
67.72/34.81	10232[label="Neg vuz3170",fontsize=16,color="green",shape="box"];10233[label="Pos vuz3190",fontsize=16,color="green",shape="box"];10234[label="Neg vuz3170",fontsize=16,color="green",shape="box"];10235[label="Pos vuz3190",fontsize=16,color="green",shape="box"];10236[label="vuz367",fontsize=16,color="green",shape="box"];10237[label="vuz371",fontsize=16,color="green",shape="box"];10257[label="vuz375",fontsize=16,color="green",shape="box"];10258[label="vuz379",fontsize=16,color="green",shape="box"];10278[label="absReal1 vuz554 (not (primCmpInt vuz555 (fromInt (Pos Zero)) == LT))",fontsize=16,color="burlywood",shape="box"];11113[label="vuz555/Pos vuz5550",fontsize=10,color="white",style="solid",shape="box"];10278 -> 11113[label="",style="solid", color="burlywood", weight=9];
67.72/34.81	11113 -> 10293[label="",style="solid", color="burlywood", weight=3];
67.72/34.81	11114[label="vuz555/Neg vuz5550",fontsize=10,color="white",style="solid",shape="box"];10278 -> 11114[label="",style="solid", color="burlywood", weight=9];
67.72/34.81	11114 -> 10294[label="",style="solid", color="burlywood", weight=3];
67.72/34.81	10298 -> 9987[label="",style="dashed", color="red", weight=0];
67.72/34.81	10298[label="vuz549 `rem` vuz542 == fromInt (Pos Zero)",fontsize=16,color="magenta"];10298 -> 10306[label="",style="dashed", color="magenta", weight=3];
67.72/34.81	10297[label="gcd0Gcd'1 vuz556 vuz542 (vuz549 `rem` vuz542)",fontsize=16,color="burlywood",shape="triangle"];11115[label="vuz556/False",fontsize=10,color="white",style="solid",shape="box"];10297 -> 11115[label="",style="solid", color="burlywood", weight=9];
67.72/34.81	11115 -> 10307[label="",style="solid", color="burlywood", weight=3];
67.72/34.81	11116[label="vuz556/True",fontsize=10,color="white",style="solid",shape="box"];10297 -> 11116[label="",style="solid", color="burlywood", weight=9];
67.72/34.81	11116 -> 10308[label="",style="solid", color="burlywood", weight=3];
67.72/34.81	10299[label="primDivNatS (Succ vuz4160) (Succ vuz54900)",fontsize=16,color="black",shape="box"];10299 -> 10313[label="",style="solid", color="black", weight=3];
67.72/34.81	10300[label="primDivNatS Zero (Succ vuz54900)",fontsize=16,color="black",shape="box"];10300 -> 10314[label="",style="solid", color="black", weight=3];
67.72/34.81	10301[label="vuz54900",fontsize=16,color="green",shape="box"];10302[label="vuz428",fontsize=16,color="green",shape="box"];10303[label="vuz55200",fontsize=16,color="green",shape="box"];10304[label="vuz428",fontsize=16,color="green",shape="box"];10305[label="vuz55200",fontsize=16,color="green",shape="box"];10293[label="absReal1 vuz554 (not (primCmpInt (Pos vuz5550) (fromInt (Pos Zero)) == LT))",fontsize=16,color="burlywood",shape="box"];11117[label="vuz5550/Succ vuz55500",fontsize=10,color="white",style="solid",shape="box"];10293 -> 11117[label="",style="solid", color="burlywood", weight=9];
67.72/34.81	11117 -> 10309[label="",style="solid", color="burlywood", weight=3];
67.72/34.81	11118[label="vuz5550/Zero",fontsize=10,color="white",style="solid",shape="box"];10293 -> 11118[label="",style="solid", color="burlywood", weight=9];
67.72/34.81	11118 -> 10310[label="",style="solid", color="burlywood", weight=3];
67.72/34.81	10294[label="absReal1 vuz554 (not (primCmpInt (Neg vuz5550) (fromInt (Pos Zero)) == LT))",fontsize=16,color="burlywood",shape="box"];11119[label="vuz5550/Succ vuz55500",fontsize=10,color="white",style="solid",shape="box"];10294 -> 11119[label="",style="solid", color="burlywood", weight=9];
67.72/34.81	11119 -> 10311[label="",style="solid", color="burlywood", weight=3];
67.72/34.81	11120[label="vuz5550/Zero",fontsize=10,color="white",style="solid",shape="box"];10294 -> 11120[label="",style="solid", color="burlywood", weight=9];
67.72/34.81	11120 -> 10312[label="",style="solid", color="burlywood", weight=3];
67.72/34.81	10306[label="vuz549 `rem` vuz542",fontsize=16,color="black",shape="triangle"];10306 -> 10315[label="",style="solid", color="black", weight=3];
67.72/34.81	10307[label="gcd0Gcd'1 False vuz542 (vuz549 `rem` vuz542)",fontsize=16,color="black",shape="box"];10307 -> 10316[label="",style="solid", color="black", weight=3];
67.72/34.81	10308[label="gcd0Gcd'1 True vuz542 (vuz549 `rem` vuz542)",fontsize=16,color="black",shape="box"];10308 -> 10317[label="",style="solid", color="black", weight=3];
67.72/34.81	10313[label="primDivNatS0 vuz4160 vuz54900 (primGEqNatS vuz4160 vuz54900)",fontsize=16,color="burlywood",shape="box"];11121[label="vuz4160/Succ vuz41600",fontsize=10,color="white",style="solid",shape="box"];10313 -> 11121[label="",style="solid", color="burlywood", weight=9];
67.72/34.81	11121 -> 10322[label="",style="solid", color="burlywood", weight=3];
67.72/34.81	11122[label="vuz4160/Zero",fontsize=10,color="white",style="solid",shape="box"];10313 -> 11122[label="",style="solid", color="burlywood", weight=9];
67.72/34.81	11122 -> 10323[label="",style="solid", color="burlywood", weight=3];
67.72/34.81	10314[label="Zero",fontsize=16,color="green",shape="box"];10309[label="absReal1 vuz554 (not (primCmpInt (Pos (Succ vuz55500)) (fromInt (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];10309 -> 10318[label="",style="solid", color="black", weight=3];
67.72/34.81	10310[label="absReal1 vuz554 (not (primCmpInt (Pos Zero) (fromInt (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];10310 -> 10319[label="",style="solid", color="black", weight=3];
67.72/34.81	10311[label="absReal1 vuz554 (not (primCmpInt (Neg (Succ vuz55500)) (fromInt (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];10311 -> 10320[label="",style="solid", color="black", weight=3];
67.72/34.81	10312[label="absReal1 vuz554 (not (primCmpInt (Neg Zero) (fromInt (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];10312 -> 10321[label="",style="solid", color="black", weight=3];
67.72/34.81	10315[label="primRemInt vuz549 vuz542",fontsize=16,color="burlywood",shape="box"];11123[label="vuz549/Pos vuz5490",fontsize=10,color="white",style="solid",shape="box"];10315 -> 11123[label="",style="solid", color="burlywood", weight=9];
67.72/34.81	11123 -> 10324[label="",style="solid", color="burlywood", weight=3];
67.72/34.81	11124[label="vuz549/Neg vuz5490",fontsize=10,color="white",style="solid",shape="box"];10315 -> 11124[label="",style="solid", color="burlywood", weight=9];
67.72/34.81	11124 -> 10325[label="",style="solid", color="burlywood", weight=3];
67.72/34.81	10316 -> 10326[label="",style="dashed", color="red", weight=0];
67.72/34.81	10316[label="gcd0Gcd'0 vuz542 (vuz549 `rem` vuz542)",fontsize=16,color="magenta"];10316 -> 10327[label="",style="dashed", color="magenta", weight=3];
67.72/34.81	10317[label="vuz542",fontsize=16,color="green",shape="box"];10322[label="primDivNatS0 (Succ vuz41600) vuz54900 (primGEqNatS (Succ vuz41600) vuz54900)",fontsize=16,color="burlywood",shape="box"];11125[label="vuz54900/Succ vuz549000",fontsize=10,color="white",style="solid",shape="box"];10322 -> 11125[label="",style="solid", color="burlywood", weight=9];
67.72/34.81	11125 -> 10328[label="",style="solid", color="burlywood", weight=3];
67.72/34.81	11126[label="vuz54900/Zero",fontsize=10,color="white",style="solid",shape="box"];10322 -> 11126[label="",style="solid", color="burlywood", weight=9];
67.72/34.81	11126 -> 10329[label="",style="solid", color="burlywood", weight=3];
67.72/34.81	10323[label="primDivNatS0 Zero vuz54900 (primGEqNatS Zero vuz54900)",fontsize=16,color="burlywood",shape="box"];11127[label="vuz54900/Succ vuz549000",fontsize=10,color="white",style="solid",shape="box"];10323 -> 11127[label="",style="solid", color="burlywood", weight=9];
67.72/34.81	11127 -> 10330[label="",style="solid", color="burlywood", weight=3];
67.72/34.81	11128[label="vuz54900/Zero",fontsize=10,color="white",style="solid",shape="box"];10323 -> 11128[label="",style="solid", color="burlywood", weight=9];
67.72/34.81	11128 -> 10331[label="",style="solid", color="burlywood", weight=3];
67.72/34.81	10318[label="absReal1 vuz554 (not (primCmpInt (Pos (Succ vuz55500)) (Pos Zero) == LT))",fontsize=16,color="black",shape="box"];10318 -> 10332[label="",style="solid", color="black", weight=3];
67.72/34.81	10319[label="absReal1 vuz554 (not (primCmpInt (Pos Zero) (Pos Zero) == LT))",fontsize=16,color="black",shape="box"];10319 -> 10333[label="",style="solid", color="black", weight=3];
67.72/34.81	10320[label="absReal1 vuz554 (not (primCmpInt (Neg (Succ vuz55500)) (Pos Zero) == LT))",fontsize=16,color="black",shape="box"];10320 -> 10334[label="",style="solid", color="black", weight=3];
67.72/34.81	10321[label="absReal1 vuz554 (not (primCmpInt (Neg Zero) (Pos Zero) == LT))",fontsize=16,color="black",shape="box"];10321 -> 10335[label="",style="solid", color="black", weight=3];
67.72/34.81	10324[label="primRemInt (Pos vuz5490) vuz542",fontsize=16,color="burlywood",shape="box"];11129[label="vuz542/Pos vuz5420",fontsize=10,color="white",style="solid",shape="box"];10324 -> 11129[label="",style="solid", color="burlywood", weight=9];
67.72/34.81	11129 -> 10336[label="",style="solid", color="burlywood", weight=3];
67.72/34.81	11130[label="vuz542/Neg vuz5420",fontsize=10,color="white",style="solid",shape="box"];10324 -> 11130[label="",style="solid", color="burlywood", weight=9];
67.72/34.81	11130 -> 10337[label="",style="solid", color="burlywood", weight=3];
67.72/34.81	10325[label="primRemInt (Neg vuz5490) vuz542",fontsize=16,color="burlywood",shape="box"];11131[label="vuz542/Pos vuz5420",fontsize=10,color="white",style="solid",shape="box"];10325 -> 11131[label="",style="solid", color="burlywood", weight=9];
67.72/34.81	11131 -> 10338[label="",style="solid", color="burlywood", weight=3];
67.72/34.81	11132[label="vuz542/Neg vuz5420",fontsize=10,color="white",style="solid",shape="box"];10325 -> 11132[label="",style="solid", color="burlywood", weight=9];
67.72/34.81	11132 -> 10339[label="",style="solid", color="burlywood", weight=3];
67.72/34.81	10327 -> 10306[label="",style="dashed", color="red", weight=0];
67.72/34.81	10327[label="vuz549 `rem` vuz542",fontsize=16,color="magenta"];10326[label="gcd0Gcd'0 vuz542 vuz557",fontsize=16,color="black",shape="triangle"];10326 -> 10340[label="",style="solid", color="black", weight=3];
67.72/34.81	10328[label="primDivNatS0 (Succ vuz41600) (Succ vuz549000) (primGEqNatS (Succ vuz41600) (Succ vuz549000))",fontsize=16,color="black",shape="box"];10328 -> 10341[label="",style="solid", color="black", weight=3];
67.72/34.81	10329[label="primDivNatS0 (Succ vuz41600) Zero (primGEqNatS (Succ vuz41600) Zero)",fontsize=16,color="black",shape="box"];10329 -> 10342[label="",style="solid", color="black", weight=3];
67.72/34.81	10330[label="primDivNatS0 Zero (Succ vuz549000) (primGEqNatS Zero (Succ vuz549000))",fontsize=16,color="black",shape="box"];10330 -> 10343[label="",style="solid", color="black", weight=3];
67.72/34.81	10331[label="primDivNatS0 Zero Zero (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];10331 -> 10344[label="",style="solid", color="black", weight=3];
67.72/34.81	10332[label="absReal1 vuz554 (not (primCmpNat (Succ vuz55500) Zero == LT))",fontsize=16,color="black",shape="box"];10332 -> 10345[label="",style="solid", color="black", weight=3];
67.72/34.81	10333[label="absReal1 vuz554 (not (EQ == LT))",fontsize=16,color="black",shape="triangle"];10333 -> 10346[label="",style="solid", color="black", weight=3];
67.72/34.81	10334[label="absReal1 vuz554 (not (LT == LT))",fontsize=16,color="black",shape="box"];10334 -> 10347[label="",style="solid", color="black", weight=3];
67.72/34.81	10335 -> 10333[label="",style="dashed", color="red", weight=0];
67.72/34.81	10335[label="absReal1 vuz554 (not (EQ == LT))",fontsize=16,color="magenta"];10336[label="primRemInt (Pos vuz5490) (Pos vuz5420)",fontsize=16,color="burlywood",shape="box"];11133[label="vuz5420/Succ vuz54200",fontsize=10,color="white",style="solid",shape="box"];10336 -> 11133[label="",style="solid", color="burlywood", weight=9];
67.72/34.81	11133 -> 10348[label="",style="solid", color="burlywood", weight=3];
67.72/34.81	11134[label="vuz5420/Zero",fontsize=10,color="white",style="solid",shape="box"];10336 -> 11134[label="",style="solid", color="burlywood", weight=9];
67.72/34.81	11134 -> 10349[label="",style="solid", color="burlywood", weight=3];
67.72/34.81	10337[label="primRemInt (Pos vuz5490) (Neg vuz5420)",fontsize=16,color="burlywood",shape="box"];11135[label="vuz5420/Succ vuz54200",fontsize=10,color="white",style="solid",shape="box"];10337 -> 11135[label="",style="solid", color="burlywood", weight=9];
67.72/34.81	11135 -> 10350[label="",style="solid", color="burlywood", weight=3];
67.72/34.81	11136[label="vuz5420/Zero",fontsize=10,color="white",style="solid",shape="box"];10337 -> 11136[label="",style="solid", color="burlywood", weight=9];
67.72/34.81	11136 -> 10351[label="",style="solid", color="burlywood", weight=3];
67.72/34.81	10338[label="primRemInt (Neg vuz5490) (Pos vuz5420)",fontsize=16,color="burlywood",shape="box"];11137[label="vuz5420/Succ vuz54200",fontsize=10,color="white",style="solid",shape="box"];10338 -> 11137[label="",style="solid", color="burlywood", weight=9];
67.72/34.81	11137 -> 10352[label="",style="solid", color="burlywood", weight=3];
67.72/34.81	11138[label="vuz5420/Zero",fontsize=10,color="white",style="solid",shape="box"];10338 -> 11138[label="",style="solid", color="burlywood", weight=9];
67.72/34.81	11138 -> 10353[label="",style="solid", color="burlywood", weight=3];
67.72/34.81	10339[label="primRemInt (Neg vuz5490) (Neg vuz5420)",fontsize=16,color="burlywood",shape="box"];11139[label="vuz5420/Succ vuz54200",fontsize=10,color="white",style="solid",shape="box"];10339 -> 11139[label="",style="solid", color="burlywood", weight=9];
67.72/34.81	11139 -> 10354[label="",style="solid", color="burlywood", weight=3];
67.72/34.81	11140[label="vuz5420/Zero",fontsize=10,color="white",style="solid",shape="box"];10339 -> 11140[label="",style="solid", color="burlywood", weight=9];
67.72/34.81	11140 -> 10355[label="",style="solid", color="burlywood", weight=3];
67.72/34.81	10340 -> 10252[label="",style="dashed", color="red", weight=0];
67.72/34.81	10340[label="gcd0Gcd' vuz557 (vuz542 `rem` vuz557)",fontsize=16,color="magenta"];10340 -> 10356[label="",style="dashed", color="magenta", weight=3];
67.72/34.81	10340 -> 10357[label="",style="dashed", color="magenta", weight=3];
67.72/34.81	10341 -> 10629[label="",style="dashed", color="red", weight=0];
67.72/34.81	10341[label="primDivNatS0 (Succ vuz41600) (Succ vuz549000) (primGEqNatS vuz41600 vuz549000)",fontsize=16,color="magenta"];10341 -> 10630[label="",style="dashed", color="magenta", weight=3];
67.72/34.81	10341 -> 10631[label="",style="dashed", color="magenta", weight=3];
67.72/34.81	10341 -> 10632[label="",style="dashed", color="magenta", weight=3];
67.72/34.81	10341 -> 10633[label="",style="dashed", color="magenta", weight=3];
67.72/34.81	10342[label="primDivNatS0 (Succ vuz41600) Zero True",fontsize=16,color="black",shape="box"];10342 -> 10360[label="",style="solid", color="black", weight=3];
67.72/34.81	10343[label="primDivNatS0 Zero (Succ vuz549000) False",fontsize=16,color="black",shape="box"];10343 -> 10361[label="",style="solid", color="black", weight=3];
67.72/34.81	10344[label="primDivNatS0 Zero Zero True",fontsize=16,color="black",shape="box"];10344 -> 10362[label="",style="solid", color="black", weight=3];
67.72/34.81	10345[label="absReal1 vuz554 (not (GT == LT))",fontsize=16,color="black",shape="box"];10345 -> 10363[label="",style="solid", color="black", weight=3];
67.72/34.81	10346[label="absReal1 vuz554 (not False)",fontsize=16,color="black",shape="triangle"];10346 -> 10364[label="",style="solid", color="black", weight=3];
67.72/34.81	10347[label="absReal1 vuz554 (not True)",fontsize=16,color="black",shape="box"];10347 -> 10365[label="",style="solid", color="black", weight=3];
67.72/34.81	10348[label="primRemInt (Pos vuz5490) (Pos (Succ vuz54200))",fontsize=16,color="black",shape="box"];10348 -> 10366[label="",style="solid", color="black", weight=3];
67.72/34.81	10349[label="primRemInt (Pos vuz5490) (Pos Zero)",fontsize=16,color="black",shape="box"];10349 -> 10367[label="",style="solid", color="black", weight=3];
67.72/34.81	10350[label="primRemInt (Pos vuz5490) (Neg (Succ vuz54200))",fontsize=16,color="black",shape="box"];10350 -> 10368[label="",style="solid", color="black", weight=3];
67.72/34.81	10351[label="primRemInt (Pos vuz5490) (Neg Zero)",fontsize=16,color="black",shape="box"];10351 -> 10369[label="",style="solid", color="black", weight=3];
67.72/34.81	10352[label="primRemInt (Neg vuz5490) (Pos (Succ vuz54200))",fontsize=16,color="black",shape="box"];10352 -> 10370[label="",style="solid", color="black", weight=3];
67.72/34.81	10353[label="primRemInt (Neg vuz5490) (Pos Zero)",fontsize=16,color="black",shape="box"];10353 -> 10371[label="",style="solid", color="black", weight=3];
67.72/34.81	10354[label="primRemInt (Neg vuz5490) (Neg (Succ vuz54200))",fontsize=16,color="black",shape="box"];10354 -> 10372[label="",style="solid", color="black", weight=3];
67.72/34.81	10355[label="primRemInt (Neg vuz5490) (Neg Zero)",fontsize=16,color="black",shape="box"];10355 -> 10373[label="",style="solid", color="black", weight=3];
67.72/34.81	10356[label="vuz542",fontsize=16,color="green",shape="box"];10357[label="vuz557",fontsize=16,color="green",shape="box"];10630[label="vuz41600",fontsize=16,color="green",shape="box"];10631[label="vuz41600",fontsize=16,color="green",shape="box"];10632[label="vuz549000",fontsize=16,color="green",shape="box"];10633[label="vuz549000",fontsize=16,color="green",shape="box"];10629[label="primDivNatS0 (Succ vuz574) (Succ vuz575) (primGEqNatS vuz576 vuz577)",fontsize=16,color="burlywood",shape="triangle"];11141[label="vuz576/Succ vuz5760",fontsize=10,color="white",style="solid",shape="box"];10629 -> 11141[label="",style="solid", color="burlywood", weight=9];
67.72/34.81	11141 -> 10662[label="",style="solid", color="burlywood", weight=3];
67.72/34.81	11142[label="vuz576/Zero",fontsize=10,color="white",style="solid",shape="box"];10629 -> 11142[label="",style="solid", color="burlywood", weight=9];
67.72/34.81	11142 -> 10663[label="",style="solid", color="burlywood", weight=3];
67.72/34.81	10360[label="Succ (primDivNatS (primMinusNatS (Succ vuz41600) Zero) (Succ Zero))",fontsize=16,color="green",shape="box"];10360 -> 10378[label="",style="dashed", color="green", weight=3];
67.72/34.81	10361[label="Zero",fontsize=16,color="green",shape="box"];10362[label="Succ (primDivNatS (primMinusNatS Zero Zero) (Succ Zero))",fontsize=16,color="green",shape="box"];10362 -> 10379[label="",style="dashed", color="green", weight=3];
67.72/34.81	10363 -> 10346[label="",style="dashed", color="red", weight=0];
67.72/34.81	10363[label="absReal1 vuz554 (not False)",fontsize=16,color="magenta"];10364[label="absReal1 vuz554 True",fontsize=16,color="black",shape="box"];10364 -> 10380[label="",style="solid", color="black", weight=3];
67.72/34.81	10365[label="absReal1 vuz554 False",fontsize=16,color="black",shape="box"];10365 -> 10381[label="",style="solid", color="black", weight=3];
67.72/34.81	10366[label="Pos (primModNatS vuz5490 (Succ vuz54200))",fontsize=16,color="green",shape="box"];10366 -> 10382[label="",style="dashed", color="green", weight=3];
67.72/34.81	10367 -> 10275[label="",style="dashed", color="red", weight=0];
67.72/34.81	10367[label="error []",fontsize=16,color="magenta"];10368[label="Pos (primModNatS vuz5490 (Succ vuz54200))",fontsize=16,color="green",shape="box"];10368 -> 10383[label="",style="dashed", color="green", weight=3];
67.72/34.81	10369 -> 10275[label="",style="dashed", color="red", weight=0];
67.72/34.81	10369[label="error []",fontsize=16,color="magenta"];10370[label="Neg (primModNatS vuz5490 (Succ vuz54200))",fontsize=16,color="green",shape="box"];10370 -> 10384[label="",style="dashed", color="green", weight=3];
67.72/34.81	10371 -> 10275[label="",style="dashed", color="red", weight=0];
67.72/34.81	10371[label="error []",fontsize=16,color="magenta"];10372[label="Neg (primModNatS vuz5490 (Succ vuz54200))",fontsize=16,color="green",shape="box"];10372 -> 10385[label="",style="dashed", color="green", weight=3];
67.72/34.81	10373 -> 10275[label="",style="dashed", color="red", weight=0];
67.72/34.81	10373[label="error []",fontsize=16,color="magenta"];10662[label="primDivNatS0 (Succ vuz574) (Succ vuz575) (primGEqNatS (Succ vuz5760) vuz577)",fontsize=16,color="burlywood",shape="box"];11143[label="vuz577/Succ vuz5770",fontsize=10,color="white",style="solid",shape="box"];10662 -> 11143[label="",style="solid", color="burlywood", weight=9];
67.72/34.81	11143 -> 10670[label="",style="solid", color="burlywood", weight=3];
67.72/34.81	11144[label="vuz577/Zero",fontsize=10,color="white",style="solid",shape="box"];10662 -> 11144[label="",style="solid", color="burlywood", weight=9];
67.72/34.81	11144 -> 10671[label="",style="solid", color="burlywood", weight=3];
67.72/34.81	10663[label="primDivNatS0 (Succ vuz574) (Succ vuz575) (primGEqNatS Zero vuz577)",fontsize=16,color="burlywood",shape="box"];11145[label="vuz577/Succ vuz5770",fontsize=10,color="white",style="solid",shape="box"];10663 -> 11145[label="",style="solid", color="burlywood", weight=9];
67.72/34.81	11145 -> 10672[label="",style="solid", color="burlywood", weight=3];
67.72/34.81	11146[label="vuz577/Zero",fontsize=10,color="white",style="solid",shape="box"];10663 -> 11146[label="",style="solid", color="burlywood", weight=9];
67.72/34.81	11146 -> 10673[label="",style="solid", color="burlywood", weight=3];
67.72/34.81	10378 -> 10290[label="",style="dashed", color="red", weight=0];
67.72/34.81	10378[label="primDivNatS (primMinusNatS (Succ vuz41600) Zero) (Succ Zero)",fontsize=16,color="magenta"];10378 -> 10390[label="",style="dashed", color="magenta", weight=3];
67.72/34.81	10378 -> 10391[label="",style="dashed", color="magenta", weight=3];
67.72/34.81	10379 -> 10290[label="",style="dashed", color="red", weight=0];
67.72/34.81	10379[label="primDivNatS (primMinusNatS Zero Zero) (Succ Zero)",fontsize=16,color="magenta"];10379 -> 10392[label="",style="dashed", color="magenta", weight=3];
67.72/34.81	10379 -> 10393[label="",style="dashed", color="magenta", weight=3];
67.72/34.81	10380[label="vuz554",fontsize=16,color="green",shape="box"];10381[label="absReal0 vuz554 otherwise",fontsize=16,color="black",shape="box"];10381 -> 10394[label="",style="solid", color="black", weight=3];
67.72/34.81	10382[label="primModNatS vuz5490 (Succ vuz54200)",fontsize=16,color="burlywood",shape="triangle"];11147[label="vuz5490/Succ vuz54900",fontsize=10,color="white",style="solid",shape="box"];10382 -> 11147[label="",style="solid", color="burlywood", weight=9];
67.72/34.81	11147 -> 10395[label="",style="solid", color="burlywood", weight=3];
67.72/34.81	11148[label="vuz5490/Zero",fontsize=10,color="white",style="solid",shape="box"];10382 -> 11148[label="",style="solid", color="burlywood", weight=9];
67.72/34.81	11148 -> 10396[label="",style="solid", color="burlywood", weight=3];
67.72/34.81	10383 -> 10382[label="",style="dashed", color="red", weight=0];
67.72/34.81	10383[label="primModNatS vuz5490 (Succ vuz54200)",fontsize=16,color="magenta"];10383 -> 10397[label="",style="dashed", color="magenta", weight=3];
67.72/34.81	10384 -> 10382[label="",style="dashed", color="red", weight=0];
67.72/34.81	10384[label="primModNatS vuz5490 (Succ vuz54200)",fontsize=16,color="magenta"];10384 -> 10398[label="",style="dashed", color="magenta", weight=3];
67.72/34.81	10385 -> 10382[label="",style="dashed", color="red", weight=0];
67.72/34.81	10385[label="primModNatS vuz5490 (Succ vuz54200)",fontsize=16,color="magenta"];10385 -> 10399[label="",style="dashed", color="magenta", weight=3];
67.72/34.81	10385 -> 10400[label="",style="dashed", color="magenta", weight=3];
67.72/34.81	10670[label="primDivNatS0 (Succ vuz574) (Succ vuz575) (primGEqNatS (Succ vuz5760) (Succ vuz5770))",fontsize=16,color="black",shape="box"];10670 -> 10682[label="",style="solid", color="black", weight=3];
67.72/34.81	10671[label="primDivNatS0 (Succ vuz574) (Succ vuz575) (primGEqNatS (Succ vuz5760) Zero)",fontsize=16,color="black",shape="box"];10671 -> 10683[label="",style="solid", color="black", weight=3];
67.72/34.81	10672[label="primDivNatS0 (Succ vuz574) (Succ vuz575) (primGEqNatS Zero (Succ vuz5770))",fontsize=16,color="black",shape="box"];10672 -> 10684[label="",style="solid", color="black", weight=3];
67.72/34.81	10673[label="primDivNatS0 (Succ vuz574) (Succ vuz575) (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];10673 -> 10685[label="",style="solid", color="black", weight=3];
67.72/34.81	10390[label="primMinusNatS (Succ vuz41600) Zero",fontsize=16,color="black",shape="triangle"];10390 -> 10406[label="",style="solid", color="black", weight=3];
67.72/34.81	10391[label="Zero",fontsize=16,color="green",shape="box"];10392[label="primMinusNatS Zero Zero",fontsize=16,color="black",shape="triangle"];10392 -> 10407[label="",style="solid", color="black", weight=3];
67.72/34.81	10393[label="Zero",fontsize=16,color="green",shape="box"];10394[label="absReal0 vuz554 True",fontsize=16,color="black",shape="box"];10394 -> 10408[label="",style="solid", color="black", weight=3];
67.72/34.81	10395[label="primModNatS (Succ vuz54900) (Succ vuz54200)",fontsize=16,color="black",shape="box"];10395 -> 10409[label="",style="solid", color="black", weight=3];
67.72/34.81	10396[label="primModNatS Zero (Succ vuz54200)",fontsize=16,color="black",shape="box"];10396 -> 10410[label="",style="solid", color="black", weight=3];
67.72/34.81	10397[label="vuz54200",fontsize=16,color="green",shape="box"];10398[label="vuz5490",fontsize=16,color="green",shape="box"];10399[label="vuz5490",fontsize=16,color="green",shape="box"];10400[label="vuz54200",fontsize=16,color="green",shape="box"];10682 -> 10629[label="",style="dashed", color="red", weight=0];
67.72/34.81	10682[label="primDivNatS0 (Succ vuz574) (Succ vuz575) (primGEqNatS vuz5760 vuz5770)",fontsize=16,color="magenta"];10682 -> 10692[label="",style="dashed", color="magenta", weight=3];
67.72/34.81	10682 -> 10693[label="",style="dashed", color="magenta", weight=3];
67.72/34.81	10683[label="primDivNatS0 (Succ vuz574) (Succ vuz575) True",fontsize=16,color="black",shape="triangle"];10683 -> 10694[label="",style="solid", color="black", weight=3];
67.72/34.81	10684[label="primDivNatS0 (Succ vuz574) (Succ vuz575) False",fontsize=16,color="black",shape="box"];10684 -> 10695[label="",style="solid", color="black", weight=3];
67.72/34.81	10685 -> 10683[label="",style="dashed", color="red", weight=0];
67.72/34.81	10685[label="primDivNatS0 (Succ vuz574) (Succ vuz575) True",fontsize=16,color="magenta"];10406[label="Succ vuz41600",fontsize=16,color="green",shape="box"];10407[label="Zero",fontsize=16,color="green",shape="box"];10408 -> 7115[label="",style="dashed", color="red", weight=0];
67.72/34.81	10408[label="`negate` vuz554",fontsize=16,color="magenta"];10408 -> 10417[label="",style="dashed", color="magenta", weight=3];
67.72/34.81	10409[label="primModNatS0 vuz54900 vuz54200 (primGEqNatS vuz54900 vuz54200)",fontsize=16,color="burlywood",shape="box"];11149[label="vuz54900/Succ vuz549000",fontsize=10,color="white",style="solid",shape="box"];10409 -> 11149[label="",style="solid", color="burlywood", weight=9];
67.72/34.81	11149 -> 10418[label="",style="solid", color="burlywood", weight=3];
67.72/34.81	11150[label="vuz54900/Zero",fontsize=10,color="white",style="solid",shape="box"];10409 -> 11150[label="",style="solid", color="burlywood", weight=9];
67.72/34.81	11150 -> 10419[label="",style="solid", color="burlywood", weight=3];
67.72/34.81	10410[label="Zero",fontsize=16,color="green",shape="box"];10692[label="vuz5760",fontsize=16,color="green",shape="box"];10693[label="vuz5770",fontsize=16,color="green",shape="box"];10694[label="Succ (primDivNatS (primMinusNatS (Succ vuz574) (Succ vuz575)) (Succ (Succ vuz575)))",fontsize=16,color="green",shape="box"];10694 -> 10700[label="",style="dashed", color="green", weight=3];
67.72/34.81	10695[label="Zero",fontsize=16,color="green",shape="box"];10417[label="vuz554",fontsize=16,color="green",shape="box"];10418[label="primModNatS0 (Succ vuz549000) vuz54200 (primGEqNatS (Succ vuz549000) vuz54200)",fontsize=16,color="burlywood",shape="box"];11151[label="vuz54200/Succ vuz542000",fontsize=10,color="white",style="solid",shape="box"];10418 -> 11151[label="",style="solid", color="burlywood", weight=9];
67.72/34.81	11151 -> 10428[label="",style="solid", color="burlywood", weight=3];
67.72/34.81	11152[label="vuz54200/Zero",fontsize=10,color="white",style="solid",shape="box"];10418 -> 11152[label="",style="solid", color="burlywood", weight=9];
67.72/34.81	11152 -> 10429[label="",style="solid", color="burlywood", weight=3];
67.72/34.81	10419[label="primModNatS0 Zero vuz54200 (primGEqNatS Zero vuz54200)",fontsize=16,color="burlywood",shape="box"];11153[label="vuz54200/Succ vuz542000",fontsize=10,color="white",style="solid",shape="box"];10419 -> 11153[label="",style="solid", color="burlywood", weight=9];
67.72/34.81	11153 -> 10430[label="",style="solid", color="burlywood", weight=3];
67.72/34.81	11154[label="vuz54200/Zero",fontsize=10,color="white",style="solid",shape="box"];10419 -> 11154[label="",style="solid", color="burlywood", weight=9];
67.72/34.81	11154 -> 10431[label="",style="solid", color="burlywood", weight=3];
67.72/34.81	10700 -> 10290[label="",style="dashed", color="red", weight=0];
67.72/34.81	10700[label="primDivNatS (primMinusNatS (Succ vuz574) (Succ vuz575)) (Succ (Succ vuz575))",fontsize=16,color="magenta"];10700 -> 10704[label="",style="dashed", color="magenta", weight=3];
67.72/34.81	10700 -> 10705[label="",style="dashed", color="magenta", weight=3];
67.72/34.81	10428[label="primModNatS0 (Succ vuz549000) (Succ vuz542000) (primGEqNatS (Succ vuz549000) (Succ vuz542000))",fontsize=16,color="black",shape="box"];10428 -> 10439[label="",style="solid", color="black", weight=3];
67.72/34.81	10429[label="primModNatS0 (Succ vuz549000) Zero (primGEqNatS (Succ vuz549000) Zero)",fontsize=16,color="black",shape="box"];10429 -> 10440[label="",style="solid", color="black", weight=3];
67.72/34.81	10430[label="primModNatS0 Zero (Succ vuz542000) (primGEqNatS Zero (Succ vuz542000))",fontsize=16,color="black",shape="box"];10430 -> 10441[label="",style="solid", color="black", weight=3];
67.72/34.81	10431[label="primModNatS0 Zero Zero (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];10431 -> 10442[label="",style="solid", color="black", weight=3];
67.72/34.81	10704[label="primMinusNatS (Succ vuz574) (Succ vuz575)",fontsize=16,color="black",shape="box"];10704 -> 10709[label="",style="solid", color="black", weight=3];
67.72/34.81	10705[label="Succ vuz575",fontsize=16,color="green",shape="box"];10439 -> 10769[label="",style="dashed", color="red", weight=0];
67.72/34.81	10439[label="primModNatS0 (Succ vuz549000) (Succ vuz542000) (primGEqNatS vuz549000 vuz542000)",fontsize=16,color="magenta"];10439 -> 10770[label="",style="dashed", color="magenta", weight=3];
67.72/34.81	10439 -> 10771[label="",style="dashed", color="magenta", weight=3];
67.72/34.81	10439 -> 10772[label="",style="dashed", color="magenta", weight=3];
67.72/34.81	10439 -> 10773[label="",style="dashed", color="magenta", weight=3];
67.72/34.81	10440[label="primModNatS0 (Succ vuz549000) Zero True",fontsize=16,color="black",shape="box"];10440 -> 10452[label="",style="solid", color="black", weight=3];
67.72/34.81	10441[label="primModNatS0 Zero (Succ vuz542000) False",fontsize=16,color="black",shape="box"];10441 -> 10453[label="",style="solid", color="black", weight=3];
67.72/34.81	10442[label="primModNatS0 Zero Zero True",fontsize=16,color="black",shape="box"];10442 -> 10454[label="",style="solid", color="black", weight=3];
67.72/34.81	10709[label="primMinusNatS vuz574 vuz575",fontsize=16,color="burlywood",shape="triangle"];11155[label="vuz574/Succ vuz5740",fontsize=10,color="white",style="solid",shape="box"];10709 -> 11155[label="",style="solid", color="burlywood", weight=9];
67.72/34.81	11155 -> 10712[label="",style="solid", color="burlywood", weight=3];
67.72/34.81	11156[label="vuz574/Zero",fontsize=10,color="white",style="solid",shape="box"];10709 -> 11156[label="",style="solid", color="burlywood", weight=9];
67.72/34.81	11156 -> 10713[label="",style="solid", color="burlywood", weight=3];
67.72/34.81	10770[label="vuz549000",fontsize=16,color="green",shape="box"];10771[label="vuz542000",fontsize=16,color="green",shape="box"];10772[label="vuz549000",fontsize=16,color="green",shape="box"];10773[label="vuz542000",fontsize=16,color="green",shape="box"];10769[label="primModNatS0 (Succ vuz594) (Succ vuz595) (primGEqNatS vuz596 vuz597)",fontsize=16,color="burlywood",shape="triangle"];11157[label="vuz596/Succ vuz5960",fontsize=10,color="white",style="solid",shape="box"];10769 -> 11157[label="",style="solid", color="burlywood", weight=9];
67.72/34.81	11157 -> 10802[label="",style="solid", color="burlywood", weight=3];
67.72/34.81	11158[label="vuz596/Zero",fontsize=10,color="white",style="solid",shape="box"];10769 -> 11158[label="",style="solid", color="burlywood", weight=9];
67.72/34.81	11158 -> 10803[label="",style="solid", color="burlywood", weight=3];
67.72/34.81	10452 -> 10382[label="",style="dashed", color="red", weight=0];
67.72/34.81	10452[label="primModNatS (primMinusNatS (Succ vuz549000) Zero) (Succ Zero)",fontsize=16,color="magenta"];10452 -> 10467[label="",style="dashed", color="magenta", weight=3];
67.72/34.81	10452 -> 10468[label="",style="dashed", color="magenta", weight=3];
67.72/34.81	10453[label="Succ Zero",fontsize=16,color="green",shape="box"];10454 -> 10382[label="",style="dashed", color="red", weight=0];
67.72/34.81	10454[label="primModNatS (primMinusNatS Zero Zero) (Succ Zero)",fontsize=16,color="magenta"];10454 -> 10469[label="",style="dashed", color="magenta", weight=3];
67.72/34.81	10454 -> 10470[label="",style="dashed", color="magenta", weight=3];
67.72/34.81	10712[label="primMinusNatS (Succ vuz5740) vuz575",fontsize=16,color="burlywood",shape="box"];11159[label="vuz575/Succ vuz5750",fontsize=10,color="white",style="solid",shape="box"];10712 -> 11159[label="",style="solid", color="burlywood", weight=9];
67.72/34.81	11159 -> 10745[label="",style="solid", color="burlywood", weight=3];
67.72/34.81	11160[label="vuz575/Zero",fontsize=10,color="white",style="solid",shape="box"];10712 -> 11160[label="",style="solid", color="burlywood", weight=9];
67.72/34.81	11160 -> 10746[label="",style="solid", color="burlywood", weight=3];
67.72/34.81	10713[label="primMinusNatS Zero vuz575",fontsize=16,color="burlywood",shape="box"];11161[label="vuz575/Succ vuz5750",fontsize=10,color="white",style="solid",shape="box"];10713 -> 11161[label="",style="solid", color="burlywood", weight=9];
67.72/34.81	11161 -> 10747[label="",style="solid", color="burlywood", weight=3];
67.72/34.81	11162[label="vuz575/Zero",fontsize=10,color="white",style="solid",shape="box"];10713 -> 11162[label="",style="solid", color="burlywood", weight=9];
67.72/34.81	11162 -> 10748[label="",style="solid", color="burlywood", weight=3];
67.72/34.81	10802[label="primModNatS0 (Succ vuz594) (Succ vuz595) (primGEqNatS (Succ vuz5960) vuz597)",fontsize=16,color="burlywood",shape="box"];11163[label="vuz597/Succ vuz5970",fontsize=10,color="white",style="solid",shape="box"];10802 -> 11163[label="",style="solid", color="burlywood", weight=9];
67.72/34.81	11163 -> 10804[label="",style="solid", color="burlywood", weight=3];
67.72/34.81	11164[label="vuz597/Zero",fontsize=10,color="white",style="solid",shape="box"];10802 -> 11164[label="",style="solid", color="burlywood", weight=9];
67.72/34.81	11164 -> 10805[label="",style="solid", color="burlywood", weight=3];
67.72/34.81	10803[label="primModNatS0 (Succ vuz594) (Succ vuz595) (primGEqNatS Zero vuz597)",fontsize=16,color="burlywood",shape="box"];11165[label="vuz597/Succ vuz5970",fontsize=10,color="white",style="solid",shape="box"];10803 -> 11165[label="",style="solid", color="burlywood", weight=9];
67.72/34.81	11165 -> 10806[label="",style="solid", color="burlywood", weight=3];
67.72/34.81	11166[label="vuz597/Zero",fontsize=10,color="white",style="solid",shape="box"];10803 -> 11166[label="",style="solid", color="burlywood", weight=9];
67.72/34.81	11166 -> 10807[label="",style="solid", color="burlywood", weight=3];
67.72/34.81	10467 -> 10390[label="",style="dashed", color="red", weight=0];
67.72/34.81	10467[label="primMinusNatS (Succ vuz549000) Zero",fontsize=16,color="magenta"];10467 -> 10482[label="",style="dashed", color="magenta", weight=3];
67.72/34.81	10468[label="Zero",fontsize=16,color="green",shape="box"];10469 -> 10392[label="",style="dashed", color="red", weight=0];
67.72/34.81	10469[label="primMinusNatS Zero Zero",fontsize=16,color="magenta"];10470[label="Zero",fontsize=16,color="green",shape="box"];10745[label="primMinusNatS (Succ vuz5740) (Succ vuz5750)",fontsize=16,color="black",shape="box"];10745 -> 10755[label="",style="solid", color="black", weight=3];
67.72/34.81	10746[label="primMinusNatS (Succ vuz5740) Zero",fontsize=16,color="black",shape="box"];10746 -> 10756[label="",style="solid", color="black", weight=3];
67.72/34.81	10747[label="primMinusNatS Zero (Succ vuz5750)",fontsize=16,color="black",shape="box"];10747 -> 10757[label="",style="solid", color="black", weight=3];
67.72/34.81	10748[label="primMinusNatS Zero Zero",fontsize=16,color="black",shape="box"];10748 -> 10758[label="",style="solid", color="black", weight=3];
67.72/34.81	10804[label="primModNatS0 (Succ vuz594) (Succ vuz595) (primGEqNatS (Succ vuz5960) (Succ vuz5970))",fontsize=16,color="black",shape="box"];10804 -> 10808[label="",style="solid", color="black", weight=3];
67.72/34.81	10805[label="primModNatS0 (Succ vuz594) (Succ vuz595) (primGEqNatS (Succ vuz5960) Zero)",fontsize=16,color="black",shape="box"];10805 -> 10809[label="",style="solid", color="black", weight=3];
67.72/34.81	10806[label="primModNatS0 (Succ vuz594) (Succ vuz595) (primGEqNatS Zero (Succ vuz5970))",fontsize=16,color="black",shape="box"];10806 -> 10810[label="",style="solid", color="black", weight=3];
67.72/34.81	10807[label="primModNatS0 (Succ vuz594) (Succ vuz595) (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];10807 -> 10811[label="",style="solid", color="black", weight=3];
67.72/34.81	10482[label="vuz549000",fontsize=16,color="green",shape="box"];10755 -> 10709[label="",style="dashed", color="red", weight=0];
67.72/34.81	10755[label="primMinusNatS vuz5740 vuz5750",fontsize=16,color="magenta"];10755 -> 10765[label="",style="dashed", color="magenta", weight=3];
67.72/34.81	10755 -> 10766[label="",style="dashed", color="magenta", weight=3];
67.72/34.81	10756[label="Succ vuz5740",fontsize=16,color="green",shape="box"];10757[label="Zero",fontsize=16,color="green",shape="box"];10758[label="Zero",fontsize=16,color="green",shape="box"];10808 -> 10769[label="",style="dashed", color="red", weight=0];
67.72/34.81	10808[label="primModNatS0 (Succ vuz594) (Succ vuz595) (primGEqNatS vuz5960 vuz5970)",fontsize=16,color="magenta"];10808 -> 10812[label="",style="dashed", color="magenta", weight=3];
67.72/34.81	10808 -> 10813[label="",style="dashed", color="magenta", weight=3];
67.72/34.81	10809[label="primModNatS0 (Succ vuz594) (Succ vuz595) True",fontsize=16,color="black",shape="triangle"];10809 -> 10814[label="",style="solid", color="black", weight=3];
67.72/34.81	10810[label="primModNatS0 (Succ vuz594) (Succ vuz595) False",fontsize=16,color="black",shape="box"];10810 -> 10815[label="",style="solid", color="black", weight=3];
67.72/34.81	10811 -> 10809[label="",style="dashed", color="red", weight=0];
67.72/34.81	10811[label="primModNatS0 (Succ vuz594) (Succ vuz595) True",fontsize=16,color="magenta"];10765[label="vuz5740",fontsize=16,color="green",shape="box"];10766[label="vuz5750",fontsize=16,color="green",shape="box"];10812[label="vuz5970",fontsize=16,color="green",shape="box"];10813[label="vuz5960",fontsize=16,color="green",shape="box"];10814 -> 10382[label="",style="dashed", color="red", weight=0];
67.72/34.81	10814[label="primModNatS (primMinusNatS (Succ vuz594) (Succ vuz595)) (Succ (Succ vuz595))",fontsize=16,color="magenta"];10814 -> 10816[label="",style="dashed", color="magenta", weight=3];
67.72/34.81	10814 -> 10817[label="",style="dashed", color="magenta", weight=3];
67.72/34.81	10815[label="Succ (Succ vuz594)",fontsize=16,color="green",shape="box"];10816 -> 10709[label="",style="dashed", color="red", weight=0];
67.72/34.81	10816[label="primMinusNatS (Succ vuz594) (Succ vuz595)",fontsize=16,color="magenta"];10816 -> 10818[label="",style="dashed", color="magenta", weight=3];
67.72/34.81	10816 -> 10819[label="",style="dashed", color="magenta", weight=3];
67.72/34.81	10817[label="Succ vuz595",fontsize=16,color="green",shape="box"];10818[label="Succ vuz594",fontsize=16,color="green",shape="box"];10819[label="Succ vuz595",fontsize=16,color="green",shape="box"];}
67.72/34.81	
67.72/34.81	----------------------------------------
67.72/34.81	
67.72/34.81	(12)
67.72/34.81	Complex Obligation (AND)
67.72/34.81	
67.72/34.81	----------------------------------------
67.72/34.81	
67.72/34.81	(13)
67.72/34.81	Obligation:
67.72/34.81	Q DP problem:
67.72/34.81	The TRS P consists of the following rules:
67.72/34.81	
67.72/34.81	   new_primQuotInt8(Succ(vuz4090), Succ(vuz4080), vuz411, vuz410, vuz3190, vuz31700) -> new_primQuotInt8(vuz4090, vuz4080, vuz4090, vuz4080, vuz3190, vuz31700)
67.72/34.81	
67.72/34.81	R is empty.
67.72/34.81	Q is empty.
67.72/34.81	We have to consider all minimal (P,Q,R)-chains.
67.72/34.81	----------------------------------------
67.72/34.81	
67.72/34.81	(14) TransformationProof (EQUIVALENT)
67.72/34.81	By instantiating [LPAR04] the rule new_primQuotInt8(Succ(vuz4090), Succ(vuz4080), vuz411, vuz410, vuz3190, vuz31700) -> new_primQuotInt8(vuz4090, vuz4080, vuz4090, vuz4080, vuz3190, vuz31700) we obtained the following new rules [LPAR04]:
67.72/34.81	
67.72/34.81	   (new_primQuotInt8(Succ(x0), Succ(x1), Succ(x0), Succ(x1), z4, z5) -> new_primQuotInt8(x0, x1, x0, x1, z4, z5),new_primQuotInt8(Succ(x0), Succ(x1), Succ(x0), Succ(x1), z4, z5) -> new_primQuotInt8(x0, x1, x0, x1, z4, z5))
67.72/34.81	
67.72/34.81	
67.72/34.81	----------------------------------------
67.72/34.81	
67.72/34.81	(15)
67.72/34.81	Obligation:
67.72/34.81	Q DP problem:
67.72/34.81	The TRS P consists of the following rules:
67.72/34.81	
67.72/34.81	   new_primQuotInt8(Succ(x0), Succ(x1), Succ(x0), Succ(x1), z4, z5) -> new_primQuotInt8(x0, x1, x0, x1, z4, z5)
67.72/34.81	
67.72/34.81	R is empty.
67.72/34.81	Q is empty.
67.72/34.81	We have to consider all minimal (P,Q,R)-chains.
67.72/34.81	----------------------------------------
67.72/34.81	
67.72/34.81	(16) QDPSizeChangeProof (EQUIVALENT)
67.72/34.81	By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 
67.72/34.81	
67.72/34.81	From the DPs we obtained the following set of size-change graphs:
67.72/34.81	*new_primQuotInt8(Succ(x0), Succ(x1), Succ(x0), Succ(x1), z4, z5) -> new_primQuotInt8(x0, x1, x0, x1, z4, z5)
67.72/34.81	The graph contains the following edges 1 > 1, 3 > 1, 2 > 2, 4 > 2, 1 > 3, 3 > 3, 2 > 4, 4 > 4, 5 >= 5, 6 >= 6
67.72/34.81	
67.72/34.81	
67.72/34.81	----------------------------------------
67.72/34.81	
67.72/34.81	(17)
67.72/34.81	YES
67.72/34.81	
67.72/34.81	----------------------------------------
67.72/34.81	
67.72/34.81	(18)
67.72/34.81	Obligation:
67.72/34.81	Q DP problem:
67.72/34.81	The TRS P consists of the following rules:
67.72/34.81	
67.72/34.81	   new_iterate(vuz4, vuz3, vuz5) -> new_iterate(vuz4, vuz3, new_ps(new_ps(vuz4, new_negate(vuz3), ty_Int), vuz5, ty_Int))
67.72/34.81	
67.72/34.81	The TRS R consists of the following rules:
67.72/34.81	
67.72/34.81	   new_abs4(vuz3190, vuz3170) -> new_absReal1(new_sr(Neg(vuz3190), Pos(vuz3170)), new_sr(Neg(vuz3190), Pos(vuz3170)))
67.72/34.81	   new_primQuotInt44(vuz398) -> error([])
67.72/34.81	   new_primQuotInt80(vuz386, vuz389, Pos(vuz3180), vuz3190, vuz388, vuz387) -> new_primQuotInt30(vuz386, vuz389, new_primMulNat0(vuz3180, vuz3190), vuz388, new_primMulNat0(vuz3180, vuz3190), vuz387)
67.72/34.81	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.72/34.81	   new_primQuotInt56(Succ(vuz4570), Succ(vuz4560), vuz459, vuz458, vuz3190, vuz31700) -> new_primQuotInt56(vuz4570, vuz4560, vuz4570, vuz4560, vuz3190, vuz31700)
67.72/34.81	   new_primQuotInt27(vuz374, False, vuz511, vuz375) -> new_primQuotInt26(vuz374, vuz511, vuz375)
67.72/34.81	   new_primQuotInt62(Succ(vuz4010), Succ(vuz4000), vuz403, vuz402, vuz3190, vuz31700) -> new_primQuotInt62(vuz4010, vuz4000, vuz4010, vuz4000, vuz3190, vuz31700)
67.72/34.81	   new_quot(Neg(vuz3160), Pos(vuz3170), Neg(Zero), Neg(Zero), ty_Int) -> new_primQuotInt40(new_primMulNat0(vuz3160, vuz3170), new_primMulNat0(vuz3160, vuz3170), vuz3170)
67.72/34.81	   new_quot(Neg(vuz3160), Pos(vuz3170), Neg(Succ(vuz31800)), Neg(Succ(vuz31900)), ty_Int) -> new_primQuotInt74(new_primPlusNat1(new_primMulNat0(vuz31800, Succ(vuz31900)), Succ(vuz31900)), new_primMulNat0(vuz3160, vuz3170), new_primPlusNat1(new_primMulNat0(vuz31800, Succ(vuz31900)), Succ(vuz31900)), new_primMulNat0(vuz3160, vuz3170), vuz31900, vuz3170)
67.72/34.81	   new_abs1(vuz427) -> new_absReal1(Neg(vuz427), Neg(vuz427))
67.72/34.81	   new_quot(Neg(Zero), Neg(Succ(vuz31700)), Pos(vuz3180), Neg(vuz3190), ty_Int) -> new_primQuotInt56(Zero, new_primMulNat0(vuz3180, vuz3190), Zero, new_primMulNat0(vuz3180, vuz3190), vuz3190, vuz31700)
67.72/34.81	   new_quot(Neg(Zero), Neg(Zero), Neg(vuz3180), Pos(vuz3190), ty_Int) -> new_primQuotInt77(new_primMulNat0(vuz3180, vuz3190), new_primMulNat0(vuz3180, vuz3190), vuz3190)
67.72/34.81	   new_primQuotInt69(vuz366, True, vuz505, vuz367) -> new_primQuotInt83(vuz366, new_esEs(Pos(vuz367)), vuz505, vuz367)
67.72/34.81	   new_primDivNatS1(Zero, vuz54900) -> Zero
67.72/34.81	   new_quot(Neg(Succ(vuz31600)), Neg(Succ(vuz31700)), Neg(vuz3180), Pos(vuz3190), ty_Int) -> new_primQuotInt76(new_primPlusNat1(new_primMulNat0(vuz31600, Succ(vuz31700)), Succ(vuz31700)), new_primMulNat0(vuz3180, vuz3190), new_primPlusNat1(new_primMulNat0(vuz31600, Succ(vuz31700)), Succ(vuz31700)), new_primMulNat0(vuz3180, vuz3190), vuz3190, vuz31700)
67.72/34.81	   new_quot(Neg(vuz3160), Pos(vuz3170), Pos(Zero), Pos(Succ(vuz31900)), ty_Int) -> new_primQuotInt72(Zero, new_primMulNat0(vuz3160, vuz3170), Zero, new_primMulNat0(vuz3160, vuz3170), vuz31900, vuz3170)
67.72/34.81	   new_primQuotInt57(vuz382, vuz385, Neg(vuz3180), vuz3190, vuz384, vuz383) -> new_primQuotInt53(vuz382, vuz385, new_primMulNat0(vuz3180, vuz3190), vuz384, new_primMulNat0(vuz3180, vuz3190), vuz383)
67.72/34.81	   new_primDivNatS1(Succ(Succ(vuz41600)), Zero) -> Succ(new_primDivNatS1(new_primMinusNatS0(vuz41600), Zero))
67.72/34.81	   new_primQuotInt20(vuz446, True, vuz447, vuz3190, vuz3170) -> new_primQuotInt87(vuz446, new_esEs(new_sr(Neg(vuz3190), Pos(vuz3170))), vuz447, vuz3190, vuz3170)
67.72/34.81	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.72/34.81	   new_primQuotInt73(Zero, vuz445, vuz3170) -> new_primQuotInt18(Zero, Zero, Zero, vuz3170)
67.72/34.81	   new_primQuotInt80(vuz386, vuz389, Neg(vuz3180), vuz3190, vuz388, vuz387) -> new_primQuotInt29(vuz386, vuz389, new_primMulNat0(vuz3180, vuz3190), vuz388, new_primMulNat0(vuz3180, vuz3190), vuz387)
67.72/34.81	   new_primQuotInt15(vuz348, True, vuz349, vuz3190, vuz3170) -> new_primQuotInt55(vuz348)
67.72/34.81	   new_quot0(Neg(vuz3190), Pos(vuz3170), Pos(vuz3160), vuz318, ty_Int) -> new_primQuotInt57(new_primMulNat0(vuz3190, vuz3170), new_primMulNat0(vuz3160, vuz3170), vuz318, vuz3190, new_primMulNat0(vuz3160, vuz3170), new_primMulNat0(vuz3190, vuz3170))
67.72/34.81	   new_primQuotInt81(vuz390, vuz393, Pos(vuz3180), vuz3190, vuz392, vuz391) -> new_primQuotInt90(vuz390, vuz393, new_primMulNat0(vuz3180, vuz3190), vuz392, new_primMulNat0(vuz3180, vuz3190), vuz391)
67.72/34.81	   new_primQuotInt27(vuz374, True, vuz511, vuz375) -> new_primQuotInt55(vuz374)
67.72/34.81	   new_primQuotInt36(Zero, Zero, vuz411, vuz410, vuz3190, vuz31700) -> new_primQuotInt18(Zero, Zero, vuz3190, Succ(vuz31700))
67.72/34.81	   new_primDivNatS01(vuz574, vuz575, Zero, Succ(vuz5770)) -> Zero
67.72/34.81	   new_primQuotInt67(Succ(vuz4190), Succ(vuz4180), vuz421, vuz420, vuz31900, vuz3170) -> new_primQuotInt67(vuz4190, vuz4180, vuz4190, vuz4180, vuz31900, vuz3170)
67.72/34.81	   new_quot(Pos(vuz3160), Neg(vuz3170), Pos(vuz3180), Neg(vuz3190), ty_Int) -> new_primQuotInt48(new_primPlusNat1(new_primMulNat0(vuz3160, vuz3170), new_primMulNat0(vuz3180, vuz3190)), new_primPlusNat1(new_primMulNat0(vuz3160, vuz3170), new_primMulNat0(vuz3180, vuz3190)), vuz3190, vuz3170)
67.72/34.81	   new_primQuotInt50(vuz428, vuz429, vuz3190, vuz3170) -> new_primQuotInt51(vuz428, new_esEs(Neg(vuz429)), vuz429, vuz3190, vuz3170)
67.72/34.81	   new_primDivNatS02(vuz574, vuz575) -> Succ(new_primDivNatS1(new_primMinusNatS2(vuz574, vuz575), Succ(vuz575)))
67.72/34.81	   new_primQuotInt79(vuz370, vuz373, Pos(vuz3180), vuz3190, vuz372, vuz371) -> new_primQuotInt11(vuz370, vuz373, new_primMulNat0(vuz3180, vuz3190), vuz372, new_primMulNat0(vuz3180, vuz3190), vuz371)
67.72/34.81	   new_primQuotInt28(vuz374, vuz377, Neg(vuz3180), vuz3190, vuz376, vuz375) -> new_primQuotInt30(vuz374, vuz377, new_primMulNat0(vuz3180, vuz3190), vuz376, new_primMulNat0(vuz3180, vuz3190), vuz375)
67.72/34.81	   new_primQuotInt76(Zero, Succ(vuz4640), vuz467, vuz466, vuz3190, vuz31700) -> new_primQuotInt50(Succ(vuz4640), Succ(vuz4640), vuz3190, Succ(vuz31700))
67.72/34.81	   new_primQuotInt76(Zero, Zero, vuz467, vuz466, vuz3190, vuz31700) -> new_primQuotInt68(Zero, Zero, vuz3190, Succ(vuz31700))
67.72/34.81	   new_quot(Pos(vuz3160), Neg(vuz3170), Neg(Succ(vuz31800)), Neg(Zero), ty_Int) -> new_primQuotInt58(new_primMulNat0(vuz3160, vuz3170), new_primMulNat0(vuz3160, vuz3170), vuz3170)
67.72/34.81	   new_primQuotInt39(vuz374, Zero, Succ(vuz3770), vuz375) -> new_primQuotInt25(vuz374, new_primEqInt3(Succ(vuz3770)), Succ(vuz3770), vuz375)
67.72/34.81	   new_primQuotInt53(vuz378, vuz381, vuz493, vuz380, vuz492, vuz379) -> new_primQuotInt54(vuz378, new_primEqInt4(new_primPlusNat1(vuz381, vuz493)), new_primPlusNat1(vuz381, vuz493), vuz379)
67.72/34.81	   new_primQuotInt79(vuz370, vuz373, Neg(vuz3180), vuz3190, vuz372, vuz371) -> new_primQuotInt90(vuz370, vuz373, new_primMulNat0(vuz3180, vuz3190), vuz372, new_primMulNat0(vuz3180, vuz3190), vuz371)
67.72/34.81	   new_primDivNatS1(Succ(Zero), Succ(vuz549000)) -> Zero
67.72/34.81	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.72/34.81	   new_primQuotInt72(Zero, Zero, vuz441, vuz440, vuz31900, vuz3170) -> new_primQuotInt18(Zero, Zero, Succ(vuz31900), vuz3170)
67.72/34.81	   new_primQuotInt24(Succ(vuz4060), vuz407, vuz3190) -> new_primQuotInt19(Succ(vuz4060), Succ(vuz4060), vuz3190, Zero)
67.72/34.81	   new_primQuotInt67(Zero, Zero, vuz421, vuz420, vuz31900, vuz3170) -> new_primQuotInt68(Zero, Zero, Succ(vuz31900), vuz3170)
67.72/34.81	   new_quot(Pos(Succ(vuz31600)), Pos(Zero), Neg(vuz3180), Pos(vuz3190), ty_Int) -> new_primQuotInt16(new_primMulNat0(vuz3180, vuz3190), new_primMulNat0(vuz3180, vuz3190), vuz3190)
67.72/34.81	   new_quot0(Neg(vuz3190), Pos(vuz3170), Neg(vuz3160), vuz318, ty_Int) -> new_primQuotInt80(new_primMulNat0(vuz3190, vuz3170), new_primMulNat0(vuz3160, vuz3170), vuz318, vuz3190, new_primMulNat0(vuz3160, vuz3170), new_primMulNat0(vuz3190, vuz3170))
67.72/34.81	   new_absReal1(vuz554, Pos(Succ(vuz55500))) -> new_absReal10(vuz554)
67.72/34.81	   new_gcd0Gcd'10(False, vuz542, vuz549) -> new_gcd0Gcd'00(vuz542, new_rem(vuz549, vuz542))
67.72/34.81	   new_primQuotInt30(vuz374, vuz377, vuz491, vuz376, vuz490, vuz375) -> new_primQuotInt25(vuz374, new_primEqInt3(new_primPlusNat1(vuz377, vuz491)), new_primPlusNat1(vuz377, vuz491), vuz375)
67.72/34.81	   new_primQuotInt74(Zero, Succ(vuz4480), vuz451, vuz450, vuz31900, vuz3170) -> new_primQuotInt19(Succ(vuz4480), Succ(vuz4480), Succ(vuz31900), vuz3170)
67.72/34.81	   new_absReal1(vuz554, Pos(Zero)) -> new_absReal11(vuz554)
67.72/34.81	   new_primQuotInt74(Succ(vuz4490), Zero, vuz451, vuz450, vuz31900, vuz3170) -> new_primQuotInt22(Succ(vuz4490), Succ(vuz4490), Succ(vuz31900), vuz3170)
67.72/34.81	   new_primQuotInt25(vuz374, True, vuz511, vuz375) -> new_primQuotInt27(vuz374, new_esEs(Neg(vuz375)), vuz511, vuz375)
67.72/34.81	   new_absReal11(vuz554) -> new_absReal10(vuz554)
67.72/34.81	   new_primQuotInt56(Succ(vuz4570), Zero, vuz459, vuz458, vuz3190, vuz31700) -> new_primQuotInt45(Succ(vuz4570), Succ(vuz4570), vuz3190, Succ(vuz31700))
67.72/34.81	   new_primQuotInt32(vuz416, Neg(Succ(vuz54900))) -> Neg(new_primDivNatS1(vuz416, vuz54900))
67.72/34.81	   new_primQuotInt56(Zero, Succ(vuz4560), vuz459, vuz458, vuz3190, vuz31700) -> new_primQuotInt48(Succ(vuz4560), Succ(vuz4560), vuz3190, Succ(vuz31700))
67.72/34.81	   new_quot(Neg(vuz3160), Pos(vuz3170), Neg(Zero), Neg(Succ(vuz31900)), ty_Int) -> new_primQuotInt74(Zero, new_primMulNat0(vuz3160, vuz3170), Zero, new_primMulNat0(vuz3160, vuz3170), vuz31900, vuz3170)
67.72/34.81	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.72/34.81	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.72/34.81	   new_primQuotInt47(Zero, Succ(vuz4300), vuz433, vuz432, vuz31900, vuz3170) -> new_primQuotInt48(Succ(vuz4300), Succ(vuz4300), Succ(vuz31900), vuz3170)
67.72/34.81	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.72/34.81	   new_primEqInt4(Zero) -> new_primEqInt1
67.72/34.81	   new_quot(Pos(vuz3160), Neg(vuz3170), Pos(Succ(vuz31800)), Pos(Zero), ty_Int) -> new_primQuotInt71(new_primMulNat0(vuz3160, vuz3170), new_primMulNat0(vuz3160, vuz3170), vuz3170)
67.72/34.81	   new_primQuotInt64(vuz394, vuz397, Neg(vuz3180), vuz3190, vuz396, vuz395) -> new_primQuotInt65(vuz394, vuz397, new_primMulNat0(vuz3180, vuz3190), vuz396, new_primMulNat0(vuz3180, vuz3190), vuz395)
67.72/34.81	   new_quot(Neg(vuz3160), Pos(vuz3170), Pos(vuz3180), Neg(vuz3190), ty_Int) -> new_primQuotInt19(new_primPlusNat1(new_primMulNat0(vuz3160, vuz3170), new_primMulNat0(vuz3180, vuz3190)), new_primPlusNat1(new_primMulNat0(vuz3160, vuz3170), new_primMulNat0(vuz3180, vuz3190)), vuz3190, vuz3170)
67.72/34.81	   new_quot(Pos(vuz3160), Neg(vuz3170), Pos(Zero), Pos(Zero), ty_Int) -> new_primQuotInt71(new_primMulNat0(vuz3160, vuz3170), new_primMulNat0(vuz3160, vuz3170), vuz3170)
67.72/34.81	   new_quot0(Pos(vuz3190), Neg(vuz3170), Pos(vuz3160), vuz318, ty_Int) -> new_primQuotInt28(new_primMulNat0(vuz3190, vuz3170), new_primMulNat0(vuz3160, vuz3170), vuz318, vuz3190, new_primMulNat0(vuz3160, vuz3170), new_primMulNat0(vuz3190, vuz3170))
67.72/34.81	   new_primQuotInt11(vuz370, vuz373, vuz485, vuz372, vuz484, vuz371) -> new_primQuotInt12(vuz370, vuz485, vuz373, vuz371)
67.72/34.81	   new_primDivNatS01(vuz574, vuz575, Succ(vuz5760), Succ(vuz5770)) -> new_primDivNatS01(vuz574, vuz575, vuz5760, vuz5770)
67.72/34.81	   new_primQuotInt13(vuz348, False, vuz349, vuz3190, vuz3170) -> new_primQuotInt14(vuz348, vuz349, vuz3190, vuz3170)
67.72/34.81	   new_quot(Pos(Zero), Pos(Succ(vuz31700)), Pos(vuz3180), Neg(vuz3190), ty_Int) -> new_primQuotInt62(Zero, new_primMulNat0(vuz3180, vuz3190), Zero, new_primMulNat0(vuz3180, vuz3190), vuz3190, vuz31700)
67.72/34.81	   new_quot0(Pos(vuz3190), Pos(vuz3170), Neg(vuz3160), vuz318, ty_Int) -> new_primQuotInt79(new_primMulNat0(vuz3190, vuz3170), new_primMulNat0(vuz3160, vuz3170), vuz318, vuz3190, new_primMulNat0(vuz3160, vuz3170), new_primMulNat0(vuz3190, vuz3170))
67.72/34.81	   new_primQuotInt32(vuz416, Pos(Zero)) -> new_error
67.72/34.81	   new_primQuotInt20(vuz446, False, vuz447, vuz3190, vuz3170) -> new_primQuotInt88(vuz446, vuz447, vuz3190, vuz3170)
67.72/34.81	   new_primMulNat0(Zero, Zero) -> Zero
67.72/34.81	   new_quot(Pos(vuz3160), Neg(vuz3170), Pos(Zero), Pos(Succ(vuz31900)), ty_Int) -> new_primQuotInt67(Zero, new_primMulNat0(vuz3160, vuz3170), Zero, new_primMulNat0(vuz3160, vuz3170), vuz31900, vuz3170)
67.72/34.81	   new_abs0(vuz3190, vuz3170) -> new_absReal1(new_sr(Pos(vuz3190), Neg(vuz3170)), new_sr(Pos(vuz3190), Neg(vuz3170)))
67.72/34.81	   new_primQuotInt12(vuz366, Succ(vuz3690), Zero, vuz367) -> new_primQuotInt69(vuz366, new_primEqInt4(Succ(vuz3690)), Succ(vuz3690), vuz367)
67.72/34.81	   new_primQuotInt59(vuz378, vuz381, Neg(vuz3180), vuz3190, vuz380, vuz379) -> new_primQuotInt38(vuz378, vuz381, new_primMulNat0(vuz3180, vuz3190), vuz380, new_primMulNat0(vuz3180, vuz3190), vuz379)
67.72/34.81	   new_primQuotInt85(vuz370, vuz508, vuz371) -> new_primQuotInt31(vuz370, new_esEs(new_abs(vuz371)), new_abs1(vuz508), new_abs(vuz371))
67.72/34.81	   new_quot(Neg(vuz3160), Pos(vuz3170), Neg(Succ(vuz31800)), Neg(Zero), ty_Int) -> new_primQuotInt40(new_primMulNat0(vuz3160, vuz3170), new_primMulNat0(vuz3160, vuz3170), vuz3170)
67.72/34.81	   new_primQuotInt78(vuz366, vuz369, Pos(vuz3180), vuz3190, vuz368, vuz367) -> new_primQuotInt65(vuz366, vuz369, new_primMulNat0(vuz3180, vuz3190), vuz368, new_primMulNat0(vuz3180, vuz3190), vuz367)
67.72/34.81	   new_primQuotInt40(Succ(vuz4540), vuz455, vuz3170) -> new_primQuotInt19(Succ(vuz4540), Succ(vuz4540), Zero, vuz3170)
67.72/34.81	   new_primQuotInt29(vuz374, vuz377, vuz489, vuz376, vuz488, vuz375) -> new_primQuotInt39(vuz374, vuz489, vuz377, vuz375)
67.72/34.81	   new_primQuotInt19(vuz446, vuz447, vuz3190, vuz3170) -> new_primQuotInt20(vuz446, new_esEs(Neg(vuz447)), vuz447, vuz3190, vuz3170)
67.72/34.81	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.72/34.81	   new_primQuotInt74(Zero, Zero, vuz451, vuz450, vuz31900, vuz3170) -> new_primQuotInt22(Zero, Zero, Succ(vuz31900), vuz3170)
67.72/34.81	   new_primQuotInt51(vuz428, True, vuz429, vuz3190, vuz3170) -> new_primQuotInt82(vuz428, new_esEs(new_sr(Pos(vuz3190), Neg(vuz3170))), vuz429, vuz3190, vuz3170)
67.72/34.81	   new_primQuotInt90(vuz370, vuz373, vuz487, vuz372, vuz486, vuz371) -> new_primQuotInt91(vuz370, new_primEqInt3(new_primPlusNat1(vuz373, vuz487)), new_primPlusNat1(vuz373, vuz487), vuz371)
67.72/34.81	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.72/34.81	   new_primQuotInt32(vuz416, Pos(Succ(vuz54900))) -> Pos(new_primDivNatS1(vuz416, vuz54900))
67.72/34.81	   new_primQuotInt83(vuz366, True, vuz505, vuz367) -> new_primQuotInt44(vuz366)
67.72/34.81	   new_primQuotInt33(vuz398, False, vuz399, vuz3190, vuz3170) -> new_primQuotInt34(vuz398, vuz399, vuz3190, vuz3170)
67.72/34.81	   new_primQuotInt36(Succ(vuz4090), Zero, vuz411, vuz410, vuz3190, vuz31700) -> new_primQuotInt18(Succ(vuz4090), Succ(vuz4090), vuz3190, Succ(vuz31700))
67.72/34.81	   new_quot(Neg(Succ(vuz31600)), Neg(Zero), Pos(vuz3180), Neg(vuz3190), ty_Int) -> new_primQuotInt75(new_primMulNat0(vuz3180, vuz3190), new_primMulNat0(vuz3180, vuz3190), vuz3190)
67.72/34.81	   new_primQuotInt81(vuz390, vuz393, Neg(vuz3180), vuz3190, vuz392, vuz391) -> new_primQuotInt11(vuz390, vuz393, new_primMulNat0(vuz3180, vuz3190), vuz392, new_primMulNat0(vuz3180, vuz3190), vuz391)
67.72/34.81	   new_primQuotInt71(Succ(vuz4240), vuz425, vuz3170) -> new_primQuotInt50(Succ(vuz4240), Succ(vuz4240), Zero, vuz3170)
67.72/34.81	   new_primQuotInt40(Zero, vuz455, vuz3170) -> new_primQuotInt22(Zero, Zero, Zero, vuz3170)
67.72/34.81	   new_negate0(Neg(vuz300)) -> Pos(vuz300)
67.72/34.81	   new_primQuotInt62(Zero, Succ(vuz4000), vuz403, vuz402, vuz3190, vuz31700) -> new_primQuotInt19(Succ(vuz4000), Succ(vuz4000), vuz3190, Succ(vuz31700))
67.72/34.81	   new_reduce2Reduce1(vuz316, vuz317, vuz318, vuz319, False, ba) -> :%(new_quot(vuz316, vuz317, vuz318, vuz319, ba), new_quot0(vuz319, vuz317, vuz316, vuz318, ba))
67.72/34.81	   new_primQuotInt9(vuz428, vuz429, vuz3190, vuz3170) -> new_primQuotInt10(vuz428, new_esEs(new_abs0(vuz3190, vuz3170)), new_abs1(vuz429), new_abs0(vuz3190, vuz3170))
67.72/34.81	   new_primQuotInt73(Succ(vuz4440), vuz445, vuz3170) -> new_primQuotInt17(Succ(vuz4440), Succ(vuz4440), Zero, vuz3170)
67.72/34.81	   new_primQuotInt87(vuz446, True, vuz447, vuz3190, vuz3170) -> new_primQuotInt55(vuz446)
67.72/34.81	   new_primQuotInt71(Zero, vuz425, vuz3170) -> new_primQuotInt68(Zero, Zero, Zero, vuz3170)
67.72/34.81	   new_primQuotInt13(vuz348, True, vuz349, vuz3190, vuz3170) -> new_primQuotInt15(vuz348, new_esEs(new_sr(Pos(vuz3190), Pos(vuz3170))), vuz349, vuz3190, vuz3170)
67.72/34.81	   new_quot(Neg(vuz3160), Pos(vuz3170), Pos(Succ(vuz31800)), Pos(Succ(vuz31900)), ty_Int) -> new_primQuotInt72(new_primPlusNat1(new_primMulNat0(vuz31800, Succ(vuz31900)), Succ(vuz31900)), new_primMulNat0(vuz3160, vuz3170), new_primPlusNat1(new_primMulNat0(vuz31800, Succ(vuz31900)), Succ(vuz31900)), new_primMulNat0(vuz3160, vuz3170), vuz31900, vuz3170)
67.72/34.81	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.72/34.81	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.72/34.81	   new_primQuotInt69(vuz366, False, vuz505, vuz367) -> new_primQuotInt49(vuz366, vuz505, vuz367)
67.72/34.81	   new_primMinusNatS2(Zero, Zero) -> Zero
67.72/34.81	   new_primQuotInt84(vuz370, True, vuz508, vuz371) -> new_primQuotInt44(vuz370)
67.72/34.81	   new_primQuotInt25(vuz374, False, vuz511, vuz375) -> new_primQuotInt26(vuz374, vuz511, vuz375)
67.72/34.81	   new_primQuotInt39(vuz374, Zero, Zero, vuz375) -> new_primQuotInt54(vuz374, new_primEqInt4(Zero), Zero, vuz375)
67.72/34.81	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.72/34.81	   new_primQuotInt86(vuz416, False, vuz417, vuz3190, vuz3170) -> new_primQuotInt37(vuz416, vuz417, vuz3190, vuz3170)
67.72/34.81	   new_primQuotInt10(vuz428, False, vuz552, vuz544) -> new_primQuotInt70(vuz428, new_gcd0Gcd'2(vuz544, vuz552))
67.72/34.81	   new_quot(Neg(vuz3160), Neg(vuz3170), Neg(vuz3180), Neg(vuz3190), ty_Int) -> new_primQuotInt45(new_primPlusNat1(new_primMulNat0(vuz3160, vuz3170), new_primMulNat0(vuz3180, vuz3190)), new_primPlusNat1(new_primMulNat0(vuz3160, vuz3170), new_primMulNat0(vuz3180, vuz3190)), vuz3190, vuz3170)
67.72/34.81	   new_primDivNatS1(Succ(Zero), Zero) -> Succ(new_primDivNatS1(new_primMinusNatS1, Zero))
67.72/34.81	   new_quot(Pos(Zero), Pos(Zero), Neg(vuz3180), Pos(vuz3190), ty_Int) -> new_primQuotInt16(new_primMulNat0(vuz3180, vuz3190), new_primMulNat0(vuz3180, vuz3190), vuz3190)
67.72/34.81	   new_primQuotInt35(vuz398, True, vuz399, vuz3190, vuz3170) -> new_primQuotInt44(vuz398)
67.72/34.81	   new_quot(Neg(vuz3160), Pos(vuz3170), Neg(vuz3180), Pos(vuz3190), ty_Int) -> new_primQuotInt17(new_primPlusNat1(new_primMulNat0(vuz3160, vuz3170), new_primMulNat0(vuz3180, vuz3190)), new_primPlusNat1(new_primMulNat0(vuz3160, vuz3170), new_primMulNat0(vuz3180, vuz3190)), vuz3190, vuz3170)
67.72/34.81	   new_primQuotInt23(vuz416, False, vuz417, vuz3190, vuz3170) -> new_primQuotInt37(vuz416, vuz417, vuz3190, vuz3170)
67.72/34.81	   new_sr(Pos(vuz30610), Neg(vuz30710)) -> Neg(new_primMulNat0(vuz30610, vuz30710))
67.72/34.81	   new_sr(Neg(vuz30610), Pos(vuz30710)) -> Neg(new_primMulNat0(vuz30610, vuz30710))
67.72/34.81	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.72/34.81	   new_primPlusNat1(Succ(vuz33500), Succ(vuz3071000)) -> Succ(Succ(new_primPlusNat1(vuz33500, vuz3071000)))
67.72/34.81	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.72/34.81	   new_primQuotInt46(vuz360, False, vuz361, vuz3190, vuz3170) -> new_primQuotInt60(vuz360, vuz361, vuz3190, vuz3170)
67.72/34.81	   new_quot(Neg(vuz3160), Pos(vuz3170), Pos(Succ(vuz31800)), Pos(Zero), ty_Int) -> new_primQuotInt73(new_primMulNat0(vuz3160, vuz3170), new_primMulNat0(vuz3160, vuz3170), vuz3170)
67.72/34.81	   new_primDivNatS01(vuz574, vuz575, Zero, Zero) -> new_primDivNatS02(vuz574, vuz575)
67.72/34.81	   new_primQuotInt33(vuz398, True, vuz399, vuz3190, vuz3170) -> new_primQuotInt35(vuz398, new_esEs(new_sr(Pos(vuz3190), Pos(vuz3170))), vuz399, vuz3190, vuz3170)
67.72/34.81	   new_primQuotInt70(vuz428, Pos(Succ(vuz55200))) -> Neg(new_primDivNatS1(vuz428, vuz55200))
67.72/34.81	   new_absReal1(vuz554, Neg(Zero)) -> new_absReal11(vuz554)
67.72/34.81	   new_primQuotInt56(Zero, Zero, vuz459, vuz458, vuz3190, vuz31700) -> new_primQuotInt45(Zero, Zero, vuz3190, Succ(vuz31700))
67.72/34.81	   new_primQuotInt39(vuz374, Succ(vuz4890), Zero, vuz375) -> new_primQuotInt54(vuz374, new_primEqInt4(Succ(vuz4890)), Succ(vuz4890), vuz375)
67.72/34.81	   new_quot(Pos(vuz3160), Neg(vuz3170), Neg(Succ(vuz31800)), Neg(Succ(vuz31900)), ty_Int) -> new_primQuotInt47(new_primPlusNat1(new_primMulNat0(vuz31800, Succ(vuz31900)), Succ(vuz31900)), new_primMulNat0(vuz3160, vuz3170), new_primPlusNat1(new_primMulNat0(vuz31800, Succ(vuz31900)), Succ(vuz31900)), new_primMulNat0(vuz3160, vuz3170), vuz31900, vuz3170)
67.72/34.81	   new_primQuotInt63(vuz378, False, vuz514, vuz379) -> new_primQuotInt41(vuz378, vuz514, vuz379)
67.72/34.81	   new_abs2(vuz3190, vuz3170) -> new_absReal1(new_sr(Neg(vuz3190), Neg(vuz3170)), new_sr(Neg(vuz3190), Neg(vuz3170)))
67.72/34.81	   new_primQuotInt68(vuz354, vuz355, vuz3190, vuz3170) -> new_primQuotInt92(vuz354, new_esEs(Pos(vuz355)), vuz355, vuz3190, vuz3170)
67.72/34.81	   new_primQuotInt36(Zero, Succ(vuz4080), vuz411, vuz410, vuz3190, vuz31700) -> new_primQuotInt17(Succ(vuz4080), Succ(vuz4080), vuz3190, Succ(vuz31700))
67.72/34.81	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.72/34.81	   new_quot(Pos(Succ(vuz31600)), Pos(Succ(vuz31700)), Neg(vuz3180), Pos(vuz3190), ty_Int) -> new_primQuotInt36(new_primPlusNat1(new_primMulNat0(vuz31600, Succ(vuz31700)), Succ(vuz31700)), new_primMulNat0(vuz3180, vuz3190), new_primPlusNat1(new_primMulNat0(vuz31600, Succ(vuz31700)), Succ(vuz31700)), new_primMulNat0(vuz3180, vuz3190), vuz3190, vuz31700)
67.72/34.81	   new_primQuotInt77(Succ(vuz4700), vuz471, vuz3190) -> new_primQuotInt50(Succ(vuz4700), Succ(vuz4700), vuz3190, Zero)
67.72/34.81	   new_primQuotInt67(Succ(vuz4190), Zero, vuz421, vuz420, vuz31900, vuz3170) -> new_primQuotInt68(Succ(vuz4190), Succ(vuz4190), Succ(vuz31900), vuz3170)
67.72/34.81	   new_primQuotInt65(vuz366, vuz369, vuz481, vuz368, vuz480, vuz367) -> new_primQuotInt69(vuz366, new_primEqInt4(new_primPlusNat1(vuz369, vuz481)), new_primPlusNat1(vuz369, vuz481), vuz367)
67.72/34.81	   new_primQuotInt31(vuz416, False, vuz549, vuz542) -> new_primQuotInt32(vuz416, new_gcd0Gcd'2(vuz542, vuz549))
67.72/34.81	   new_primQuotInt82(vuz428, True, vuz429, vuz3190, vuz3170) -> new_primQuotInt55(vuz428)
67.72/34.81	   new_primQuotInt14(vuz348, vuz349, vuz3190, vuz3170) -> new_primQuotInt10(vuz348, new_esEs(new_abs3(vuz3190, vuz3170)), new_abs1(vuz349), new_abs3(vuz3190, vuz3170))
67.72/34.81	   new_gcd0Gcd'2(vuz542, vuz549) -> new_gcd0Gcd'10(new_esEs(new_rem(vuz549, vuz542)), vuz542, vuz549)
67.72/34.81	   new_primQuotInt77(Zero, vuz471, vuz3190) -> new_primQuotInt68(Zero, Zero, vuz3190, Zero)
67.72/34.81	   new_primQuotInt66(vuz426, False, vuz427, vuz3190, vuz3170) -> new_primQuotInt21(vuz426, vuz427, vuz3190, vuz3170)
67.72/34.81	   new_quot(Pos(vuz3160), Neg(vuz3170), Pos(Succ(vuz31800)), Pos(Succ(vuz31900)), ty_Int) -> new_primQuotInt67(new_primPlusNat1(new_primMulNat0(vuz31800, Succ(vuz31900)), Succ(vuz31900)), new_primMulNat0(vuz3160, vuz3170), new_primPlusNat1(new_primMulNat0(vuz31800, Succ(vuz31900)), Succ(vuz31900)), new_primMulNat0(vuz3160, vuz3170), vuz31900, vuz3170)
67.72/34.81	   new_primQuotInt48(vuz426, vuz427, vuz3190, vuz3170) -> new_primQuotInt66(vuz426, new_esEs(Neg(vuz427)), vuz427, vuz3190, vuz3170)
67.72/34.81	   new_quot(Pos(Succ(vuz31600)), Pos(Zero), Pos(vuz3180), Neg(vuz3190), ty_Int) -> new_primQuotInt24(new_primMulNat0(vuz3180, vuz3190), new_primMulNat0(vuz3180, vuz3190), vuz3190)
67.72/34.81	   new_primQuotInt22(vuz416, vuz417, vuz3190, vuz3170) -> new_primQuotInt23(vuz416, new_esEs(Pos(vuz417)), vuz417, vuz3190, vuz3170)
67.72/34.81	   new_sr(Neg(vuz30610), Neg(vuz30710)) -> Pos(new_primMulNat0(vuz30610, vuz30710))
67.72/34.81	   new_primDivNatS01(vuz574, vuz575, Succ(vuz5760), Zero) -> new_primDivNatS02(vuz574, vuz575)
67.72/34.81	   new_primQuotInt89(vuz426, False, vuz427, vuz3190, vuz3170) -> new_primQuotInt21(vuz426, vuz427, vuz3190, vuz3170)
67.72/34.81	   new_esEs0(vuz3061, vuz3071, ty_Integer) -> error([])
67.72/34.81	   new_primQuotInt87(vuz446, False, vuz447, vuz3190, vuz3170) -> new_primQuotInt88(vuz446, vuz447, vuz3190, vuz3170)
67.72/34.81	   new_negate0(Pos(vuz300)) -> Neg(vuz300)
67.72/34.81	   new_primQuotInt64(vuz394, vuz397, Pos(vuz3180), vuz3190, vuz396, vuz395) -> new_primQuotInt52(vuz394, vuz397, new_primMulNat0(vuz3180, vuz3190), vuz396, new_primMulNat0(vuz3180, vuz3190), vuz395)
67.72/34.81	   new_primQuotInt88(vuz446, vuz447, vuz3190, vuz3170) -> new_primQuotInt10(vuz446, new_esEs(new_abs4(vuz3190, vuz3170)), new_abs1(vuz447), new_abs4(vuz3190, vuz3170))
67.72/34.81	   new_primQuotInt42(vuz354, True, vuz355, vuz3190, vuz3170) -> new_primQuotInt44(vuz354)
67.72/34.81	   new_primQuotInt76(Succ(vuz4650), Succ(vuz4640), vuz467, vuz466, vuz3190, vuz31700) -> new_primQuotInt76(vuz4650, vuz4640, vuz4650, vuz4640, vuz3190, vuz31700)
67.72/34.81	   new_primQuotInt72(Succ(vuz4390), Zero, vuz441, vuz440, vuz31900, vuz3170) -> new_primQuotInt18(Succ(vuz4390), Succ(vuz4390), Succ(vuz31900), vuz3170)
67.72/34.81	   new_primQuotInt59(vuz378, vuz381, Pos(vuz3180), vuz3190, vuz380, vuz379) -> new_primQuotInt53(vuz378, vuz381, new_primMulNat0(vuz3180, vuz3190), vuz380, new_primMulNat0(vuz3180, vuz3190), vuz379)
67.72/34.81	   new_primQuotInt75(Zero, vuz463, vuz3190) -> new_primQuotInt45(Zero, Zero, vuz3190, Zero)
67.72/34.81	   new_primEqInt3(Zero) -> new_primEqInt2
67.72/34.81	   new_primMinusNatS1 -> Zero
67.72/34.81	   new_negate(:%(vuz30, vuz31)) -> :%(new_negate0(vuz30), vuz31)
67.72/34.81	   new_primQuotInt70(vuz428, Neg(Zero)) -> new_error
67.72/34.81	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.72/34.81	   new_quot(Pos(vuz3160), Pos(vuz3170), Neg(vuz3180), Neg(vuz3190), ty_Int) -> new_primQuotInt22(new_primPlusNat1(new_primMulNat0(vuz3160, vuz3170), new_primMulNat0(vuz3180, vuz3190)), new_primPlusNat1(new_primMulNat0(vuz3160, vuz3170), new_primMulNat0(vuz3180, vuz3190)), vuz3190, vuz3170)
67.72/34.81	   new_gcd0Gcd'10(True, vuz542, vuz549) -> vuz542
67.72/34.81	   new_primQuotInt12(vuz366, Succ(vuz3690), Succ(vuz4830), vuz367) -> new_primQuotInt12(vuz366, vuz3690, vuz4830, vuz367)
67.72/34.81	   new_primQuotInt57(vuz382, vuz385, Pos(vuz3180), vuz3190, vuz384, vuz383) -> new_primQuotInt38(vuz382, vuz385, new_primMulNat0(vuz3180, vuz3190), vuz384, new_primMulNat0(vuz3180, vuz3190), vuz383)
67.72/34.81	   new_primEqInt4(Succ(vuz3250)) -> new_primEqInt(vuz3250)
67.72/34.81	   new_primQuotInt78(vuz366, vuz369, Neg(vuz3180), vuz3190, vuz368, vuz367) -> new_primQuotInt52(vuz366, vuz369, new_primMulNat0(vuz3180, vuz3190), vuz368, new_primMulNat0(vuz3180, vuz3190), vuz367)
67.72/34.81	   new_quot0(Neg(vuz3190), Neg(vuz3170), Neg(vuz3160), vuz318, ty_Int) -> new_primQuotInt64(new_primMulNat0(vuz3190, vuz3170), new_primMulNat0(vuz3160, vuz3170), vuz318, vuz3190, new_primMulNat0(vuz3160, vuz3170), new_primMulNat0(vuz3190, vuz3170))
67.72/34.81	   new_quot(Pos(vuz3160), Neg(vuz3170), Neg(Zero), Neg(Succ(vuz31900)), ty_Int) -> new_primQuotInt47(Zero, new_primMulNat0(vuz3160, vuz3170), Zero, new_primMulNat0(vuz3160, vuz3170), vuz31900, vuz3170)
67.72/34.81	   new_absReal10(vuz554) -> vuz554
67.72/34.81	   new_primQuotInt52(vuz366, vuz369, vuz483, vuz368, vuz482, vuz367) -> new_primQuotInt12(vuz366, vuz369, vuz483, vuz367)
67.72/34.81	   new_primQuotInt86(vuz416, True, vuz417, vuz3190, vuz3170) -> new_primQuotInt44(vuz416)
67.72/34.81	   new_primQuotInt45(vuz360, vuz361, vuz3190, vuz3170) -> new_primQuotInt46(vuz360, new_esEs(Pos(vuz361)), vuz361, vuz3190, vuz3170)
67.72/34.81	   new_primQuotInt12(vuz366, Zero, Succ(vuz4830), vuz367) -> new_primQuotInt91(vuz366, new_primEqInt3(Succ(vuz4830)), Succ(vuz4830), vuz367)
67.72/34.81	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.72/34.81	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.72/34.81	   new_primQuotInt17(vuz348, vuz349, vuz3190, vuz3170) -> new_primQuotInt13(vuz348, new_esEs(Neg(vuz349)), vuz349, vuz3190, vuz3170)
67.72/34.81	   new_primQuotInt67(Zero, Succ(vuz4180), vuz421, vuz420, vuz31900, vuz3170) -> new_primQuotInt50(Succ(vuz4180), Succ(vuz4180), Succ(vuz31900), vuz3170)
67.72/34.81	   new_primQuotInt92(vuz354, False, vuz355, vuz3190, vuz3170) -> new_primQuotInt43(vuz354, vuz355, vuz3190, vuz3170)
67.72/34.81	   new_quot(Pos(Zero), Pos(Zero), Pos(vuz3180), Neg(vuz3190), ty_Int) -> new_primQuotInt24(new_primMulNat0(vuz3180, vuz3190), new_primMulNat0(vuz3180, vuz3190), vuz3190)
67.72/34.81	   new_primQuotInt75(Succ(vuz4620), vuz463, vuz3190) -> new_primQuotInt48(Succ(vuz4620), Succ(vuz4620), vuz3190, Zero)
67.72/34.81	   new_primQuotInt70(vuz428, Neg(Succ(vuz55200))) -> Pos(new_primDivNatS1(vuz428, vuz55200))
67.72/34.81	   new_quot(Pos(vuz3160), Pos(vuz3170), Pos(vuz3180), Pos(vuz3190), ty_Int) -> new_primQuotInt18(new_primPlusNat1(new_primMulNat0(vuz3160, vuz3170), new_primMulNat0(vuz3180, vuz3190)), new_primPlusNat1(new_primMulNat0(vuz3160, vuz3170), new_primMulNat0(vuz3180, vuz3190)), vuz3190, vuz3170)
67.72/34.81	   new_primPlusNat0(Succ(vuz3350), vuz307100) -> Succ(Succ(new_primPlusNat1(vuz3350, vuz307100)))
67.72/34.81	   new_primQuotInt84(vuz370, False, vuz508, vuz371) -> new_primQuotInt85(vuz370, vuz508, vuz371)
67.72/34.81	   new_primQuotInt42(vuz354, False, vuz355, vuz3190, vuz3170) -> new_primQuotInt43(vuz354, vuz355, vuz3190, vuz3170)
67.72/34.81	   new_primQuotInt43(vuz354, vuz355, vuz3190, vuz3170) -> new_primQuotInt31(vuz354, new_esEs(new_abs0(vuz3190, vuz3170)), new_abs(vuz355), new_abs0(vuz3190, vuz3170))
67.72/34.81	   new_primEqInt2 -> True
67.72/34.81	   new_primQuotInt62(Zero, Zero, vuz403, vuz402, vuz3190, vuz31700) -> new_primQuotInt22(Zero, Zero, vuz3190, Succ(vuz31700))
67.72/34.81	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.72/34.81	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.72/34.81	   new_primPlusNat1(Zero, Zero) -> Zero
67.72/34.81	   new_primQuotInt16(Succ(vuz4140), vuz415, vuz3190) -> new_primQuotInt17(Succ(vuz4140), Succ(vuz4140), vuz3190, Zero)
67.72/34.81	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.72/34.81	   new_primMulNat0(Succ(vuz306100), Zero) -> Zero
67.72/34.81	   new_primMulNat0(Zero, Succ(vuz307100)) -> Zero
67.72/34.81	   new_primQuotInt16(Zero, vuz415, vuz3190) -> new_primQuotInt18(Zero, Zero, vuz3190, Zero)
67.72/34.81	   new_sr(Pos(vuz30610), Pos(vuz30710)) -> Pos(new_primMulNat0(vuz30610, vuz30710))
67.72/34.81	   new_primQuotInt55(vuz426) -> error([])
67.72/34.81	   new_primQuotInt12(vuz366, Zero, Zero, vuz367) -> new_primQuotInt69(vuz366, new_primEqInt4(Zero), Zero, vuz367)
67.72/34.81	   new_primPlusNat0(Zero, vuz307100) -> Succ(vuz307100)
67.72/34.81	   new_primQuotInt92(vuz354, True, vuz355, vuz3190, vuz3170) -> new_primQuotInt42(vuz354, new_esEs(new_sr(Pos(vuz3190), Neg(vuz3170))), vuz355, vuz3190, vuz3170)
67.72/34.81	   new_primQuotInt72(Zero, Succ(vuz4380), vuz441, vuz440, vuz31900, vuz3170) -> new_primQuotInt17(Succ(vuz4380), Succ(vuz4380), Succ(vuz31900), vuz3170)
67.72/34.81	   new_quot(Pos(Succ(vuz31600)), Pos(Succ(vuz31700)), Pos(vuz3180), Neg(vuz3190), ty_Int) -> new_primQuotInt62(new_primPlusNat1(new_primMulNat0(vuz31600, Succ(vuz31700)), Succ(vuz31700)), new_primMulNat0(vuz3180, vuz3190), new_primPlusNat1(new_primMulNat0(vuz31600, Succ(vuz31700)), Succ(vuz31700)), new_primMulNat0(vuz3180, vuz3190), vuz3190, vuz31700)
67.72/34.81	   new_primQuotInt21(vuz426, vuz427, vuz3190, vuz3170) -> new_primQuotInt10(vuz426, new_esEs(new_abs2(vuz3190, vuz3170)), new_abs1(vuz427), new_abs2(vuz3190, vuz3170))
67.72/34.81	   new_primQuotInt91(vuz370, True, vuz508, vuz371) -> new_primQuotInt84(vuz370, new_esEs(Pos(vuz371)), vuz508, vuz371)
67.72/34.81	   new_primQuotInt51(vuz428, False, vuz429, vuz3190, vuz3170) -> new_primQuotInt9(vuz428, vuz429, vuz3190, vuz3170)
67.72/34.81	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.72/34.81	   new_primQuotInt47(Succ(vuz4310), Zero, vuz433, vuz432, vuz31900, vuz3170) -> new_primQuotInt45(Succ(vuz4310), Succ(vuz4310), Succ(vuz31900), vuz3170)
67.72/34.81	   new_primQuotInt83(vuz366, False, vuz505, vuz367) -> new_primQuotInt49(vuz366, vuz505, vuz367)
67.72/34.81	   new_quot(Neg(Zero), Neg(Zero), Pos(vuz3180), Neg(vuz3190), ty_Int) -> new_primQuotInt75(new_primMulNat0(vuz3180, vuz3190), new_primMulNat0(vuz3180, vuz3190), vuz3190)
67.72/34.81	   new_primEqInt0(vuz3260) -> False
67.72/34.81	   new_primQuotInt18(vuz398, vuz399, vuz3190, vuz3170) -> new_primQuotInt33(vuz398, new_esEs(Pos(vuz399)), vuz399, vuz3190, vuz3170)
67.72/34.81	   new_abs3(vuz3190, vuz3170) -> new_absReal1(new_sr(Pos(vuz3190), Pos(vuz3170)), new_sr(Pos(vuz3190), Pos(vuz3170)))
67.72/34.81	   new_quot(Neg(vuz3160), Pos(vuz3170), Pos(Zero), Pos(Zero), ty_Int) -> new_primQuotInt73(new_primMulNat0(vuz3160, vuz3170), new_primMulNat0(vuz3160, vuz3170), vuz3170)
67.72/34.81	   new_primQuotInt28(vuz374, vuz377, Pos(vuz3180), vuz3190, vuz376, vuz375) -> new_primQuotInt29(vuz374, vuz377, new_primMulNat0(vuz3180, vuz3190), vuz376, new_primMulNat0(vuz3180, vuz3190), vuz375)
67.72/34.81	   new_primQuotInt58(Succ(vuz4360), vuz437, vuz3170) -> new_primQuotInt48(Succ(vuz4360), Succ(vuz4360), Zero, vuz3170)
67.72/34.81	   new_quot(Neg(vuz3160), Neg(vuz3170), Pos(vuz3180), Pos(vuz3190), ty_Int) -> new_primQuotInt68(new_primPlusNat1(new_primMulNat0(vuz3160, vuz3170), new_primMulNat0(vuz3180, vuz3190)), new_primPlusNat1(new_primMulNat0(vuz3160, vuz3170), new_primMulNat0(vuz3180, vuz3190)), vuz3190, vuz3170)
67.72/34.81	   new_primMulNat0(Succ(vuz306100), Succ(vuz307100)) -> new_primPlusNat0(new_primMulNat0(vuz306100, Succ(vuz307100)), vuz307100)
67.72/34.81	   new_primQuotInt10(vuz428, True, vuz552, vuz544) -> new_primQuotInt70(vuz428, vuz552)
67.72/34.81	   new_primQuotInt49(vuz366, vuz505, vuz367) -> new_primQuotInt31(vuz366, new_esEs(new_abs(vuz367)), new_abs(vuz505), new_abs(vuz367))
67.72/34.81	   new_primEqInt3(Succ(vuz3260)) -> new_primEqInt0(vuz3260)
67.72/34.81	   new_primQuotInt61(vuz360, False, vuz361, vuz3190, vuz3170) -> new_primQuotInt60(vuz360, vuz361, vuz3190, vuz3170)
67.72/34.81	   new_primQuotInt61(vuz360, True, vuz361, vuz3190, vuz3170) -> new_primQuotInt44(vuz360)
67.72/34.81	   new_primQuotInt54(vuz378, True, vuz514, vuz379) -> new_primQuotInt63(vuz378, new_esEs(Neg(vuz379)), vuz514, vuz379)
67.72/34.81	   new_primPlusNat1(Succ(vuz33500), Zero) -> Succ(vuz33500)
67.72/34.81	   new_primPlusNat1(Zero, Succ(vuz3071000)) -> Succ(vuz3071000)
67.72/34.81	   new_primQuotInt82(vuz428, False, vuz429, vuz3190, vuz3170) -> new_primQuotInt9(vuz428, vuz429, vuz3190, vuz3170)
67.72/34.81	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.72/34.81	   new_primQuotInt74(Succ(vuz4490), Succ(vuz4480), vuz451, vuz450, vuz31900, vuz3170) -> new_primQuotInt74(vuz4490, vuz4480, vuz4490, vuz4480, vuz31900, vuz3170)
67.72/34.81	   new_primQuotInt38(vuz378, vuz381, vuz495, vuz380, vuz494, vuz379) -> new_primQuotInt39(vuz378, vuz381, vuz495, vuz379)
67.72/34.81	   new_primQuotInt66(vuz426, True, vuz427, vuz3190, vuz3170) -> new_primQuotInt89(vuz426, new_esEs(new_sr(Neg(vuz3190), Neg(vuz3170))), vuz427, vuz3190, vuz3170)
67.72/34.81	   new_quot(Pos(vuz3160), Neg(vuz3170), Neg(Zero), Neg(Zero), ty_Int) -> new_primQuotInt58(new_primMulNat0(vuz3160, vuz3170), new_primMulNat0(vuz3160, vuz3170), vuz3170)
67.72/34.81	   new_primQuotInt24(Zero, vuz407, vuz3190) -> new_primQuotInt22(Zero, Zero, vuz3190, Zero)
67.72/34.81	   new_quot0(vuz319, vuz317, vuz316, vuz318, ty_Integer) -> error([])
67.72/34.81	   new_primQuotInt70(vuz428, Pos(Zero)) -> new_error
67.72/34.81	   new_esEs0(vuz3061, vuz3071, ty_Int) -> new_esEs(new_sr(vuz3061, vuz3071))
67.72/34.81	   new_primQuotInt76(Succ(vuz4650), Zero, vuz467, vuz466, vuz3190, vuz31700) -> new_primQuotInt68(Succ(vuz4650), Succ(vuz4650), vuz3190, Succ(vuz31700))
67.72/34.81	   new_primDivNatS1(Succ(Succ(vuz41600)), Succ(vuz549000)) -> new_primDivNatS01(vuz41600, vuz549000, vuz41600, vuz549000)
67.72/34.81	   new_primEqInt1 -> True
67.72/34.81	   new_quot0(Pos(vuz3190), Neg(vuz3170), Neg(vuz3160), vuz318, ty_Int) -> new_primQuotInt59(new_primMulNat0(vuz3190, vuz3170), new_primMulNat0(vuz3160, vuz3170), vuz318, vuz3190, new_primMulNat0(vuz3160, vuz3170), new_primMulNat0(vuz3190, vuz3170))
67.72/34.81	   new_primQuotInt41(vuz378, vuz514, vuz379) -> new_primQuotInt10(vuz378, new_esEs(new_abs1(vuz379)), new_abs(vuz514), new_abs1(vuz379))
67.72/34.81	   new_primEqInt(vuz3250) -> False
67.72/34.81	   new_ps(:%(vuz3060, vuz3061), :%(vuz3070, vuz3071), h) -> new_reduce2Reduce1(vuz3060, vuz3071, vuz3070, vuz3061, new_esEs0(vuz3061, vuz3071, h), h)
67.72/34.81	   new_primQuotInt54(vuz378, False, vuz514, vuz379) -> new_primQuotInt41(vuz378, vuz514, vuz379)
67.72/34.81	   new_primQuotInt23(vuz416, True, vuz417, vuz3190, vuz3170) -> new_primQuotInt86(vuz416, new_esEs(new_sr(Neg(vuz3190), Pos(vuz3170))), vuz417, vuz3190, vuz3170)
67.72/34.81	   new_reduce2Reduce1(vuz316, vuz317, vuz318, vuz319, True, ba) -> error([])
67.72/34.81	   new_primQuotInt37(vuz416, vuz417, vuz3190, vuz3170) -> new_primQuotInt31(vuz416, new_esEs(new_abs4(vuz3190, vuz3170)), new_abs(vuz417), new_abs4(vuz3190, vuz3170))
67.72/34.81	   new_primQuotInt26(vuz374, vuz511, vuz375) -> new_primQuotInt10(vuz374, new_esEs(new_abs1(vuz375)), new_abs1(vuz511), new_abs1(vuz375))
67.72/34.81	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.72/34.81	   new_quot(Neg(Succ(vuz31600)), Neg(Succ(vuz31700)), Pos(vuz3180), Neg(vuz3190), ty_Int) -> new_primQuotInt56(new_primPlusNat1(new_primMulNat0(vuz31600, Succ(vuz31700)), Succ(vuz31700)), new_primMulNat0(vuz3180, vuz3190), new_primPlusNat1(new_primMulNat0(vuz31600, Succ(vuz31700)), Succ(vuz31700)), new_primMulNat0(vuz3180, vuz3190), vuz3190, vuz31700)
67.72/34.81	   new_primQuotInt32(vuz416, Neg(Zero)) -> new_error
67.72/34.81	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.72/34.81	   new_gcd0Gcd'00(vuz542, vuz557) -> new_gcd0Gcd'2(vuz557, vuz542)
67.72/34.81	   new_abs(vuz399) -> new_absReal1(Pos(vuz399), Pos(vuz399))
67.72/34.81	   new_quot(vuz316, vuz317, vuz318, vuz319, ty_Integer) -> error([])
67.72/34.81	   new_quot0(Pos(vuz3190), Pos(vuz3170), Pos(vuz3160), vuz318, ty_Int) -> new_primQuotInt78(new_primMulNat0(vuz3190, vuz3170), new_primMulNat0(vuz3160, vuz3170), vuz318, vuz3190, new_primMulNat0(vuz3160, vuz3170), new_primMulNat0(vuz3190, vuz3170))
67.72/34.81	   new_primQuotInt47(Succ(vuz4310), Succ(vuz4300), vuz433, vuz432, vuz31900, vuz3170) -> new_primQuotInt47(vuz4310, vuz4300, vuz4310, vuz4300, vuz31900, vuz3170)
67.72/34.81	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.72/34.81	   new_quot(Pos(vuz3160), Neg(vuz3170), Neg(vuz3180), Pos(vuz3190), ty_Int) -> new_primQuotInt50(new_primPlusNat1(new_primMulNat0(vuz3160, vuz3170), new_primMulNat0(vuz3180, vuz3190)), new_primPlusNat1(new_primMulNat0(vuz3160, vuz3170), new_primMulNat0(vuz3180, vuz3190)), vuz3190, vuz3170)
67.72/34.81	   new_primQuotInt15(vuz348, False, vuz349, vuz3190, vuz3170) -> new_primQuotInt14(vuz348, vuz349, vuz3190, vuz3170)
67.72/34.81	   new_primModNatS1(Zero, vuz54200) -> Zero
67.72/34.81	   new_quot(Pos(Zero), Pos(Succ(vuz31700)), Neg(vuz3180), Pos(vuz3190), ty_Int) -> new_primQuotInt36(Zero, new_primMulNat0(vuz3180, vuz3190), Zero, new_primMulNat0(vuz3180, vuz3190), vuz3190, vuz31700)
67.72/34.81	   new_quot(Neg(Zero), Neg(Succ(vuz31700)), Neg(vuz3180), Pos(vuz3190), ty_Int) -> new_primQuotInt76(Zero, new_primMulNat0(vuz3180, vuz3190), Zero, new_primMulNat0(vuz3180, vuz3190), vuz3190, vuz31700)
67.72/34.81	   new_primQuotInt46(vuz360, True, vuz361, vuz3190, vuz3170) -> new_primQuotInt61(vuz360, new_esEs(new_sr(Neg(vuz3190), Neg(vuz3170))), vuz361, vuz3190, vuz3170)
67.72/34.81	   new_quot(Neg(Succ(vuz31600)), Neg(Zero), Neg(vuz3180), Pos(vuz3190), ty_Int) -> new_primQuotInt77(new_primMulNat0(vuz3180, vuz3190), new_primMulNat0(vuz3180, vuz3190), vuz3190)
67.72/34.81	   new_quot0(Neg(vuz3190), Neg(vuz3170), Pos(vuz3160), vuz318, ty_Int) -> new_primQuotInt81(new_primMulNat0(vuz3190, vuz3170), new_primMulNat0(vuz3160, vuz3170), vuz318, vuz3190, new_primMulNat0(vuz3160, vuz3170), new_primMulNat0(vuz3190, vuz3170))
67.72/34.81	   new_primQuotInt60(vuz360, vuz361, vuz3190, vuz3170) -> new_primQuotInt31(vuz360, new_esEs(new_abs2(vuz3190, vuz3170)), new_abs(vuz361), new_abs2(vuz3190, vuz3170))
67.72/34.81	   new_error -> error([])
67.72/34.81	   new_primQuotInt36(Succ(vuz4090), Succ(vuz4080), vuz411, vuz410, vuz3190, vuz31700) -> new_primQuotInt36(vuz4090, vuz4080, vuz4090, vuz4080, vuz3190, vuz31700)
67.72/34.81	   new_primQuotInt34(vuz398, vuz399, vuz3190, vuz3170) -> new_primQuotInt31(vuz398, new_esEs(new_abs3(vuz3190, vuz3170)), new_abs(vuz399), new_abs3(vuz3190, vuz3170))
67.72/34.81	   new_primQuotInt35(vuz398, False, vuz399, vuz3190, vuz3170) -> new_primQuotInt34(vuz398, vuz399, vuz3190, vuz3170)
67.72/34.81	   new_primQuotInt62(Succ(vuz4010), Zero, vuz403, vuz402, vuz3190, vuz31700) -> new_primQuotInt22(Succ(vuz4010), Succ(vuz4010), vuz3190, Succ(vuz31700))
67.72/34.81	   new_primQuotInt63(vuz378, True, vuz514, vuz379) -> new_primQuotInt55(vuz378)
67.72/34.81	   new_primQuotInt72(Succ(vuz4390), Succ(vuz4380), vuz441, vuz440, vuz31900, vuz3170) -> new_primQuotInt72(vuz4390, vuz4380, vuz4390, vuz4380, vuz31900, vuz3170)
67.72/34.81	   new_primQuotInt39(vuz374, Succ(vuz4890), Succ(vuz3770), vuz375) -> new_primQuotInt39(vuz374, vuz4890, vuz3770, vuz375)
67.72/34.81	   new_absReal1(vuz554, Neg(Succ(vuz55500))) -> new_negate0(vuz554)
67.72/34.81	   new_primQuotInt31(vuz416, True, vuz549, vuz542) -> new_primQuotInt32(vuz416, vuz549)
67.72/34.81	   new_primQuotInt91(vuz370, False, vuz508, vuz371) -> new_primQuotInt85(vuz370, vuz508, vuz371)
67.72/34.81	   new_primQuotInt58(Zero, vuz437, vuz3170) -> new_primQuotInt45(Zero, Zero, Zero, vuz3170)
67.72/34.81	   new_primQuotInt89(vuz426, True, vuz427, vuz3190, vuz3170) -> new_primQuotInt55(vuz426)
67.72/34.81	   new_primQuotInt47(Zero, Zero, vuz433, vuz432, vuz31900, vuz3170) -> new_primQuotInt45(Zero, Zero, Succ(vuz31900), vuz3170)
67.72/34.81	
67.72/34.81	The set Q consists of the following terms:
67.72/34.81	
67.72/34.81	   new_primQuotInt20(x0, True, x1, x2, x3)
67.72/34.81	   new_primQuotInt26(x0, x1, x2)
67.72/34.81	   new_primPlusNat1(Succ(x0), Zero)
67.72/34.81	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.72/34.81	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.72/34.81	   new_primQuotInt23(x0, True, x1, x2, x3)
67.72/34.81	   new_primQuotInt15(x0, True, x1, x2, x3)
67.72/34.81	   new_primMinusNatS2(Succ(x0), Zero)
67.72/34.81	   new_primQuotInt85(x0, x1, x2)
67.72/34.81	   new_quot(Pos(x0), Neg(x1), Pos(Succ(x2)), Pos(Zero), ty_Int)
67.72/34.81	   new_quot(Neg(x0), Pos(x1), Pos(Succ(x2)), Pos(Zero), ty_Int)
67.72/34.81	   new_primQuotInt91(x0, True, x1, x2)
67.72/34.81	   new_primQuotInt48(x0, x1, x2, x3)
67.72/34.81	   new_absReal1(x0, Neg(Zero))
67.72/34.81	   new_primQuotInt92(x0, True, x1, x2, x3)
67.72/34.81	   new_primDivNatS1(Zero, x0)
67.72/34.81	   new_quot(Pos(x0), Neg(x1), Neg(Succ(x2)), Neg(Zero), ty_Int)
67.72/34.81	   new_quot(Neg(x0), Pos(x1), Neg(Succ(x2)), Neg(Zero), ty_Int)
67.72/34.81	   new_primDivNatS1(Succ(Zero), Zero)
67.72/34.81	   new_primQuotInt67(Succ(x0), Succ(x1), x2, x3, x4, x5)
67.72/34.81	   new_primQuotInt28(x0, x1, Pos(x2), x3, x4, x5)
67.72/34.81	   new_primQuotInt58(Zero, x0, x1)
67.72/34.81	   new_primQuotInt70(x0, Pos(Succ(x1)))
67.72/34.81	   new_primQuotInt12(x0, Succ(x1), Succ(x2), x3)
67.72/34.81	   new_primMulNat0(Zero, Zero)
67.72/34.81	   new_primPlusNat1(Zero, Zero)
67.72/34.81	   new_primQuotInt86(x0, False, x1, x2, x3)
67.72/34.81	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.72/34.81	   new_primQuotInt75(Succ(x0), x1, x2)
67.72/34.81	   new_primPlusNat0(Zero, x0)
67.72/34.81	   new_primQuotInt60(x0, x1, x2, x3)
67.72/34.81	   new_absReal1(x0, Pos(Zero))
67.72/34.81	   new_primDivNatS01(x0, x1, Succ(x2), Succ(x3))
67.72/34.81	   new_primQuotInt87(x0, False, x1, x2, x3)
67.72/34.81	   new_primDivNatS01(x0, x1, Zero, Zero)
67.72/34.81	   new_esEs0(x0, x1, ty_Int)
67.72/34.81	   new_primQuotInt54(x0, True, x1, x2)
67.72/34.81	   new_primQuotInt28(x0, x1, Neg(x2), x3, x4, x5)
67.72/34.81	   new_primQuotInt41(x0, x1, x2)
67.72/34.81	   new_primQuotInt63(x0, False, x1, x2)
67.72/34.81	   new_primEqInt1
67.72/34.81	   new_primQuotInt44(x0)
67.72/34.81	   new_primQuotInt53(x0, x1, x2, x3, x4, x5)
67.72/34.81	   new_quot0(Neg(x0), Neg(x1), Neg(x2), x3, ty_Int)
67.72/34.81	   new_primQuotInt31(x0, True, x1, x2)
67.72/34.81	   new_primQuotInt39(x0, Succ(x1), Zero, x2)
67.72/34.81	   new_primDivNatS1(Succ(Zero), Succ(x0))
67.72/34.81	   new_quot(Neg(x0), Neg(x1), Neg(x2), Neg(x3), ty_Int)
67.72/34.81	   new_quot0(Neg(x0), Pos(x1), Pos(x2), x3, ty_Int)
67.72/34.81	   new_quot0(Pos(x0), Neg(x1), Pos(x2), x3, ty_Int)
67.72/34.81	   new_quot0(Pos(x0), Pos(x1), Neg(x2), x3, ty_Int)
67.72/34.81	   new_primQuotInt82(x0, False, x1, x2, x3)
67.72/34.81	   new_reduce2Reduce1(x0, x1, x2, x3, True, x4)
67.72/34.81	   new_quot(Pos(x0), Neg(x1), Pos(x2), Neg(x3), ty_Int)
67.72/34.81	   new_quot(Neg(x0), Pos(x1), Pos(x2), Neg(x3), ty_Int)
67.72/34.81	   new_quot(Neg(x0), Pos(x1), Neg(x2), Pos(x3), ty_Int)
67.72/34.81	   new_quot(Pos(x0), Pos(x1), Neg(x2), Neg(x3), ty_Int)
67.72/34.81	   new_quot(Neg(x0), Neg(x1), Pos(x2), Pos(x3), ty_Int)
67.72/34.81	   new_quot(Pos(x0), Neg(x1), Neg(x2), Pos(x3), ty_Int)
67.72/34.81	   new_primQuotInt40(Zero, x0, x1)
67.72/34.81	   new_error
67.72/34.81	   new_primQuotInt50(x0, x1, x2, x3)
67.72/34.81	   new_primQuotInt71(Succ(x0), x1, x2)
67.72/34.81	   new_primQuotInt46(x0, True, x1, x2, x3)
67.72/34.81	   new_primQuotInt32(x0, Neg(Succ(x1)))
67.72/34.81	   new_primQuotInt90(x0, x1, x2, x3, x4, x5)
67.72/34.81	   new_primQuotInt9(x0, x1, x2, x3)
67.72/34.81	   new_primQuotInt13(x0, True, x1, x2, x3)
67.72/34.81	   new_primMinusNatS2(Zero, Succ(x0))
67.72/34.81	   new_rem(Pos(x0), Neg(Succ(x1)))
67.72/34.81	   new_rem(Neg(x0), Pos(Succ(x1)))
67.72/34.81	   new_primQuotInt79(x0, x1, Neg(x2), x3, x4, x5)
67.72/34.81	   new_negate(:%(x0, x1))
67.72/34.81	   new_primQuotInt56(Zero, Zero, x0, x1, x2, x3)
67.72/34.81	   new_primQuotInt40(Succ(x0), x1, x2)
67.72/34.81	   new_primQuotInt66(x0, False, x1, x2, x3)
67.72/34.81	   new_primQuotInt74(Zero, Zero, x0, x1, x2, x3)
67.72/34.81	   new_quot(Pos(x0), Neg(x1), Pos(Zero), Pos(Zero), ty_Int)
67.72/34.81	   new_quot(Neg(x0), Pos(x1), Pos(Zero), Pos(Zero), ty_Int)
67.72/34.81	   new_primQuotInt80(x0, x1, Neg(x2), x3, x4, x5)
67.72/34.81	   new_primQuotInt12(x0, Zero, Succ(x1), x2)
67.72/34.81	   new_primQuotInt10(x0, True, x1, x2)
67.72/34.81	   new_primQuotInt72(Zero, Succ(x0), x1, x2, x3, x4)
67.72/34.81	   new_primQuotInt56(Succ(x0), Zero, x1, x2, x3, x4)
67.72/34.81	   new_primQuotInt69(x0, True, x1, x2)
67.72/34.81	   new_primQuotInt36(Succ(x0), Zero, x1, x2, x3, x4)
67.72/34.81	   new_primQuotInt25(x0, True, x1, x2)
67.72/34.81	   new_ps(:%(x0, x1), :%(x2, x3), x4)
67.72/34.81	   new_primQuotInt68(x0, x1, x2, x3)
67.72/34.81	   new_abs2(x0, x1)
67.72/34.81	   new_primQuotInt17(x0, x1, x2, x3)
67.72/34.81	   new_rem(Neg(x0), Neg(Succ(x1)))
67.72/34.81	   new_quot(Neg(x0), Pos(x1), Neg(Zero), Neg(Zero), ty_Int)
67.72/34.81	   new_quot(Pos(x0), Neg(x1), Neg(Zero), Neg(Zero), ty_Int)
67.72/34.81	   new_primQuotInt55(x0)
67.72/34.81	   new_quot(Pos(Succ(x0)), Pos(Succ(x1)), Neg(x2), Pos(x3), ty_Int)
67.72/34.81	   new_primQuotInt84(x0, False, x1, x2)
67.72/34.81	   new_quot(Pos(Succ(x0)), Pos(Succ(x1)), Pos(x2), Neg(x3), ty_Int)
67.72/34.81	   new_primQuotInt61(x0, False, x1, x2, x3)
67.72/34.81	   new_abs4(x0, x1)
67.72/34.81	   new_negate0(Neg(x0))
67.72/34.81	   new_primQuotInt33(x0, True, x1, x2, x3)
67.72/34.81	   new_primMulNat0(Zero, Succ(x0))
67.72/34.81	   new_primQuotInt57(x0, x1, Neg(x2), x3, x4, x5)
67.72/34.81	   new_esEs(Pos(Zero))
67.72/34.81	   new_absReal1(x0, Pos(Succ(x1)))
67.72/34.81	   new_quot(Pos(x0), Pos(x1), Pos(x2), Pos(x3), ty_Int)
67.72/34.81	   new_quot(Neg(x0), Pos(x1), Neg(Zero), Neg(Succ(x2)), ty_Int)
67.72/34.81	   new_quot(Pos(x0), Neg(x1), Neg(Zero), Neg(Succ(x2)), ty_Int)
67.72/34.81	   new_primQuotInt84(x0, True, x1, x2)
67.72/34.81	   new_primQuotInt62(Succ(x0), Zero, x1, x2, x3, x4)
67.72/34.81	   new_primModNatS1(Zero, x0)
67.72/34.81	   new_primQuotInt73(Zero, x0, x1)
67.72/34.81	   new_primQuotInt61(x0, True, x1, x2, x3)
67.72/34.81	   new_quot(Pos(Succ(x0)), Pos(Zero), Neg(x1), Pos(x2), ty_Int)
67.72/34.81	   new_quot(Pos(Succ(x0)), Pos(Zero), Pos(x1), Neg(x2), ty_Int)
67.72/34.81	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.72/34.81	   new_abs1(x0)
67.72/34.81	   new_primEqInt3(Zero)
67.72/34.81	   new_primQuotInt78(x0, x1, Pos(x2), x3, x4, x5)
67.72/34.81	   new_primQuotInt39(x0, Zero, Zero, x1)
67.72/34.81	   new_primQuotInt46(x0, False, x1, x2, x3)
67.72/34.81	   new_primQuotInt21(x0, x1, x2, x3)
67.72/34.81	   new_primQuotInt36(Zero, Succ(x0), x1, x2, x3, x4)
67.72/34.81	   new_primEqInt4(Succ(x0))
67.72/34.81	   new_primQuotInt62(Succ(x0), Succ(x1), x2, x3, x4, x5)
67.72/34.81	   new_quot0(Neg(x0), Pos(x1), Neg(x2), x3, ty_Int)
67.72/34.81	   new_quot0(Pos(x0), Neg(x1), Neg(x2), x3, ty_Int)
67.72/34.81	   new_quot0(Neg(x0), Neg(x1), Pos(x2), x3, ty_Int)
67.72/34.81	   new_primQuotInt31(x0, False, x1, x2)
67.72/34.81	   new_primDivNatS02(x0, x1)
67.72/34.81	   new_primMulNat0(Succ(x0), Succ(x1))
67.72/34.81	   new_primQuotInt56(Succ(x0), Succ(x1), x2, x3, x4, x5)
67.72/34.81	   new_primQuotInt75(Zero, x0, x1)
67.72/34.81	   new_primModNatS1(Succ(Zero), Succ(x0))
67.72/34.81	   new_primQuotInt77(Zero, x0, x1)
67.72/34.81	   new_quot(Pos(Zero), Pos(Zero), Neg(x0), Pos(x1), ty_Int)
67.72/34.81	   new_quot(Pos(Zero), Pos(Zero), Pos(x0), Neg(x1), ty_Int)
67.72/34.81	   new_absReal10(x0)
67.72/34.81	   new_primQuotInt30(x0, x1, x2, x3, x4, x5)
67.72/34.81	   new_gcd0Gcd'2(x0, x1)
67.72/34.81	   new_primQuotInt64(x0, x1, Pos(x2), x3, x4, x5)
67.72/34.81	   new_sr(Pos(x0), Neg(x1))
67.72/34.81	   new_sr(Neg(x0), Pos(x1))
67.72/34.81	   new_primQuotInt42(x0, False, x1, x2, x3)
67.72/34.81	   new_primQuotInt66(x0, True, x1, x2, x3)
67.72/34.81	   new_primQuotInt79(x0, x1, Pos(x2), x3, x4, x5)
67.72/34.81	   new_primQuotInt32(x0, Pos(Succ(x1)))
67.72/34.81	   new_primQuotInt16(Zero, x0, x1)
67.72/34.81	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.72/34.81	   new_primQuotInt70(x0, Neg(Succ(x1)))
67.72/34.81	   new_gcd0Gcd'10(False, x0, x1)
67.72/34.81	   new_esEs0(x0, x1, ty_Integer)
67.72/34.81	   new_primQuotInt47(Zero, Zero, x0, x1, x2, x3)
67.72/34.81	   new_primQuotInt14(x0, x1, x2, x3)
67.72/34.81	   new_quot(Pos(Zero), Pos(Succ(x0)), Pos(x1), Neg(x2), ty_Int)
67.72/34.81	   new_quot(Pos(Zero), Pos(Succ(x0)), Neg(x1), Pos(x2), ty_Int)
67.72/34.81	   new_quot0(x0, x1, x2, x3, ty_Integer)
67.72/34.81	   new_primQuotInt18(x0, x1, x2, x3)
67.72/34.81	   new_primQuotInt47(Succ(x0), Succ(x1), x2, x3, x4, x5)
67.72/34.81	   new_primQuotInt65(x0, x1, x2, x3, x4, x5)
67.72/34.81	   new_primMulNat0(Succ(x0), Zero)
67.72/34.81	   new_primQuotInt69(x0, False, x1, x2)
67.72/34.81	   new_primQuotInt51(x0, True, x1, x2, x3)
67.72/34.81	   new_primQuotInt67(Zero, Zero, x0, x1, x2, x3)
67.72/34.81	   new_primQuotInt72(Succ(x0), Succ(x1), x2, x3, x4, x5)
67.72/34.81	   new_primQuotInt11(x0, x1, x2, x3, x4, x5)
67.72/34.81	   new_primQuotInt34(x0, x1, x2, x3)
67.72/34.81	   new_quot(Neg(x0), Pos(x1), Pos(Succ(x2)), Pos(Succ(x3)), ty_Int)
67.72/34.81	   new_quot(Pos(x0), Neg(x1), Pos(Succ(x2)), Pos(Succ(x3)), ty_Int)
67.72/34.81	   new_primQuotInt15(x0, False, x1, x2, x3)
67.72/34.81	   new_primDivNatS1(Succ(Succ(x0)), Succ(x1))
67.72/34.81	   new_primQuotInt72(Zero, Zero, x0, x1, x2, x3)
67.72/34.81	   new_primQuotInt20(x0, False, x1, x2, x3)
67.72/34.81	   new_primQuotInt87(x0, True, x1, x2, x3)
67.72/34.81	   new_primQuotInt12(x0, Zero, Zero, x1)
67.72/34.81	   new_primEqInt0(x0)
67.72/34.81	   new_primQuotInt54(x0, False, x1, x2)
67.72/34.81	   new_primQuotInt64(x0, x1, Neg(x2), x3, x4, x5)
67.72/34.81	   new_primDivNatS01(x0, x1, Succ(x2), Zero)
67.72/34.81	   new_primQuotInt42(x0, True, x1, x2, x3)
67.72/34.81	   new_primQuotInt92(x0, False, x1, x2, x3)
67.72/34.81	   new_rem(Pos(x0), Neg(Zero))
67.72/34.81	   new_rem(Neg(x0), Pos(Zero))
67.72/34.81	   new_primDivNatS01(x0, x1, Zero, Succ(x2))
67.72/34.81	   new_primQuotInt76(Zero, Zero, x0, x1, x2, x3)
67.72/34.81	   new_primQuotInt38(x0, x1, x2, x3, x4, x5)
67.72/34.81	   new_primQuotInt29(x0, x1, x2, x3, x4, x5)
67.72/34.81	   new_primQuotInt36(Succ(x0), Succ(x1), x2, x3, x4, x5)
67.72/34.81	   new_sr(Neg(x0), Neg(x1))
67.72/34.81	   new_primQuotInt45(x0, x1, x2, x3)
67.72/34.81	   new_gcd0Gcd'00(x0, x1)
67.72/34.81	   new_quot(Neg(x0), Pos(x1), Neg(Succ(x2)), Neg(Succ(x3)), ty_Int)
67.72/34.81	   new_quot(Pos(x0), Neg(x1), Neg(Succ(x2)), Neg(Succ(x3)), ty_Int)
67.72/34.81	   new_primQuotInt76(Succ(x0), Zero, x1, x2, x3, x4)
67.72/34.81	   new_primModNatS1(Succ(Zero), Zero)
67.72/34.81	   new_rem(Pos(x0), Pos(Zero))
67.72/34.81	   new_primQuotInt37(x0, x1, x2, x3)
67.72/34.81	   new_primQuotInt12(x0, Succ(x1), Zero, x2)
67.72/34.81	   new_primQuotInt71(Zero, x0, x1)
67.72/34.81	   new_sr(Pos(x0), Pos(x1))
67.72/34.81	   new_primQuotInt81(x0, x1, Neg(x2), x3, x4, x5)
67.72/34.81	   new_primQuotInt83(x0, True, x1, x2)
67.72/34.81	   new_absReal11(x0)
67.72/34.81	   new_primEqInt(x0)
67.72/34.81	   new_gcd0Gcd'10(True, x0, x1)
67.72/34.81	   new_primQuotInt58(Succ(x0), x1, x2)
67.72/34.81	   new_primQuotInt78(x0, x1, Neg(x2), x3, x4, x5)
67.72/34.81	   new_primPlusNat1(Zero, Succ(x0))
67.72/34.81	   new_abs(x0)
67.72/34.81	   new_primQuotInt67(Succ(x0), Zero, x1, x2, x3, x4)
67.72/34.81	   new_primQuotInt74(Succ(x0), Zero, x1, x2, x3, x4)
67.72/34.81	   new_primQuotInt36(Zero, Zero, x0, x1, x2, x3)
67.72/34.81	   new_abs3(x0, x1)
67.72/34.81	   new_primQuotInt59(x0, x1, Neg(x2), x3, x4, x5)
67.72/34.81	   new_primQuotInt57(x0, x1, Pos(x2), x3, x4, x5)
67.72/34.81	   new_primQuotInt33(x0, False, x1, x2, x3)
67.72/34.81	   new_primPlusNat1(Succ(x0), Succ(x1))
67.72/34.81	   new_primQuotInt70(x0, Neg(Zero))
67.72/34.81	   new_primEqInt3(Succ(x0))
67.72/34.81	   new_primQuotInt47(Succ(x0), Zero, x1, x2, x3, x4)
67.72/34.81	   new_primQuotInt32(x0, Neg(Zero))
67.72/34.81	   new_primQuotInt88(x0, x1, x2, x3)
67.72/34.81	   new_quot(Neg(Succ(x0)), Neg(Succ(x1)), Neg(x2), Pos(x3), ty_Int)
67.72/34.81	   new_quot(Neg(Succ(x0)), Neg(Succ(x1)), Pos(x2), Neg(x3), ty_Int)
67.72/34.81	   new_primQuotInt59(x0, x1, Pos(x2), x3, x4, x5)
67.72/34.81	   new_primQuotInt27(x0, False, x1, x2)
67.72/34.81	   new_primQuotInt67(Zero, Succ(x0), x1, x2, x3, x4)
67.72/34.81	   new_quot(x0, x1, x2, x3, ty_Integer)
67.72/34.81	   new_primQuotInt32(x0, Pos(Zero))
67.72/34.81	   new_primQuotInt22(x0, x1, x2, x3)
67.72/34.81	   new_primMinusNatS2(Zero, Zero)
67.72/34.81	   new_primQuotInt49(x0, x1, x2)
67.72/34.81	   new_primQuotInt62(Zero, Succ(x0), x1, x2, x3, x4)
67.72/34.81	   new_primQuotInt62(Zero, Zero, x0, x1, x2, x3)
67.72/34.81	   new_primModNatS01(x0, x1, Zero, Zero)
67.72/34.81	   new_esEs(Pos(Succ(x0)))
67.72/34.81	   new_primQuotInt83(x0, False, x1, x2)
67.72/34.81	   new_primQuotInt39(x0, Zero, Succ(x1), x2)
67.72/34.81	   new_quot(Neg(Zero), Neg(Zero), Neg(x0), Pos(x1), ty_Int)
67.72/34.81	   new_primQuotInt35(x0, True, x1, x2, x3)
67.72/34.81	   new_quot(Neg(Zero), Neg(Zero), Pos(x0), Neg(x1), ty_Int)
67.72/34.81	   new_rem(Pos(x0), Pos(Succ(x1)))
67.72/34.81	   new_negate0(Pos(x0))
67.72/34.81	   new_quot0(Pos(x0), Pos(x1), Pos(x2), x3, ty_Int)
67.72/34.81	   new_primQuotInt89(x0, False, x1, x2, x3)
67.72/34.81	   new_primQuotInt19(x0, x1, x2, x3)
67.72/34.81	   new_primQuotInt35(x0, False, x1, x2, x3)
67.72/34.81	   new_absReal1(x0, Neg(Succ(x1)))
67.72/34.81	   new_abs0(x0, x1)
67.72/34.81	   new_primQuotInt47(Zero, Succ(x0), x1, x2, x3, x4)
67.72/34.81	   new_primQuotInt24(Zero, x0, x1)
67.72/34.81	   new_primQuotInt70(x0, Pos(Zero))
67.72/34.81	   new_primMinusNatS0(x0)
67.72/34.81	   new_primQuotInt24(Succ(x0), x1, x2)
67.72/34.81	   new_primQuotInt52(x0, x1, x2, x3, x4, x5)
67.72/34.81	   new_primQuotInt25(x0, False, x1, x2)
67.72/34.81	   new_esEs(Neg(Succ(x0)))
67.72/34.81	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.72/34.81	   new_primQuotInt89(x0, True, x1, x2, x3)
67.72/34.81	   new_primQuotInt27(x0, True, x1, x2)
67.72/34.81	   new_quot(Neg(Zero), Neg(Succ(x0)), Pos(x1), Neg(x2), ty_Int)
67.72/34.81	   new_quot(Neg(Zero), Neg(Succ(x0)), Neg(x1), Pos(x2), ty_Int)
67.72/34.81	   new_primQuotInt56(Zero, Succ(x0), x1, x2, x3, x4)
67.72/34.81	   new_rem(Neg(x0), Neg(Zero))
67.72/34.81	   new_primQuotInt80(x0, x1, Pos(x2), x3, x4, x5)
67.72/34.81	   new_reduce2Reduce1(x0, x1, x2, x3, False, x4)
67.72/34.81	   new_primQuotInt16(Succ(x0), x1, x2)
67.72/34.81	   new_primMinusNatS1
67.72/34.81	   new_primEqInt4(Zero)
67.74/34.81	   new_primQuotInt63(x0, True, x1, x2)
67.74/34.81	   new_primDivNatS1(Succ(Succ(x0)), Zero)
67.74/34.81	   new_primQuotInt76(Succ(x0), Succ(x1), x2, x3, x4, x5)
67.74/34.81	   new_primQuotInt10(x0, False, x1, x2)
67.74/34.81	   new_primQuotInt91(x0, False, x1, x2)
67.74/34.81	   new_primQuotInt74(Zero, Succ(x0), x1, x2, x3, x4)
67.74/34.81	   new_primQuotInt73(Succ(x0), x1, x2)
67.74/34.81	   new_primQuotInt86(x0, True, x1, x2, x3)
67.74/34.81	   new_primModNatS02(x0, x1)
67.74/34.81	   new_primQuotInt43(x0, x1, x2, x3)
67.74/34.81	   new_primQuotInt81(x0, x1, Pos(x2), x3, x4, x5)
67.74/34.81	   new_primQuotInt77(Succ(x0), x1, x2)
67.74/34.81	   new_primQuotInt82(x0, True, x1, x2, x3)
67.74/34.81	   new_primQuotInt13(x0, False, x1, x2, x3)
67.74/34.81	   new_primQuotInt72(Succ(x0), Zero, x1, x2, x3, x4)
67.74/34.81	   new_quot(Neg(Succ(x0)), Neg(Zero), Pos(x1), Neg(x2), ty_Int)
67.74/34.81	   new_quot(Neg(Succ(x0)), Neg(Zero), Neg(x1), Pos(x2), ty_Int)
67.74/34.81	   new_primQuotInt39(x0, Succ(x1), Succ(x2), x3)
67.74/34.81	   new_quot(Neg(x0), Pos(x1), Pos(Zero), Pos(Succ(x2)), ty_Int)
67.74/34.81	   new_quot(Pos(x0), Neg(x1), Pos(Zero), Pos(Succ(x2)), ty_Int)
67.74/34.81	   new_primQuotInt76(Zero, Succ(x0), x1, x2, x3, x4)
67.74/34.81	   new_primQuotInt23(x0, False, x1, x2, x3)
67.74/34.81	   new_primEqInt2
67.74/34.81	   new_primQuotInt74(Succ(x0), Succ(x1), x2, x3, x4, x5)
67.74/34.81	   new_esEs(Neg(Zero))
67.74/34.81	   new_primPlusNat0(Succ(x0), x1)
67.74/34.81	   new_primQuotInt51(x0, False, x1, x2, x3)
67.74/34.81	
67.74/34.81	We have to consider all minimal (P,Q,R)-chains.
67.74/34.81	----------------------------------------
67.74/34.81	
67.74/34.81	(19) MNOCProof (EQUIVALENT)
67.74/34.81	We use the modular non-overlap check [FROCOS05] to decrease Q to the empty set.
67.74/34.81	----------------------------------------
67.74/34.81	
67.74/34.81	(20)
67.74/34.81	Obligation:
67.74/34.81	Q DP problem:
67.74/34.81	The TRS P consists of the following rules:
67.74/34.81	
67.74/34.81	   new_iterate(vuz4, vuz3, vuz5) -> new_iterate(vuz4, vuz3, new_ps(new_ps(vuz4, new_negate(vuz3), ty_Int), vuz5, ty_Int))
67.74/34.81	
67.74/34.81	The TRS R consists of the following rules:
67.74/34.81	
67.74/34.81	   new_abs4(vuz3190, vuz3170) -> new_absReal1(new_sr(Neg(vuz3190), Pos(vuz3170)), new_sr(Neg(vuz3190), Pos(vuz3170)))
67.74/34.81	   new_primQuotInt44(vuz398) -> error([])
67.74/34.81	   new_primQuotInt80(vuz386, vuz389, Pos(vuz3180), vuz3190, vuz388, vuz387) -> new_primQuotInt30(vuz386, vuz389, new_primMulNat0(vuz3180, vuz3190), vuz388, new_primMulNat0(vuz3180, vuz3190), vuz387)
67.74/34.81	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.81	   new_primQuotInt56(Succ(vuz4570), Succ(vuz4560), vuz459, vuz458, vuz3190, vuz31700) -> new_primQuotInt56(vuz4570, vuz4560, vuz4570, vuz4560, vuz3190, vuz31700)
67.74/34.81	   new_primQuotInt27(vuz374, False, vuz511, vuz375) -> new_primQuotInt26(vuz374, vuz511, vuz375)
67.74/34.81	   new_primQuotInt62(Succ(vuz4010), Succ(vuz4000), vuz403, vuz402, vuz3190, vuz31700) -> new_primQuotInt62(vuz4010, vuz4000, vuz4010, vuz4000, vuz3190, vuz31700)
67.74/34.81	   new_quot(Neg(vuz3160), Pos(vuz3170), Neg(Zero), Neg(Zero), ty_Int) -> new_primQuotInt40(new_primMulNat0(vuz3160, vuz3170), new_primMulNat0(vuz3160, vuz3170), vuz3170)
67.74/34.81	   new_quot(Neg(vuz3160), Pos(vuz3170), Neg(Succ(vuz31800)), Neg(Succ(vuz31900)), ty_Int) -> new_primQuotInt74(new_primPlusNat1(new_primMulNat0(vuz31800, Succ(vuz31900)), Succ(vuz31900)), new_primMulNat0(vuz3160, vuz3170), new_primPlusNat1(new_primMulNat0(vuz31800, Succ(vuz31900)), Succ(vuz31900)), new_primMulNat0(vuz3160, vuz3170), vuz31900, vuz3170)
67.74/34.81	   new_abs1(vuz427) -> new_absReal1(Neg(vuz427), Neg(vuz427))
67.74/34.81	   new_quot(Neg(Zero), Neg(Succ(vuz31700)), Pos(vuz3180), Neg(vuz3190), ty_Int) -> new_primQuotInt56(Zero, new_primMulNat0(vuz3180, vuz3190), Zero, new_primMulNat0(vuz3180, vuz3190), vuz3190, vuz31700)
67.74/34.81	   new_quot(Neg(Zero), Neg(Zero), Neg(vuz3180), Pos(vuz3190), ty_Int) -> new_primQuotInt77(new_primMulNat0(vuz3180, vuz3190), new_primMulNat0(vuz3180, vuz3190), vuz3190)
67.74/34.81	   new_primQuotInt69(vuz366, True, vuz505, vuz367) -> new_primQuotInt83(vuz366, new_esEs(Pos(vuz367)), vuz505, vuz367)
67.74/34.81	   new_primDivNatS1(Zero, vuz54900) -> Zero
67.74/34.81	   new_quot(Neg(Succ(vuz31600)), Neg(Succ(vuz31700)), Neg(vuz3180), Pos(vuz3190), ty_Int) -> new_primQuotInt76(new_primPlusNat1(new_primMulNat0(vuz31600, Succ(vuz31700)), Succ(vuz31700)), new_primMulNat0(vuz3180, vuz3190), new_primPlusNat1(new_primMulNat0(vuz31600, Succ(vuz31700)), Succ(vuz31700)), new_primMulNat0(vuz3180, vuz3190), vuz3190, vuz31700)
67.74/34.81	   new_quot(Neg(vuz3160), Pos(vuz3170), Pos(Zero), Pos(Succ(vuz31900)), ty_Int) -> new_primQuotInt72(Zero, new_primMulNat0(vuz3160, vuz3170), Zero, new_primMulNat0(vuz3160, vuz3170), vuz31900, vuz3170)
67.74/34.81	   new_primQuotInt57(vuz382, vuz385, Neg(vuz3180), vuz3190, vuz384, vuz383) -> new_primQuotInt53(vuz382, vuz385, new_primMulNat0(vuz3180, vuz3190), vuz384, new_primMulNat0(vuz3180, vuz3190), vuz383)
67.74/34.81	   new_primDivNatS1(Succ(Succ(vuz41600)), Zero) -> Succ(new_primDivNatS1(new_primMinusNatS0(vuz41600), Zero))
67.74/34.81	   new_primQuotInt20(vuz446, True, vuz447, vuz3190, vuz3170) -> new_primQuotInt87(vuz446, new_esEs(new_sr(Neg(vuz3190), Pos(vuz3170))), vuz447, vuz3190, vuz3170)
67.74/34.81	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.81	   new_primQuotInt73(Zero, vuz445, vuz3170) -> new_primQuotInt18(Zero, Zero, Zero, vuz3170)
67.74/34.81	   new_primQuotInt80(vuz386, vuz389, Neg(vuz3180), vuz3190, vuz388, vuz387) -> new_primQuotInt29(vuz386, vuz389, new_primMulNat0(vuz3180, vuz3190), vuz388, new_primMulNat0(vuz3180, vuz3190), vuz387)
67.74/34.81	   new_primQuotInt15(vuz348, True, vuz349, vuz3190, vuz3170) -> new_primQuotInt55(vuz348)
67.74/34.81	   new_quot0(Neg(vuz3190), Pos(vuz3170), Pos(vuz3160), vuz318, ty_Int) -> new_primQuotInt57(new_primMulNat0(vuz3190, vuz3170), new_primMulNat0(vuz3160, vuz3170), vuz318, vuz3190, new_primMulNat0(vuz3160, vuz3170), new_primMulNat0(vuz3190, vuz3170))
67.74/34.81	   new_primQuotInt81(vuz390, vuz393, Pos(vuz3180), vuz3190, vuz392, vuz391) -> new_primQuotInt90(vuz390, vuz393, new_primMulNat0(vuz3180, vuz3190), vuz392, new_primMulNat0(vuz3180, vuz3190), vuz391)
67.74/34.81	   new_primQuotInt27(vuz374, True, vuz511, vuz375) -> new_primQuotInt55(vuz374)
67.74/34.81	   new_primQuotInt36(Zero, Zero, vuz411, vuz410, vuz3190, vuz31700) -> new_primQuotInt18(Zero, Zero, vuz3190, Succ(vuz31700))
67.74/34.81	   new_primDivNatS01(vuz574, vuz575, Zero, Succ(vuz5770)) -> Zero
67.74/34.81	   new_primQuotInt67(Succ(vuz4190), Succ(vuz4180), vuz421, vuz420, vuz31900, vuz3170) -> new_primQuotInt67(vuz4190, vuz4180, vuz4190, vuz4180, vuz31900, vuz3170)
67.74/34.81	   new_quot(Pos(vuz3160), Neg(vuz3170), Pos(vuz3180), Neg(vuz3190), ty_Int) -> new_primQuotInt48(new_primPlusNat1(new_primMulNat0(vuz3160, vuz3170), new_primMulNat0(vuz3180, vuz3190)), new_primPlusNat1(new_primMulNat0(vuz3160, vuz3170), new_primMulNat0(vuz3180, vuz3190)), vuz3190, vuz3170)
67.74/34.81	   new_primQuotInt50(vuz428, vuz429, vuz3190, vuz3170) -> new_primQuotInt51(vuz428, new_esEs(Neg(vuz429)), vuz429, vuz3190, vuz3170)
67.74/34.81	   new_primDivNatS02(vuz574, vuz575) -> Succ(new_primDivNatS1(new_primMinusNatS2(vuz574, vuz575), Succ(vuz575)))
67.74/34.81	   new_primQuotInt79(vuz370, vuz373, Pos(vuz3180), vuz3190, vuz372, vuz371) -> new_primQuotInt11(vuz370, vuz373, new_primMulNat0(vuz3180, vuz3190), vuz372, new_primMulNat0(vuz3180, vuz3190), vuz371)
67.74/34.81	   new_primQuotInt28(vuz374, vuz377, Neg(vuz3180), vuz3190, vuz376, vuz375) -> new_primQuotInt30(vuz374, vuz377, new_primMulNat0(vuz3180, vuz3190), vuz376, new_primMulNat0(vuz3180, vuz3190), vuz375)
67.74/34.81	   new_primQuotInt76(Zero, Succ(vuz4640), vuz467, vuz466, vuz3190, vuz31700) -> new_primQuotInt50(Succ(vuz4640), Succ(vuz4640), vuz3190, Succ(vuz31700))
67.74/34.81	   new_primQuotInt76(Zero, Zero, vuz467, vuz466, vuz3190, vuz31700) -> new_primQuotInt68(Zero, Zero, vuz3190, Succ(vuz31700))
67.74/34.81	   new_quot(Pos(vuz3160), Neg(vuz3170), Neg(Succ(vuz31800)), Neg(Zero), ty_Int) -> new_primQuotInt58(new_primMulNat0(vuz3160, vuz3170), new_primMulNat0(vuz3160, vuz3170), vuz3170)
67.74/34.81	   new_primQuotInt39(vuz374, Zero, Succ(vuz3770), vuz375) -> new_primQuotInt25(vuz374, new_primEqInt3(Succ(vuz3770)), Succ(vuz3770), vuz375)
67.74/34.81	   new_primQuotInt53(vuz378, vuz381, vuz493, vuz380, vuz492, vuz379) -> new_primQuotInt54(vuz378, new_primEqInt4(new_primPlusNat1(vuz381, vuz493)), new_primPlusNat1(vuz381, vuz493), vuz379)
67.74/34.81	   new_primQuotInt79(vuz370, vuz373, Neg(vuz3180), vuz3190, vuz372, vuz371) -> new_primQuotInt90(vuz370, vuz373, new_primMulNat0(vuz3180, vuz3190), vuz372, new_primMulNat0(vuz3180, vuz3190), vuz371)
67.74/34.81	   new_primDivNatS1(Succ(Zero), Succ(vuz549000)) -> Zero
67.74/34.81	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.81	   new_primQuotInt72(Zero, Zero, vuz441, vuz440, vuz31900, vuz3170) -> new_primQuotInt18(Zero, Zero, Succ(vuz31900), vuz3170)
67.74/34.81	   new_primQuotInt24(Succ(vuz4060), vuz407, vuz3190) -> new_primQuotInt19(Succ(vuz4060), Succ(vuz4060), vuz3190, Zero)
67.74/34.81	   new_primQuotInt67(Zero, Zero, vuz421, vuz420, vuz31900, vuz3170) -> new_primQuotInt68(Zero, Zero, Succ(vuz31900), vuz3170)
67.74/34.81	   new_quot(Pos(Succ(vuz31600)), Pos(Zero), Neg(vuz3180), Pos(vuz3190), ty_Int) -> new_primQuotInt16(new_primMulNat0(vuz3180, vuz3190), new_primMulNat0(vuz3180, vuz3190), vuz3190)
67.74/34.81	   new_quot0(Neg(vuz3190), Pos(vuz3170), Neg(vuz3160), vuz318, ty_Int) -> new_primQuotInt80(new_primMulNat0(vuz3190, vuz3170), new_primMulNat0(vuz3160, vuz3170), vuz318, vuz3190, new_primMulNat0(vuz3160, vuz3170), new_primMulNat0(vuz3190, vuz3170))
67.74/34.81	   new_absReal1(vuz554, Pos(Succ(vuz55500))) -> new_absReal10(vuz554)
67.74/34.81	   new_gcd0Gcd'10(False, vuz542, vuz549) -> new_gcd0Gcd'00(vuz542, new_rem(vuz549, vuz542))
67.74/34.81	   new_primQuotInt30(vuz374, vuz377, vuz491, vuz376, vuz490, vuz375) -> new_primQuotInt25(vuz374, new_primEqInt3(new_primPlusNat1(vuz377, vuz491)), new_primPlusNat1(vuz377, vuz491), vuz375)
67.74/34.81	   new_primQuotInt74(Zero, Succ(vuz4480), vuz451, vuz450, vuz31900, vuz3170) -> new_primQuotInt19(Succ(vuz4480), Succ(vuz4480), Succ(vuz31900), vuz3170)
67.74/34.81	   new_absReal1(vuz554, Pos(Zero)) -> new_absReal11(vuz554)
67.74/34.81	   new_primQuotInt74(Succ(vuz4490), Zero, vuz451, vuz450, vuz31900, vuz3170) -> new_primQuotInt22(Succ(vuz4490), Succ(vuz4490), Succ(vuz31900), vuz3170)
67.74/34.81	   new_primQuotInt25(vuz374, True, vuz511, vuz375) -> new_primQuotInt27(vuz374, new_esEs(Neg(vuz375)), vuz511, vuz375)
67.74/34.81	   new_absReal11(vuz554) -> new_absReal10(vuz554)
67.74/34.81	   new_primQuotInt56(Succ(vuz4570), Zero, vuz459, vuz458, vuz3190, vuz31700) -> new_primQuotInt45(Succ(vuz4570), Succ(vuz4570), vuz3190, Succ(vuz31700))
67.74/34.81	   new_primQuotInt32(vuz416, Neg(Succ(vuz54900))) -> Neg(new_primDivNatS1(vuz416, vuz54900))
67.74/34.81	   new_primQuotInt56(Zero, Succ(vuz4560), vuz459, vuz458, vuz3190, vuz31700) -> new_primQuotInt48(Succ(vuz4560), Succ(vuz4560), vuz3190, Succ(vuz31700))
67.74/34.81	   new_quot(Neg(vuz3160), Pos(vuz3170), Neg(Zero), Neg(Succ(vuz31900)), ty_Int) -> new_primQuotInt74(Zero, new_primMulNat0(vuz3160, vuz3170), Zero, new_primMulNat0(vuz3160, vuz3170), vuz31900, vuz3170)
67.74/34.81	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.81	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.81	   new_primQuotInt47(Zero, Succ(vuz4300), vuz433, vuz432, vuz31900, vuz3170) -> new_primQuotInt48(Succ(vuz4300), Succ(vuz4300), Succ(vuz31900), vuz3170)
67.74/34.81	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.81	   new_primEqInt4(Zero) -> new_primEqInt1
67.74/34.81	   new_quot(Pos(vuz3160), Neg(vuz3170), Pos(Succ(vuz31800)), Pos(Zero), ty_Int) -> new_primQuotInt71(new_primMulNat0(vuz3160, vuz3170), new_primMulNat0(vuz3160, vuz3170), vuz3170)
67.74/34.81	   new_primQuotInt64(vuz394, vuz397, Neg(vuz3180), vuz3190, vuz396, vuz395) -> new_primQuotInt65(vuz394, vuz397, new_primMulNat0(vuz3180, vuz3190), vuz396, new_primMulNat0(vuz3180, vuz3190), vuz395)
67.74/34.81	   new_quot(Neg(vuz3160), Pos(vuz3170), Pos(vuz3180), Neg(vuz3190), ty_Int) -> new_primQuotInt19(new_primPlusNat1(new_primMulNat0(vuz3160, vuz3170), new_primMulNat0(vuz3180, vuz3190)), new_primPlusNat1(new_primMulNat0(vuz3160, vuz3170), new_primMulNat0(vuz3180, vuz3190)), vuz3190, vuz3170)
67.74/34.81	   new_quot(Pos(vuz3160), Neg(vuz3170), Pos(Zero), Pos(Zero), ty_Int) -> new_primQuotInt71(new_primMulNat0(vuz3160, vuz3170), new_primMulNat0(vuz3160, vuz3170), vuz3170)
67.74/34.81	   new_quot0(Pos(vuz3190), Neg(vuz3170), Pos(vuz3160), vuz318, ty_Int) -> new_primQuotInt28(new_primMulNat0(vuz3190, vuz3170), new_primMulNat0(vuz3160, vuz3170), vuz318, vuz3190, new_primMulNat0(vuz3160, vuz3170), new_primMulNat0(vuz3190, vuz3170))
67.74/34.81	   new_primQuotInt11(vuz370, vuz373, vuz485, vuz372, vuz484, vuz371) -> new_primQuotInt12(vuz370, vuz485, vuz373, vuz371)
67.74/34.81	   new_primDivNatS01(vuz574, vuz575, Succ(vuz5760), Succ(vuz5770)) -> new_primDivNatS01(vuz574, vuz575, vuz5760, vuz5770)
67.74/34.81	   new_primQuotInt13(vuz348, False, vuz349, vuz3190, vuz3170) -> new_primQuotInt14(vuz348, vuz349, vuz3190, vuz3170)
67.74/34.81	   new_quot(Pos(Zero), Pos(Succ(vuz31700)), Pos(vuz3180), Neg(vuz3190), ty_Int) -> new_primQuotInt62(Zero, new_primMulNat0(vuz3180, vuz3190), Zero, new_primMulNat0(vuz3180, vuz3190), vuz3190, vuz31700)
67.74/34.81	   new_quot0(Pos(vuz3190), Pos(vuz3170), Neg(vuz3160), vuz318, ty_Int) -> new_primQuotInt79(new_primMulNat0(vuz3190, vuz3170), new_primMulNat0(vuz3160, vuz3170), vuz318, vuz3190, new_primMulNat0(vuz3160, vuz3170), new_primMulNat0(vuz3190, vuz3170))
67.74/34.81	   new_primQuotInt32(vuz416, Pos(Zero)) -> new_error
67.74/34.81	   new_primQuotInt20(vuz446, False, vuz447, vuz3190, vuz3170) -> new_primQuotInt88(vuz446, vuz447, vuz3190, vuz3170)
67.74/34.81	   new_primMulNat0(Zero, Zero) -> Zero
67.74/34.81	   new_quot(Pos(vuz3160), Neg(vuz3170), Pos(Zero), Pos(Succ(vuz31900)), ty_Int) -> new_primQuotInt67(Zero, new_primMulNat0(vuz3160, vuz3170), Zero, new_primMulNat0(vuz3160, vuz3170), vuz31900, vuz3170)
67.74/34.81	   new_abs0(vuz3190, vuz3170) -> new_absReal1(new_sr(Pos(vuz3190), Neg(vuz3170)), new_sr(Pos(vuz3190), Neg(vuz3170)))
67.74/34.81	   new_primQuotInt12(vuz366, Succ(vuz3690), Zero, vuz367) -> new_primQuotInt69(vuz366, new_primEqInt4(Succ(vuz3690)), Succ(vuz3690), vuz367)
67.74/34.81	   new_primQuotInt59(vuz378, vuz381, Neg(vuz3180), vuz3190, vuz380, vuz379) -> new_primQuotInt38(vuz378, vuz381, new_primMulNat0(vuz3180, vuz3190), vuz380, new_primMulNat0(vuz3180, vuz3190), vuz379)
67.74/34.81	   new_primQuotInt85(vuz370, vuz508, vuz371) -> new_primQuotInt31(vuz370, new_esEs(new_abs(vuz371)), new_abs1(vuz508), new_abs(vuz371))
67.74/34.81	   new_quot(Neg(vuz3160), Pos(vuz3170), Neg(Succ(vuz31800)), Neg(Zero), ty_Int) -> new_primQuotInt40(new_primMulNat0(vuz3160, vuz3170), new_primMulNat0(vuz3160, vuz3170), vuz3170)
67.74/34.81	   new_primQuotInt78(vuz366, vuz369, Pos(vuz3180), vuz3190, vuz368, vuz367) -> new_primQuotInt65(vuz366, vuz369, new_primMulNat0(vuz3180, vuz3190), vuz368, new_primMulNat0(vuz3180, vuz3190), vuz367)
67.74/34.81	   new_primQuotInt40(Succ(vuz4540), vuz455, vuz3170) -> new_primQuotInt19(Succ(vuz4540), Succ(vuz4540), Zero, vuz3170)
67.74/34.81	   new_primQuotInt29(vuz374, vuz377, vuz489, vuz376, vuz488, vuz375) -> new_primQuotInt39(vuz374, vuz489, vuz377, vuz375)
67.74/34.81	   new_primQuotInt19(vuz446, vuz447, vuz3190, vuz3170) -> new_primQuotInt20(vuz446, new_esEs(Neg(vuz447)), vuz447, vuz3190, vuz3170)
67.74/34.81	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.81	   new_primQuotInt74(Zero, Zero, vuz451, vuz450, vuz31900, vuz3170) -> new_primQuotInt22(Zero, Zero, Succ(vuz31900), vuz3170)
67.74/34.81	   new_primQuotInt51(vuz428, True, vuz429, vuz3190, vuz3170) -> new_primQuotInt82(vuz428, new_esEs(new_sr(Pos(vuz3190), Neg(vuz3170))), vuz429, vuz3190, vuz3170)
67.74/34.81	   new_primQuotInt90(vuz370, vuz373, vuz487, vuz372, vuz486, vuz371) -> new_primQuotInt91(vuz370, new_primEqInt3(new_primPlusNat1(vuz373, vuz487)), new_primPlusNat1(vuz373, vuz487), vuz371)
67.74/34.81	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.81	   new_primQuotInt32(vuz416, Pos(Succ(vuz54900))) -> Pos(new_primDivNatS1(vuz416, vuz54900))
67.74/34.81	   new_primQuotInt83(vuz366, True, vuz505, vuz367) -> new_primQuotInt44(vuz366)
67.74/34.81	   new_primQuotInt33(vuz398, False, vuz399, vuz3190, vuz3170) -> new_primQuotInt34(vuz398, vuz399, vuz3190, vuz3170)
67.74/34.81	   new_primQuotInt36(Succ(vuz4090), Zero, vuz411, vuz410, vuz3190, vuz31700) -> new_primQuotInt18(Succ(vuz4090), Succ(vuz4090), vuz3190, Succ(vuz31700))
67.74/34.81	   new_quot(Neg(Succ(vuz31600)), Neg(Zero), Pos(vuz3180), Neg(vuz3190), ty_Int) -> new_primQuotInt75(new_primMulNat0(vuz3180, vuz3190), new_primMulNat0(vuz3180, vuz3190), vuz3190)
67.74/34.81	   new_primQuotInt81(vuz390, vuz393, Neg(vuz3180), vuz3190, vuz392, vuz391) -> new_primQuotInt11(vuz390, vuz393, new_primMulNat0(vuz3180, vuz3190), vuz392, new_primMulNat0(vuz3180, vuz3190), vuz391)
67.74/34.81	   new_primQuotInt71(Succ(vuz4240), vuz425, vuz3170) -> new_primQuotInt50(Succ(vuz4240), Succ(vuz4240), Zero, vuz3170)
67.74/34.81	   new_primQuotInt40(Zero, vuz455, vuz3170) -> new_primQuotInt22(Zero, Zero, Zero, vuz3170)
67.74/34.81	   new_negate0(Neg(vuz300)) -> Pos(vuz300)
67.74/34.81	   new_primQuotInt62(Zero, Succ(vuz4000), vuz403, vuz402, vuz3190, vuz31700) -> new_primQuotInt19(Succ(vuz4000), Succ(vuz4000), vuz3190, Succ(vuz31700))
67.74/34.81	   new_reduce2Reduce1(vuz316, vuz317, vuz318, vuz319, False, ba) -> :%(new_quot(vuz316, vuz317, vuz318, vuz319, ba), new_quot0(vuz319, vuz317, vuz316, vuz318, ba))
67.74/34.81	   new_primQuotInt9(vuz428, vuz429, vuz3190, vuz3170) -> new_primQuotInt10(vuz428, new_esEs(new_abs0(vuz3190, vuz3170)), new_abs1(vuz429), new_abs0(vuz3190, vuz3170))
67.74/34.81	   new_primQuotInt73(Succ(vuz4440), vuz445, vuz3170) -> new_primQuotInt17(Succ(vuz4440), Succ(vuz4440), Zero, vuz3170)
67.74/34.81	   new_primQuotInt87(vuz446, True, vuz447, vuz3190, vuz3170) -> new_primQuotInt55(vuz446)
67.74/34.81	   new_primQuotInt71(Zero, vuz425, vuz3170) -> new_primQuotInt68(Zero, Zero, Zero, vuz3170)
67.74/34.81	   new_primQuotInt13(vuz348, True, vuz349, vuz3190, vuz3170) -> new_primQuotInt15(vuz348, new_esEs(new_sr(Pos(vuz3190), Pos(vuz3170))), vuz349, vuz3190, vuz3170)
67.74/34.81	   new_quot(Neg(vuz3160), Pos(vuz3170), Pos(Succ(vuz31800)), Pos(Succ(vuz31900)), ty_Int) -> new_primQuotInt72(new_primPlusNat1(new_primMulNat0(vuz31800, Succ(vuz31900)), Succ(vuz31900)), new_primMulNat0(vuz3160, vuz3170), new_primPlusNat1(new_primMulNat0(vuz31800, Succ(vuz31900)), Succ(vuz31900)), new_primMulNat0(vuz3160, vuz3170), vuz31900, vuz3170)
67.74/34.81	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.81	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.81	   new_primQuotInt69(vuz366, False, vuz505, vuz367) -> new_primQuotInt49(vuz366, vuz505, vuz367)
67.74/34.81	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.81	   new_primQuotInt84(vuz370, True, vuz508, vuz371) -> new_primQuotInt44(vuz370)
67.74/34.81	   new_primQuotInt25(vuz374, False, vuz511, vuz375) -> new_primQuotInt26(vuz374, vuz511, vuz375)
67.74/34.81	   new_primQuotInt39(vuz374, Zero, Zero, vuz375) -> new_primQuotInt54(vuz374, new_primEqInt4(Zero), Zero, vuz375)
67.74/34.81	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.81	   new_primQuotInt86(vuz416, False, vuz417, vuz3190, vuz3170) -> new_primQuotInt37(vuz416, vuz417, vuz3190, vuz3170)
67.74/34.81	   new_primQuotInt10(vuz428, False, vuz552, vuz544) -> new_primQuotInt70(vuz428, new_gcd0Gcd'2(vuz544, vuz552))
67.74/34.81	   new_quot(Neg(vuz3160), Neg(vuz3170), Neg(vuz3180), Neg(vuz3190), ty_Int) -> new_primQuotInt45(new_primPlusNat1(new_primMulNat0(vuz3160, vuz3170), new_primMulNat0(vuz3180, vuz3190)), new_primPlusNat1(new_primMulNat0(vuz3160, vuz3170), new_primMulNat0(vuz3180, vuz3190)), vuz3190, vuz3170)
67.74/34.81	   new_primDivNatS1(Succ(Zero), Zero) -> Succ(new_primDivNatS1(new_primMinusNatS1, Zero))
67.74/34.81	   new_quot(Pos(Zero), Pos(Zero), Neg(vuz3180), Pos(vuz3190), ty_Int) -> new_primQuotInt16(new_primMulNat0(vuz3180, vuz3190), new_primMulNat0(vuz3180, vuz3190), vuz3190)
67.74/34.81	   new_primQuotInt35(vuz398, True, vuz399, vuz3190, vuz3170) -> new_primQuotInt44(vuz398)
67.74/34.81	   new_quot(Neg(vuz3160), Pos(vuz3170), Neg(vuz3180), Pos(vuz3190), ty_Int) -> new_primQuotInt17(new_primPlusNat1(new_primMulNat0(vuz3160, vuz3170), new_primMulNat0(vuz3180, vuz3190)), new_primPlusNat1(new_primMulNat0(vuz3160, vuz3170), new_primMulNat0(vuz3180, vuz3190)), vuz3190, vuz3170)
67.74/34.81	   new_primQuotInt23(vuz416, False, vuz417, vuz3190, vuz3170) -> new_primQuotInt37(vuz416, vuz417, vuz3190, vuz3170)
67.74/34.81	   new_sr(Pos(vuz30610), Neg(vuz30710)) -> Neg(new_primMulNat0(vuz30610, vuz30710))
67.74/34.81	   new_sr(Neg(vuz30610), Pos(vuz30710)) -> Neg(new_primMulNat0(vuz30610, vuz30710))
67.74/34.81	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.81	   new_primPlusNat1(Succ(vuz33500), Succ(vuz3071000)) -> Succ(Succ(new_primPlusNat1(vuz33500, vuz3071000)))
67.74/34.81	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.81	   new_primQuotInt46(vuz360, False, vuz361, vuz3190, vuz3170) -> new_primQuotInt60(vuz360, vuz361, vuz3190, vuz3170)
67.74/34.81	   new_quot(Neg(vuz3160), Pos(vuz3170), Pos(Succ(vuz31800)), Pos(Zero), ty_Int) -> new_primQuotInt73(new_primMulNat0(vuz3160, vuz3170), new_primMulNat0(vuz3160, vuz3170), vuz3170)
67.74/34.81	   new_primDivNatS01(vuz574, vuz575, Zero, Zero) -> new_primDivNatS02(vuz574, vuz575)
67.74/34.81	   new_primQuotInt33(vuz398, True, vuz399, vuz3190, vuz3170) -> new_primQuotInt35(vuz398, new_esEs(new_sr(Pos(vuz3190), Pos(vuz3170))), vuz399, vuz3190, vuz3170)
67.74/34.81	   new_primQuotInt70(vuz428, Pos(Succ(vuz55200))) -> Neg(new_primDivNatS1(vuz428, vuz55200))
67.74/34.81	   new_absReal1(vuz554, Neg(Zero)) -> new_absReal11(vuz554)
67.74/34.81	   new_primQuotInt56(Zero, Zero, vuz459, vuz458, vuz3190, vuz31700) -> new_primQuotInt45(Zero, Zero, vuz3190, Succ(vuz31700))
67.74/34.81	   new_primQuotInt39(vuz374, Succ(vuz4890), Zero, vuz375) -> new_primQuotInt54(vuz374, new_primEqInt4(Succ(vuz4890)), Succ(vuz4890), vuz375)
67.74/34.81	   new_quot(Pos(vuz3160), Neg(vuz3170), Neg(Succ(vuz31800)), Neg(Succ(vuz31900)), ty_Int) -> new_primQuotInt47(new_primPlusNat1(new_primMulNat0(vuz31800, Succ(vuz31900)), Succ(vuz31900)), new_primMulNat0(vuz3160, vuz3170), new_primPlusNat1(new_primMulNat0(vuz31800, Succ(vuz31900)), Succ(vuz31900)), new_primMulNat0(vuz3160, vuz3170), vuz31900, vuz3170)
67.74/34.81	   new_primQuotInt63(vuz378, False, vuz514, vuz379) -> new_primQuotInt41(vuz378, vuz514, vuz379)
67.74/34.81	   new_abs2(vuz3190, vuz3170) -> new_absReal1(new_sr(Neg(vuz3190), Neg(vuz3170)), new_sr(Neg(vuz3190), Neg(vuz3170)))
67.74/34.81	   new_primQuotInt68(vuz354, vuz355, vuz3190, vuz3170) -> new_primQuotInt92(vuz354, new_esEs(Pos(vuz355)), vuz355, vuz3190, vuz3170)
67.74/34.81	   new_primQuotInt36(Zero, Succ(vuz4080), vuz411, vuz410, vuz3190, vuz31700) -> new_primQuotInt17(Succ(vuz4080), Succ(vuz4080), vuz3190, Succ(vuz31700))
67.74/34.81	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.81	   new_quot(Pos(Succ(vuz31600)), Pos(Succ(vuz31700)), Neg(vuz3180), Pos(vuz3190), ty_Int) -> new_primQuotInt36(new_primPlusNat1(new_primMulNat0(vuz31600, Succ(vuz31700)), Succ(vuz31700)), new_primMulNat0(vuz3180, vuz3190), new_primPlusNat1(new_primMulNat0(vuz31600, Succ(vuz31700)), Succ(vuz31700)), new_primMulNat0(vuz3180, vuz3190), vuz3190, vuz31700)
67.74/34.81	   new_primQuotInt77(Succ(vuz4700), vuz471, vuz3190) -> new_primQuotInt50(Succ(vuz4700), Succ(vuz4700), vuz3190, Zero)
67.74/34.81	   new_primQuotInt67(Succ(vuz4190), Zero, vuz421, vuz420, vuz31900, vuz3170) -> new_primQuotInt68(Succ(vuz4190), Succ(vuz4190), Succ(vuz31900), vuz3170)
67.74/34.81	   new_primQuotInt65(vuz366, vuz369, vuz481, vuz368, vuz480, vuz367) -> new_primQuotInt69(vuz366, new_primEqInt4(new_primPlusNat1(vuz369, vuz481)), new_primPlusNat1(vuz369, vuz481), vuz367)
67.74/34.81	   new_primQuotInt31(vuz416, False, vuz549, vuz542) -> new_primQuotInt32(vuz416, new_gcd0Gcd'2(vuz542, vuz549))
67.74/34.81	   new_primQuotInt82(vuz428, True, vuz429, vuz3190, vuz3170) -> new_primQuotInt55(vuz428)
67.74/34.81	   new_primQuotInt14(vuz348, vuz349, vuz3190, vuz3170) -> new_primQuotInt10(vuz348, new_esEs(new_abs3(vuz3190, vuz3170)), new_abs1(vuz349), new_abs3(vuz3190, vuz3170))
67.74/34.81	   new_gcd0Gcd'2(vuz542, vuz549) -> new_gcd0Gcd'10(new_esEs(new_rem(vuz549, vuz542)), vuz542, vuz549)
67.74/34.81	   new_primQuotInt77(Zero, vuz471, vuz3190) -> new_primQuotInt68(Zero, Zero, vuz3190, Zero)
67.74/34.81	   new_primQuotInt66(vuz426, False, vuz427, vuz3190, vuz3170) -> new_primQuotInt21(vuz426, vuz427, vuz3190, vuz3170)
67.74/34.81	   new_quot(Pos(vuz3160), Neg(vuz3170), Pos(Succ(vuz31800)), Pos(Succ(vuz31900)), ty_Int) -> new_primQuotInt67(new_primPlusNat1(new_primMulNat0(vuz31800, Succ(vuz31900)), Succ(vuz31900)), new_primMulNat0(vuz3160, vuz3170), new_primPlusNat1(new_primMulNat0(vuz31800, Succ(vuz31900)), Succ(vuz31900)), new_primMulNat0(vuz3160, vuz3170), vuz31900, vuz3170)
67.74/34.81	   new_primQuotInt48(vuz426, vuz427, vuz3190, vuz3170) -> new_primQuotInt66(vuz426, new_esEs(Neg(vuz427)), vuz427, vuz3190, vuz3170)
67.74/34.81	   new_quot(Pos(Succ(vuz31600)), Pos(Zero), Pos(vuz3180), Neg(vuz3190), ty_Int) -> new_primQuotInt24(new_primMulNat0(vuz3180, vuz3190), new_primMulNat0(vuz3180, vuz3190), vuz3190)
67.74/34.81	   new_primQuotInt22(vuz416, vuz417, vuz3190, vuz3170) -> new_primQuotInt23(vuz416, new_esEs(Pos(vuz417)), vuz417, vuz3190, vuz3170)
67.74/34.81	   new_sr(Neg(vuz30610), Neg(vuz30710)) -> Pos(new_primMulNat0(vuz30610, vuz30710))
67.74/34.81	   new_primDivNatS01(vuz574, vuz575, Succ(vuz5760), Zero) -> new_primDivNatS02(vuz574, vuz575)
67.74/34.81	   new_primQuotInt89(vuz426, False, vuz427, vuz3190, vuz3170) -> new_primQuotInt21(vuz426, vuz427, vuz3190, vuz3170)
67.74/34.81	   new_esEs0(vuz3061, vuz3071, ty_Integer) -> error([])
67.74/34.81	   new_primQuotInt87(vuz446, False, vuz447, vuz3190, vuz3170) -> new_primQuotInt88(vuz446, vuz447, vuz3190, vuz3170)
67.74/34.81	   new_negate0(Pos(vuz300)) -> Neg(vuz300)
67.74/34.81	   new_primQuotInt64(vuz394, vuz397, Pos(vuz3180), vuz3190, vuz396, vuz395) -> new_primQuotInt52(vuz394, vuz397, new_primMulNat0(vuz3180, vuz3190), vuz396, new_primMulNat0(vuz3180, vuz3190), vuz395)
67.74/34.81	   new_primQuotInt88(vuz446, vuz447, vuz3190, vuz3170) -> new_primQuotInt10(vuz446, new_esEs(new_abs4(vuz3190, vuz3170)), new_abs1(vuz447), new_abs4(vuz3190, vuz3170))
67.74/34.81	   new_primQuotInt42(vuz354, True, vuz355, vuz3190, vuz3170) -> new_primQuotInt44(vuz354)
67.74/34.81	   new_primQuotInt76(Succ(vuz4650), Succ(vuz4640), vuz467, vuz466, vuz3190, vuz31700) -> new_primQuotInt76(vuz4650, vuz4640, vuz4650, vuz4640, vuz3190, vuz31700)
67.74/34.81	   new_primQuotInt72(Succ(vuz4390), Zero, vuz441, vuz440, vuz31900, vuz3170) -> new_primQuotInt18(Succ(vuz4390), Succ(vuz4390), Succ(vuz31900), vuz3170)
67.74/34.81	   new_primQuotInt59(vuz378, vuz381, Pos(vuz3180), vuz3190, vuz380, vuz379) -> new_primQuotInt53(vuz378, vuz381, new_primMulNat0(vuz3180, vuz3190), vuz380, new_primMulNat0(vuz3180, vuz3190), vuz379)
67.74/34.81	   new_primQuotInt75(Zero, vuz463, vuz3190) -> new_primQuotInt45(Zero, Zero, vuz3190, Zero)
67.74/34.81	   new_primEqInt3(Zero) -> new_primEqInt2
67.74/34.81	   new_primMinusNatS1 -> Zero
67.74/34.81	   new_negate(:%(vuz30, vuz31)) -> :%(new_negate0(vuz30), vuz31)
67.74/34.81	   new_primQuotInt70(vuz428, Neg(Zero)) -> new_error
67.74/34.81	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.81	   new_quot(Pos(vuz3160), Pos(vuz3170), Neg(vuz3180), Neg(vuz3190), ty_Int) -> new_primQuotInt22(new_primPlusNat1(new_primMulNat0(vuz3160, vuz3170), new_primMulNat0(vuz3180, vuz3190)), new_primPlusNat1(new_primMulNat0(vuz3160, vuz3170), new_primMulNat0(vuz3180, vuz3190)), vuz3190, vuz3170)
67.74/34.81	   new_gcd0Gcd'10(True, vuz542, vuz549) -> vuz542
67.74/34.81	   new_primQuotInt12(vuz366, Succ(vuz3690), Succ(vuz4830), vuz367) -> new_primQuotInt12(vuz366, vuz3690, vuz4830, vuz367)
67.74/34.81	   new_primQuotInt57(vuz382, vuz385, Pos(vuz3180), vuz3190, vuz384, vuz383) -> new_primQuotInt38(vuz382, vuz385, new_primMulNat0(vuz3180, vuz3190), vuz384, new_primMulNat0(vuz3180, vuz3190), vuz383)
67.74/34.81	   new_primEqInt4(Succ(vuz3250)) -> new_primEqInt(vuz3250)
67.74/34.81	   new_primQuotInt78(vuz366, vuz369, Neg(vuz3180), vuz3190, vuz368, vuz367) -> new_primQuotInt52(vuz366, vuz369, new_primMulNat0(vuz3180, vuz3190), vuz368, new_primMulNat0(vuz3180, vuz3190), vuz367)
67.74/34.81	   new_quot0(Neg(vuz3190), Neg(vuz3170), Neg(vuz3160), vuz318, ty_Int) -> new_primQuotInt64(new_primMulNat0(vuz3190, vuz3170), new_primMulNat0(vuz3160, vuz3170), vuz318, vuz3190, new_primMulNat0(vuz3160, vuz3170), new_primMulNat0(vuz3190, vuz3170))
67.74/34.81	   new_quot(Pos(vuz3160), Neg(vuz3170), Neg(Zero), Neg(Succ(vuz31900)), ty_Int) -> new_primQuotInt47(Zero, new_primMulNat0(vuz3160, vuz3170), Zero, new_primMulNat0(vuz3160, vuz3170), vuz31900, vuz3170)
67.74/34.81	   new_absReal10(vuz554) -> vuz554
67.74/34.81	   new_primQuotInt52(vuz366, vuz369, vuz483, vuz368, vuz482, vuz367) -> new_primQuotInt12(vuz366, vuz369, vuz483, vuz367)
67.74/34.81	   new_primQuotInt86(vuz416, True, vuz417, vuz3190, vuz3170) -> new_primQuotInt44(vuz416)
67.74/34.81	   new_primQuotInt45(vuz360, vuz361, vuz3190, vuz3170) -> new_primQuotInt46(vuz360, new_esEs(Pos(vuz361)), vuz361, vuz3190, vuz3170)
67.74/34.81	   new_primQuotInt12(vuz366, Zero, Succ(vuz4830), vuz367) -> new_primQuotInt91(vuz366, new_primEqInt3(Succ(vuz4830)), Succ(vuz4830), vuz367)
67.74/34.81	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.81	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.81	   new_primQuotInt17(vuz348, vuz349, vuz3190, vuz3170) -> new_primQuotInt13(vuz348, new_esEs(Neg(vuz349)), vuz349, vuz3190, vuz3170)
67.74/34.81	   new_primQuotInt67(Zero, Succ(vuz4180), vuz421, vuz420, vuz31900, vuz3170) -> new_primQuotInt50(Succ(vuz4180), Succ(vuz4180), Succ(vuz31900), vuz3170)
67.74/34.81	   new_primQuotInt92(vuz354, False, vuz355, vuz3190, vuz3170) -> new_primQuotInt43(vuz354, vuz355, vuz3190, vuz3170)
67.74/34.81	   new_quot(Pos(Zero), Pos(Zero), Pos(vuz3180), Neg(vuz3190), ty_Int) -> new_primQuotInt24(new_primMulNat0(vuz3180, vuz3190), new_primMulNat0(vuz3180, vuz3190), vuz3190)
67.74/34.81	   new_primQuotInt75(Succ(vuz4620), vuz463, vuz3190) -> new_primQuotInt48(Succ(vuz4620), Succ(vuz4620), vuz3190, Zero)
67.74/34.81	   new_primQuotInt70(vuz428, Neg(Succ(vuz55200))) -> Pos(new_primDivNatS1(vuz428, vuz55200))
67.74/34.81	   new_quot(Pos(vuz3160), Pos(vuz3170), Pos(vuz3180), Pos(vuz3190), ty_Int) -> new_primQuotInt18(new_primPlusNat1(new_primMulNat0(vuz3160, vuz3170), new_primMulNat0(vuz3180, vuz3190)), new_primPlusNat1(new_primMulNat0(vuz3160, vuz3170), new_primMulNat0(vuz3180, vuz3190)), vuz3190, vuz3170)
67.74/34.81	   new_primPlusNat0(Succ(vuz3350), vuz307100) -> Succ(Succ(new_primPlusNat1(vuz3350, vuz307100)))
67.74/34.81	   new_primQuotInt84(vuz370, False, vuz508, vuz371) -> new_primQuotInt85(vuz370, vuz508, vuz371)
67.74/34.81	   new_primQuotInt42(vuz354, False, vuz355, vuz3190, vuz3170) -> new_primQuotInt43(vuz354, vuz355, vuz3190, vuz3170)
67.74/34.81	   new_primQuotInt43(vuz354, vuz355, vuz3190, vuz3170) -> new_primQuotInt31(vuz354, new_esEs(new_abs0(vuz3190, vuz3170)), new_abs(vuz355), new_abs0(vuz3190, vuz3170))
67.74/34.81	   new_primEqInt2 -> True
67.74/34.81	   new_primQuotInt62(Zero, Zero, vuz403, vuz402, vuz3190, vuz31700) -> new_primQuotInt22(Zero, Zero, vuz3190, Succ(vuz31700))
67.74/34.81	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.81	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.81	   new_primPlusNat1(Zero, Zero) -> Zero
67.74/34.81	   new_primQuotInt16(Succ(vuz4140), vuz415, vuz3190) -> new_primQuotInt17(Succ(vuz4140), Succ(vuz4140), vuz3190, Zero)
67.74/34.81	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.81	   new_primMulNat0(Succ(vuz306100), Zero) -> Zero
67.74/34.81	   new_primMulNat0(Zero, Succ(vuz307100)) -> Zero
67.74/34.81	   new_primQuotInt16(Zero, vuz415, vuz3190) -> new_primQuotInt18(Zero, Zero, vuz3190, Zero)
67.74/34.81	   new_sr(Pos(vuz30610), Pos(vuz30710)) -> Pos(new_primMulNat0(vuz30610, vuz30710))
67.74/34.81	   new_primQuotInt55(vuz426) -> error([])
67.74/34.81	   new_primQuotInt12(vuz366, Zero, Zero, vuz367) -> new_primQuotInt69(vuz366, new_primEqInt4(Zero), Zero, vuz367)
67.74/34.81	   new_primPlusNat0(Zero, vuz307100) -> Succ(vuz307100)
67.74/34.81	   new_primQuotInt92(vuz354, True, vuz355, vuz3190, vuz3170) -> new_primQuotInt42(vuz354, new_esEs(new_sr(Pos(vuz3190), Neg(vuz3170))), vuz355, vuz3190, vuz3170)
67.74/34.81	   new_primQuotInt72(Zero, Succ(vuz4380), vuz441, vuz440, vuz31900, vuz3170) -> new_primQuotInt17(Succ(vuz4380), Succ(vuz4380), Succ(vuz31900), vuz3170)
67.74/34.81	   new_quot(Pos(Succ(vuz31600)), Pos(Succ(vuz31700)), Pos(vuz3180), Neg(vuz3190), ty_Int) -> new_primQuotInt62(new_primPlusNat1(new_primMulNat0(vuz31600, Succ(vuz31700)), Succ(vuz31700)), new_primMulNat0(vuz3180, vuz3190), new_primPlusNat1(new_primMulNat0(vuz31600, Succ(vuz31700)), Succ(vuz31700)), new_primMulNat0(vuz3180, vuz3190), vuz3190, vuz31700)
67.74/34.81	   new_primQuotInt21(vuz426, vuz427, vuz3190, vuz3170) -> new_primQuotInt10(vuz426, new_esEs(new_abs2(vuz3190, vuz3170)), new_abs1(vuz427), new_abs2(vuz3190, vuz3170))
67.74/34.81	   new_primQuotInt91(vuz370, True, vuz508, vuz371) -> new_primQuotInt84(vuz370, new_esEs(Pos(vuz371)), vuz508, vuz371)
67.74/34.81	   new_primQuotInt51(vuz428, False, vuz429, vuz3190, vuz3170) -> new_primQuotInt9(vuz428, vuz429, vuz3190, vuz3170)
67.74/34.81	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.81	   new_primQuotInt47(Succ(vuz4310), Zero, vuz433, vuz432, vuz31900, vuz3170) -> new_primQuotInt45(Succ(vuz4310), Succ(vuz4310), Succ(vuz31900), vuz3170)
67.74/34.81	   new_primQuotInt83(vuz366, False, vuz505, vuz367) -> new_primQuotInt49(vuz366, vuz505, vuz367)
67.74/34.81	   new_quot(Neg(Zero), Neg(Zero), Pos(vuz3180), Neg(vuz3190), ty_Int) -> new_primQuotInt75(new_primMulNat0(vuz3180, vuz3190), new_primMulNat0(vuz3180, vuz3190), vuz3190)
67.74/34.81	   new_primEqInt0(vuz3260) -> False
67.74/34.81	   new_primQuotInt18(vuz398, vuz399, vuz3190, vuz3170) -> new_primQuotInt33(vuz398, new_esEs(Pos(vuz399)), vuz399, vuz3190, vuz3170)
67.74/34.81	   new_abs3(vuz3190, vuz3170) -> new_absReal1(new_sr(Pos(vuz3190), Pos(vuz3170)), new_sr(Pos(vuz3190), Pos(vuz3170)))
67.74/34.81	   new_quot(Neg(vuz3160), Pos(vuz3170), Pos(Zero), Pos(Zero), ty_Int) -> new_primQuotInt73(new_primMulNat0(vuz3160, vuz3170), new_primMulNat0(vuz3160, vuz3170), vuz3170)
67.74/34.81	   new_primQuotInt28(vuz374, vuz377, Pos(vuz3180), vuz3190, vuz376, vuz375) -> new_primQuotInt29(vuz374, vuz377, new_primMulNat0(vuz3180, vuz3190), vuz376, new_primMulNat0(vuz3180, vuz3190), vuz375)
67.74/34.81	   new_primQuotInt58(Succ(vuz4360), vuz437, vuz3170) -> new_primQuotInt48(Succ(vuz4360), Succ(vuz4360), Zero, vuz3170)
67.74/34.81	   new_quot(Neg(vuz3160), Neg(vuz3170), Pos(vuz3180), Pos(vuz3190), ty_Int) -> new_primQuotInt68(new_primPlusNat1(new_primMulNat0(vuz3160, vuz3170), new_primMulNat0(vuz3180, vuz3190)), new_primPlusNat1(new_primMulNat0(vuz3160, vuz3170), new_primMulNat0(vuz3180, vuz3190)), vuz3190, vuz3170)
67.74/34.81	   new_primMulNat0(Succ(vuz306100), Succ(vuz307100)) -> new_primPlusNat0(new_primMulNat0(vuz306100, Succ(vuz307100)), vuz307100)
67.74/34.81	   new_primQuotInt10(vuz428, True, vuz552, vuz544) -> new_primQuotInt70(vuz428, vuz552)
67.74/34.81	   new_primQuotInt49(vuz366, vuz505, vuz367) -> new_primQuotInt31(vuz366, new_esEs(new_abs(vuz367)), new_abs(vuz505), new_abs(vuz367))
67.74/34.81	   new_primEqInt3(Succ(vuz3260)) -> new_primEqInt0(vuz3260)
67.74/34.81	   new_primQuotInt61(vuz360, False, vuz361, vuz3190, vuz3170) -> new_primQuotInt60(vuz360, vuz361, vuz3190, vuz3170)
67.74/34.81	   new_primQuotInt61(vuz360, True, vuz361, vuz3190, vuz3170) -> new_primQuotInt44(vuz360)
67.74/34.81	   new_primQuotInt54(vuz378, True, vuz514, vuz379) -> new_primQuotInt63(vuz378, new_esEs(Neg(vuz379)), vuz514, vuz379)
67.74/34.81	   new_primPlusNat1(Succ(vuz33500), Zero) -> Succ(vuz33500)
67.74/34.81	   new_primPlusNat1(Zero, Succ(vuz3071000)) -> Succ(vuz3071000)
67.74/34.81	   new_primQuotInt82(vuz428, False, vuz429, vuz3190, vuz3170) -> new_primQuotInt9(vuz428, vuz429, vuz3190, vuz3170)
67.74/34.81	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.81	   new_primQuotInt74(Succ(vuz4490), Succ(vuz4480), vuz451, vuz450, vuz31900, vuz3170) -> new_primQuotInt74(vuz4490, vuz4480, vuz4490, vuz4480, vuz31900, vuz3170)
67.74/34.81	   new_primQuotInt38(vuz378, vuz381, vuz495, vuz380, vuz494, vuz379) -> new_primQuotInt39(vuz378, vuz381, vuz495, vuz379)
67.74/34.81	   new_primQuotInt66(vuz426, True, vuz427, vuz3190, vuz3170) -> new_primQuotInt89(vuz426, new_esEs(new_sr(Neg(vuz3190), Neg(vuz3170))), vuz427, vuz3190, vuz3170)
67.74/34.81	   new_quot(Pos(vuz3160), Neg(vuz3170), Neg(Zero), Neg(Zero), ty_Int) -> new_primQuotInt58(new_primMulNat0(vuz3160, vuz3170), new_primMulNat0(vuz3160, vuz3170), vuz3170)
67.74/34.81	   new_primQuotInt24(Zero, vuz407, vuz3190) -> new_primQuotInt22(Zero, Zero, vuz3190, Zero)
67.74/34.81	   new_quot0(vuz319, vuz317, vuz316, vuz318, ty_Integer) -> error([])
67.74/34.81	   new_primQuotInt70(vuz428, Pos(Zero)) -> new_error
67.74/34.81	   new_esEs0(vuz3061, vuz3071, ty_Int) -> new_esEs(new_sr(vuz3061, vuz3071))
67.74/34.81	   new_primQuotInt76(Succ(vuz4650), Zero, vuz467, vuz466, vuz3190, vuz31700) -> new_primQuotInt68(Succ(vuz4650), Succ(vuz4650), vuz3190, Succ(vuz31700))
67.74/34.81	   new_primDivNatS1(Succ(Succ(vuz41600)), Succ(vuz549000)) -> new_primDivNatS01(vuz41600, vuz549000, vuz41600, vuz549000)
67.74/34.81	   new_primEqInt1 -> True
67.74/34.81	   new_quot0(Pos(vuz3190), Neg(vuz3170), Neg(vuz3160), vuz318, ty_Int) -> new_primQuotInt59(new_primMulNat0(vuz3190, vuz3170), new_primMulNat0(vuz3160, vuz3170), vuz318, vuz3190, new_primMulNat0(vuz3160, vuz3170), new_primMulNat0(vuz3190, vuz3170))
67.74/34.81	   new_primQuotInt41(vuz378, vuz514, vuz379) -> new_primQuotInt10(vuz378, new_esEs(new_abs1(vuz379)), new_abs(vuz514), new_abs1(vuz379))
67.74/34.81	   new_primEqInt(vuz3250) -> False
67.74/34.81	   new_ps(:%(vuz3060, vuz3061), :%(vuz3070, vuz3071), h) -> new_reduce2Reduce1(vuz3060, vuz3071, vuz3070, vuz3061, new_esEs0(vuz3061, vuz3071, h), h)
67.74/34.81	   new_primQuotInt54(vuz378, False, vuz514, vuz379) -> new_primQuotInt41(vuz378, vuz514, vuz379)
67.74/34.81	   new_primQuotInt23(vuz416, True, vuz417, vuz3190, vuz3170) -> new_primQuotInt86(vuz416, new_esEs(new_sr(Neg(vuz3190), Pos(vuz3170))), vuz417, vuz3190, vuz3170)
67.74/34.81	   new_reduce2Reduce1(vuz316, vuz317, vuz318, vuz319, True, ba) -> error([])
67.74/34.81	   new_primQuotInt37(vuz416, vuz417, vuz3190, vuz3170) -> new_primQuotInt31(vuz416, new_esEs(new_abs4(vuz3190, vuz3170)), new_abs(vuz417), new_abs4(vuz3190, vuz3170))
67.74/34.81	   new_primQuotInt26(vuz374, vuz511, vuz375) -> new_primQuotInt10(vuz374, new_esEs(new_abs1(vuz375)), new_abs1(vuz511), new_abs1(vuz375))
67.74/34.81	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.81	   new_quot(Neg(Succ(vuz31600)), Neg(Succ(vuz31700)), Pos(vuz3180), Neg(vuz3190), ty_Int) -> new_primQuotInt56(new_primPlusNat1(new_primMulNat0(vuz31600, Succ(vuz31700)), Succ(vuz31700)), new_primMulNat0(vuz3180, vuz3190), new_primPlusNat1(new_primMulNat0(vuz31600, Succ(vuz31700)), Succ(vuz31700)), new_primMulNat0(vuz3180, vuz3190), vuz3190, vuz31700)
67.74/34.81	   new_primQuotInt32(vuz416, Neg(Zero)) -> new_error
67.74/34.81	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.81	   new_gcd0Gcd'00(vuz542, vuz557) -> new_gcd0Gcd'2(vuz557, vuz542)
67.74/34.81	   new_abs(vuz399) -> new_absReal1(Pos(vuz399), Pos(vuz399))
67.74/34.81	   new_quot(vuz316, vuz317, vuz318, vuz319, ty_Integer) -> error([])
67.74/34.81	   new_quot0(Pos(vuz3190), Pos(vuz3170), Pos(vuz3160), vuz318, ty_Int) -> new_primQuotInt78(new_primMulNat0(vuz3190, vuz3170), new_primMulNat0(vuz3160, vuz3170), vuz318, vuz3190, new_primMulNat0(vuz3160, vuz3170), new_primMulNat0(vuz3190, vuz3170))
67.74/34.81	   new_primQuotInt47(Succ(vuz4310), Succ(vuz4300), vuz433, vuz432, vuz31900, vuz3170) -> new_primQuotInt47(vuz4310, vuz4300, vuz4310, vuz4300, vuz31900, vuz3170)
67.74/34.81	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.81	   new_quot(Pos(vuz3160), Neg(vuz3170), Neg(vuz3180), Pos(vuz3190), ty_Int) -> new_primQuotInt50(new_primPlusNat1(new_primMulNat0(vuz3160, vuz3170), new_primMulNat0(vuz3180, vuz3190)), new_primPlusNat1(new_primMulNat0(vuz3160, vuz3170), new_primMulNat0(vuz3180, vuz3190)), vuz3190, vuz3170)
67.74/34.81	   new_primQuotInt15(vuz348, False, vuz349, vuz3190, vuz3170) -> new_primQuotInt14(vuz348, vuz349, vuz3190, vuz3170)
67.74/34.81	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.81	   new_quot(Pos(Zero), Pos(Succ(vuz31700)), Neg(vuz3180), Pos(vuz3190), ty_Int) -> new_primQuotInt36(Zero, new_primMulNat0(vuz3180, vuz3190), Zero, new_primMulNat0(vuz3180, vuz3190), vuz3190, vuz31700)
67.74/34.81	   new_quot(Neg(Zero), Neg(Succ(vuz31700)), Neg(vuz3180), Pos(vuz3190), ty_Int) -> new_primQuotInt76(Zero, new_primMulNat0(vuz3180, vuz3190), Zero, new_primMulNat0(vuz3180, vuz3190), vuz3190, vuz31700)
67.74/34.81	   new_primQuotInt46(vuz360, True, vuz361, vuz3190, vuz3170) -> new_primQuotInt61(vuz360, new_esEs(new_sr(Neg(vuz3190), Neg(vuz3170))), vuz361, vuz3190, vuz3170)
67.74/34.81	   new_quot(Neg(Succ(vuz31600)), Neg(Zero), Neg(vuz3180), Pos(vuz3190), ty_Int) -> new_primQuotInt77(new_primMulNat0(vuz3180, vuz3190), new_primMulNat0(vuz3180, vuz3190), vuz3190)
67.74/34.81	   new_quot0(Neg(vuz3190), Neg(vuz3170), Pos(vuz3160), vuz318, ty_Int) -> new_primQuotInt81(new_primMulNat0(vuz3190, vuz3170), new_primMulNat0(vuz3160, vuz3170), vuz318, vuz3190, new_primMulNat0(vuz3160, vuz3170), new_primMulNat0(vuz3190, vuz3170))
67.74/34.81	   new_primQuotInt60(vuz360, vuz361, vuz3190, vuz3170) -> new_primQuotInt31(vuz360, new_esEs(new_abs2(vuz3190, vuz3170)), new_abs(vuz361), new_abs2(vuz3190, vuz3170))
67.74/34.81	   new_error -> error([])
67.74/34.81	   new_primQuotInt36(Succ(vuz4090), Succ(vuz4080), vuz411, vuz410, vuz3190, vuz31700) -> new_primQuotInt36(vuz4090, vuz4080, vuz4090, vuz4080, vuz3190, vuz31700)
67.74/34.81	   new_primQuotInt34(vuz398, vuz399, vuz3190, vuz3170) -> new_primQuotInt31(vuz398, new_esEs(new_abs3(vuz3190, vuz3170)), new_abs(vuz399), new_abs3(vuz3190, vuz3170))
67.74/34.81	   new_primQuotInt35(vuz398, False, vuz399, vuz3190, vuz3170) -> new_primQuotInt34(vuz398, vuz399, vuz3190, vuz3170)
67.74/34.81	   new_primQuotInt62(Succ(vuz4010), Zero, vuz403, vuz402, vuz3190, vuz31700) -> new_primQuotInt22(Succ(vuz4010), Succ(vuz4010), vuz3190, Succ(vuz31700))
67.74/34.81	   new_primQuotInt63(vuz378, True, vuz514, vuz379) -> new_primQuotInt55(vuz378)
67.74/34.81	   new_primQuotInt72(Succ(vuz4390), Succ(vuz4380), vuz441, vuz440, vuz31900, vuz3170) -> new_primQuotInt72(vuz4390, vuz4380, vuz4390, vuz4380, vuz31900, vuz3170)
67.74/34.81	   new_primQuotInt39(vuz374, Succ(vuz4890), Succ(vuz3770), vuz375) -> new_primQuotInt39(vuz374, vuz4890, vuz3770, vuz375)
67.74/34.81	   new_absReal1(vuz554, Neg(Succ(vuz55500))) -> new_negate0(vuz554)
67.74/34.81	   new_primQuotInt31(vuz416, True, vuz549, vuz542) -> new_primQuotInt32(vuz416, vuz549)
67.74/34.81	   new_primQuotInt91(vuz370, False, vuz508, vuz371) -> new_primQuotInt85(vuz370, vuz508, vuz371)
67.74/34.81	   new_primQuotInt58(Zero, vuz437, vuz3170) -> new_primQuotInt45(Zero, Zero, Zero, vuz3170)
67.74/34.81	   new_primQuotInt89(vuz426, True, vuz427, vuz3190, vuz3170) -> new_primQuotInt55(vuz426)
67.74/34.81	   new_primQuotInt47(Zero, Zero, vuz433, vuz432, vuz31900, vuz3170) -> new_primQuotInt45(Zero, Zero, Succ(vuz31900), vuz3170)
67.74/34.81	
67.74/34.81	Q is empty.
67.74/34.81	We have to consider all (P,Q,R)-chains.
67.74/34.81	----------------------------------------
67.74/34.81	
67.74/34.81	(21) NonTerminationLoopProof (COMPLETE)
67.74/34.81	We used the non-termination processor [FROCOS05] to show that the DP problem is infinite.
67.74/34.81	Found a loop by semiunifying a rule from P directly.
67.74/34.81	
67.74/34.81	s = new_iterate(vuz4, vuz3, vuz5) evaluates to  t =new_iterate(vuz4, vuz3, new_ps(new_ps(vuz4, new_negate(vuz3), ty_Int), vuz5, ty_Int))
67.74/34.81	
67.74/34.81	Thus s starts an infinite chain as s semiunifies with t with the following substitutions:
67.74/34.81	* Matcher: [vuz5 / new_ps(new_ps(vuz4, new_negate(vuz3), ty_Int), vuz5, ty_Int)]
67.74/34.81	* Semiunifier: [ ]
67.74/34.81	
67.74/34.81	--------------------------------------------------------------------------------
67.74/34.81	Rewriting sequence
67.74/34.81	
67.74/34.81	The DP semiunifies directly so there is only one rewrite step from new_iterate(vuz4, vuz3, vuz5) to new_iterate(vuz4, vuz3, new_ps(new_ps(vuz4, new_negate(vuz3), ty_Int), vuz5, ty_Int)).
67.74/34.81	
67.74/34.81	
67.74/34.81	
67.74/34.81	
67.74/34.81	----------------------------------------
67.74/34.81	
67.74/34.81	(22)
67.74/34.81	NO
67.74/34.81	
67.74/34.81	----------------------------------------
67.74/34.81	
67.74/34.81	(23)
67.74/34.81	Obligation:
67.74/34.81	Q DP problem:
67.74/34.81	The TRS P consists of the following rules:
67.74/34.81	
67.74/34.81	   new_primQuotInt7(Succ(vuz4390), Succ(vuz4380), vuz441, vuz440, vuz31900, vuz3170) -> new_primQuotInt7(vuz4390, vuz4380, vuz4390, vuz4380, vuz31900, vuz3170)
67.74/34.81	
67.74/34.81	R is empty.
67.74/34.81	Q is empty.
67.74/34.81	We have to consider all minimal (P,Q,R)-chains.
67.74/34.81	----------------------------------------
67.74/34.81	
67.74/34.81	(24) TransformationProof (EQUIVALENT)
67.74/34.81	By instantiating [LPAR04] the rule new_primQuotInt7(Succ(vuz4390), Succ(vuz4380), vuz441, vuz440, vuz31900, vuz3170) -> new_primQuotInt7(vuz4390, vuz4380, vuz4390, vuz4380, vuz31900, vuz3170) we obtained the following new rules [LPAR04]:
67.74/34.81	
67.74/34.81	   (new_primQuotInt7(Succ(x0), Succ(x1), Succ(x0), Succ(x1), z4, z5) -> new_primQuotInt7(x0, x1, x0, x1, z4, z5),new_primQuotInt7(Succ(x0), Succ(x1), Succ(x0), Succ(x1), z4, z5) -> new_primQuotInt7(x0, x1, x0, x1, z4, z5))
67.74/34.81	
67.74/34.81	
67.74/34.81	----------------------------------------
67.74/34.81	
67.74/34.81	(25)
67.74/34.81	Obligation:
67.74/34.81	Q DP problem:
67.74/34.81	The TRS P consists of the following rules:
67.74/34.81	
67.74/34.81	   new_primQuotInt7(Succ(x0), Succ(x1), Succ(x0), Succ(x1), z4, z5) -> new_primQuotInt7(x0, x1, x0, x1, z4, z5)
67.74/34.81	
67.74/34.81	R is empty.
67.74/34.81	Q is empty.
67.74/34.81	We have to consider all minimal (P,Q,R)-chains.
67.74/34.81	----------------------------------------
67.74/34.81	
67.74/34.81	(26) QDPSizeChangeProof (EQUIVALENT)
67.74/34.81	By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 
67.74/34.81	
67.74/34.81	From the DPs we obtained the following set of size-change graphs:
67.74/34.81	*new_primQuotInt7(Succ(x0), Succ(x1), Succ(x0), Succ(x1), z4, z5) -> new_primQuotInt7(x0, x1, x0, x1, z4, z5)
67.74/34.81	The graph contains the following edges 1 > 1, 3 > 1, 2 > 2, 4 > 2, 1 > 3, 3 > 3, 2 > 4, 4 > 4, 5 >= 5, 6 >= 6
67.74/34.81	
67.74/34.81	
67.74/34.81	----------------------------------------
67.74/34.81	
67.74/34.81	(27)
67.74/34.81	YES
67.74/34.81	
67.74/34.81	----------------------------------------
67.74/34.81	
67.74/34.81	(28)
67.74/34.81	Obligation:
67.74/34.81	Q DP problem:
67.74/34.81	The TRS P consists of the following rules:
67.74/34.81	
67.74/34.81	   new_primDivNatS(Succ(Succ(vuz41600)), Succ(vuz549000)) -> new_primDivNatS0(vuz41600, vuz549000, vuz41600, vuz549000)
67.74/34.81	   new_primDivNatS0(vuz574, vuz575, Zero, Zero) -> new_primDivNatS00(vuz574, vuz575)
67.74/34.81	   new_primDivNatS(Succ(Succ(vuz41600)), Zero) -> new_primDivNatS(new_primMinusNatS0(vuz41600), Zero)
67.74/34.81	   new_primDivNatS0(vuz574, vuz575, Succ(vuz5760), Succ(vuz5770)) -> new_primDivNatS0(vuz574, vuz575, vuz5760, vuz5770)
67.74/34.81	   new_primDivNatS0(vuz574, vuz575, Succ(vuz5760), Zero) -> new_primDivNatS(new_primMinusNatS2(vuz574, vuz575), Succ(vuz575))
67.74/34.81	   new_primDivNatS00(vuz574, vuz575) -> new_primDivNatS(new_primMinusNatS2(vuz574, vuz575), Succ(vuz575))
67.74/34.81	   new_primDivNatS(Succ(Zero), Zero) -> new_primDivNatS(new_primMinusNatS1, Zero)
67.74/34.81	
67.74/34.81	The TRS R consists of the following rules:
67.74/34.81	
67.74/34.81	   new_primMinusNatS1 -> Zero
67.74/34.81	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.81	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.81	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.81	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.81	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.81	
67.74/34.81	The set Q consists of the following terms:
67.74/34.81	
67.74/34.81	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.81	   new_primMinusNatS0(x0)
67.74/34.81	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.81	   new_primMinusNatS2(Zero, Zero)
67.74/34.81	   new_primMinusNatS1
67.74/34.81	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.81	
67.74/34.81	We have to consider all minimal (P,Q,R)-chains.
67.74/34.81	----------------------------------------
67.74/34.81	
67.74/34.81	(29) DependencyGraphProof (EQUIVALENT)
67.74/34.81	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 2 SCCs with 1 less node.
67.74/34.81	----------------------------------------
67.74/34.81	
67.74/34.81	(30)
67.74/34.81	Complex Obligation (AND)
67.74/34.81	
67.74/34.81	----------------------------------------
67.74/34.81	
67.74/34.81	(31)
67.74/34.81	Obligation:
67.74/34.81	Q DP problem:
67.74/34.81	The TRS P consists of the following rules:
67.74/34.81	
67.74/34.81	   new_primDivNatS(Succ(Succ(vuz41600)), Zero) -> new_primDivNatS(new_primMinusNatS0(vuz41600), Zero)
67.74/34.81	
67.74/34.81	The TRS R consists of the following rules:
67.74/34.81	
67.74/34.81	   new_primMinusNatS1 -> Zero
67.74/34.81	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.81	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.81	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.81	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.81	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.81	
67.74/34.81	The set Q consists of the following terms:
67.74/34.81	
67.74/34.81	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.81	   new_primMinusNatS0(x0)
67.74/34.81	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.81	   new_primMinusNatS2(Zero, Zero)
67.74/34.81	   new_primMinusNatS1
67.74/34.81	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.81	
67.74/34.81	We have to consider all minimal (P,Q,R)-chains.
67.74/34.81	----------------------------------------
67.74/34.81	
67.74/34.81	(32) MRRProof (EQUIVALENT)
67.74/34.81	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.
67.74/34.81	
67.74/34.81	Strictly oriented dependency pairs:
67.74/34.81	
67.74/34.81	   new_primDivNatS(Succ(Succ(vuz41600)), Zero) -> new_primDivNatS(new_primMinusNatS0(vuz41600), Zero)
67.74/34.81	
67.74/34.81	Strictly oriented rules of the TRS R:
67.74/34.81	
67.74/34.81	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.81	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.81	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.81	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.81	
67.74/34.81	Used ordering: Polynomial interpretation [POLO]:
67.74/34.81	
67.74/34.81	   POL(Succ(x_1)) = 1 + x_1
67.74/34.81	   POL(Zero) = 2
67.74/34.81	   POL(new_primDivNatS(x_1, x_2)) = x_1 + x_2
67.74/34.81	   POL(new_primMinusNatS0(x_1)) = 1 + x_1
67.74/34.81	   POL(new_primMinusNatS1) = 2
67.74/34.81	   POL(new_primMinusNatS2(x_1, x_2)) = 1 + 2*x_1 + 2*x_2
67.74/34.81	
67.74/34.81	
67.74/34.81	----------------------------------------
67.74/34.81	
67.74/34.81	(33)
67.74/34.81	Obligation:
67.74/34.81	Q DP problem:
67.74/34.81	P is empty.
67.74/34.81	The TRS R consists of the following rules:
67.74/34.81	
67.74/34.81	   new_primMinusNatS1 -> Zero
67.74/34.81	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.81	
67.74/34.81	The set Q consists of the following terms:
67.74/34.81	
67.74/34.81	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.81	   new_primMinusNatS0(x0)
67.74/34.81	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.81	   new_primMinusNatS2(Zero, Zero)
67.74/34.81	   new_primMinusNatS1
67.74/34.81	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.81	
67.74/34.81	We have to consider all minimal (P,Q,R)-chains.
67.74/34.81	----------------------------------------
67.74/34.81	
67.74/34.81	(34) PisEmptyProof (EQUIVALENT)
67.74/34.81	The TRS P is empty. Hence, there is no (P,Q,R) chain.
67.74/34.81	----------------------------------------
67.74/34.81	
67.74/34.81	(35)
67.74/34.81	YES
67.74/34.81	
67.74/34.81	----------------------------------------
67.74/34.81	
67.74/34.81	(36)
67.74/34.81	Obligation:
67.74/34.81	Q DP problem:
67.74/34.81	The TRS P consists of the following rules:
67.74/34.81	
67.74/34.81	   new_primDivNatS0(vuz574, vuz575, Zero, Zero) -> new_primDivNatS00(vuz574, vuz575)
67.74/34.81	   new_primDivNatS00(vuz574, vuz575) -> new_primDivNatS(new_primMinusNatS2(vuz574, vuz575), Succ(vuz575))
67.74/34.81	   new_primDivNatS(Succ(Succ(vuz41600)), Succ(vuz549000)) -> new_primDivNatS0(vuz41600, vuz549000, vuz41600, vuz549000)
67.74/34.81	   new_primDivNatS0(vuz574, vuz575, Succ(vuz5760), Succ(vuz5770)) -> new_primDivNatS0(vuz574, vuz575, vuz5760, vuz5770)
67.74/34.81	   new_primDivNatS0(vuz574, vuz575, Succ(vuz5760), Zero) -> new_primDivNatS(new_primMinusNatS2(vuz574, vuz575), Succ(vuz575))
67.74/34.81	
67.74/34.81	The TRS R consists of the following rules:
67.74/34.81	
67.74/34.81	   new_primMinusNatS1 -> Zero
67.74/34.81	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.81	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.81	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.81	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.81	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.81	
67.74/34.81	The set Q consists of the following terms:
67.74/34.81	
67.74/34.81	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.81	   new_primMinusNatS0(x0)
67.74/34.81	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.81	   new_primMinusNatS2(Zero, Zero)
67.74/34.81	   new_primMinusNatS1
67.74/34.81	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.81	
67.74/34.81	We have to consider all minimal (P,Q,R)-chains.
67.74/34.81	----------------------------------------
67.74/34.81	
67.74/34.81	(37) QDPSizeChangeProof (EQUIVALENT)
67.74/34.81	We used the following order together with the size-change analysis [AAECC05] to show that there are no infinite chains for this DP problem. 
67.74/34.81	
67.74/34.81	Order:Polynomial interpretation [POLO]:
67.74/34.81	
67.74/34.81	   POL(Succ(x_1)) = 1 + x_1
67.74/34.81	   POL(Zero) = 1
67.74/34.81	   POL(new_primMinusNatS2(x_1, x_2)) = x_1
67.74/34.81	
67.74/34.81	
67.74/34.81	
67.74/34.81	
67.74/34.81	From the DPs we obtained the following set of size-change graphs:
67.74/34.81	*new_primDivNatS00(vuz574, vuz575) -> new_primDivNatS(new_primMinusNatS2(vuz574, vuz575), Succ(vuz575)) (allowed arguments on rhs = {1, 2})
67.74/34.81	The graph contains the following edges 1 >= 1
67.74/34.81	
67.74/34.81	
67.74/34.81	*new_primDivNatS(Succ(Succ(vuz41600)), Succ(vuz549000)) -> new_primDivNatS0(vuz41600, vuz549000, vuz41600, vuz549000) (allowed arguments on rhs = {1, 2, 3, 4})
67.74/34.81	The graph contains the following edges 1 > 1, 2 > 2, 1 > 3, 2 > 4
67.74/34.81	
67.74/34.81	
67.74/34.81	*new_primDivNatS0(vuz574, vuz575, Succ(vuz5760), Succ(vuz5770)) -> new_primDivNatS0(vuz574, vuz575, vuz5760, vuz5770) (allowed arguments on rhs = {1, 2, 3, 4})
67.74/34.81	The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 > 4
67.74/34.81	
67.74/34.81	
67.74/34.81	*new_primDivNatS0(vuz574, vuz575, Zero, Zero) -> new_primDivNatS00(vuz574, vuz575) (allowed arguments on rhs = {1, 2})
67.74/34.81	The graph contains the following edges 1 >= 1, 2 >= 2
67.74/34.81	
67.74/34.81	
67.74/34.81	*new_primDivNatS0(vuz574, vuz575, Succ(vuz5760), Zero) -> new_primDivNatS(new_primMinusNatS2(vuz574, vuz575), Succ(vuz575)) (allowed arguments on rhs = {1, 2})
67.74/34.81	The graph contains the following edges 1 >= 1
67.74/34.81	
67.74/34.81	
67.74/34.81	
67.74/34.81	We oriented the following set of usable rules [AAECC05,FROCOS05].
67.74/34.81	
67.74/34.81	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.81	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.81	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.81	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.81	
67.74/34.81	----------------------------------------
67.74/34.81	
67.74/34.81	(38)
67.74/34.81	YES
67.74/34.81	
67.74/34.81	----------------------------------------
67.74/34.81	
67.74/34.81	(39)
67.74/34.81	Obligation:
67.74/34.81	Q DP problem:
67.74/34.81	The TRS P consists of the following rules:
67.74/34.81	
67.74/34.81	   new_primMulNat(Succ(vuz306100), Succ(vuz307100)) -> new_primMulNat(vuz306100, Succ(vuz307100))
67.74/34.81	
67.74/34.81	R is empty.
67.74/34.81	Q is empty.
67.74/34.81	We have to consider all minimal (P,Q,R)-chains.
67.74/34.81	----------------------------------------
67.74/34.81	
67.74/34.81	(40) QDPSizeChangeProof (EQUIVALENT)
67.74/34.81	By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 
67.74/34.81	
67.74/34.81	From the DPs we obtained the following set of size-change graphs:
67.74/34.81	*new_primMulNat(Succ(vuz306100), Succ(vuz307100)) -> new_primMulNat(vuz306100, Succ(vuz307100))
67.74/34.81	The graph contains the following edges 1 > 1, 2 >= 2
67.74/34.81	
67.74/34.81	
67.74/34.81	----------------------------------------
67.74/34.81	
67.74/34.81	(41)
67.74/34.81	YES
67.74/34.81	
67.74/34.81	----------------------------------------
67.74/34.81	
67.74/34.81	(42)
67.74/34.81	Obligation:
67.74/34.81	Q DP problem:
67.74/34.81	The TRS P consists of the following rules:
67.74/34.81	
67.74/34.81	   new_primMinusNatS(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS(vuz5740, vuz5750)
67.74/34.81	
67.74/34.81	R is empty.
67.74/34.81	Q is empty.
67.74/34.81	We have to consider all minimal (P,Q,R)-chains.
67.74/34.81	----------------------------------------
67.74/34.81	
67.74/34.81	(43) QDPSizeChangeProof (EQUIVALENT)
67.74/34.81	By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 
67.74/34.81	
67.74/34.81	From the DPs we obtained the following set of size-change graphs:
67.74/34.81	*new_primMinusNatS(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS(vuz5740, vuz5750)
67.74/34.81	The graph contains the following edges 1 > 1, 2 > 2
67.74/34.81	
67.74/34.81	
67.74/34.81	----------------------------------------
67.74/34.81	
67.74/34.81	(44)
67.74/34.81	YES
67.74/34.81	
67.74/34.81	----------------------------------------
67.74/34.81	
67.74/34.81	(45)
67.74/34.81	Obligation:
67.74/34.81	Q DP problem:
67.74/34.81	The TRS P consists of the following rules:
67.74/34.81	
67.74/34.81	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.81	   new_gcd0Gcd'(vuz542, vuz549) -> new_gcd0Gcd'1(new_esEs(new_rem(vuz549, vuz542)), vuz542, vuz549)
67.74/34.81	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.81	
67.74/34.81	The TRS R consists of the following rules:
67.74/34.81	
67.74/34.81	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.81	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.81	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.81	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.81	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.81	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.81	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.81	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.81	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.81	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.81	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.81	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.81	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.81	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.81	   new_error -> error([])
67.74/34.82	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.82	   new_primEqInt2 -> True
67.74/34.82	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.82	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.82	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.82	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.82	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.82	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.82	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.82	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.82	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.82	   new_primMinusNatS1 -> Zero
67.74/34.82	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.82	   new_primEqInt1 -> True
67.74/34.82	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.82	   new_primEqInt0(vuz3260) -> False
67.74/34.82	   new_primEqInt(vuz3250) -> False
67.74/34.82	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.82	
67.74/34.82	The set Q consists of the following terms:
67.74/34.82	
67.74/34.82	   new_rem(Neg(x0), Neg(Zero))
67.74/34.82	   new_primEqInt1
67.74/34.82	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.82	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.82	   new_primMinusNatS1
67.74/34.82	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.82	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.82	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.82	   new_primMinusNatS2(Zero, Zero)
67.74/34.82	   new_error
67.74/34.82	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.82	   new_rem(Pos(x0), Pos(Zero))
67.74/34.82	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.82	   new_primEqInt0(x0)
67.74/34.82	   new_esEs(Pos(Zero))
67.74/34.82	   new_esEs(Pos(Succ(x0)))
67.74/34.82	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.82	   new_primModNatS02(x0, x1)
67.74/34.82	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.82	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.82	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.82	   new_primModNatS1(Zero, x0)
67.74/34.82	   new_primEqInt(x0)
67.74/34.82	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.82	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.82	   new_rem(Pos(x0), Neg(Zero))
67.74/34.82	   new_rem(Neg(x0), Pos(Zero))
67.74/34.82	   new_primMinusNatS0(x0)
67.74/34.82	   new_primEqInt2
67.74/34.82	   new_esEs(Neg(Zero))
67.74/34.82	   new_esEs(Neg(Succ(x0)))
67.74/34.82	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.82	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.82	
67.74/34.82	We have to consider all minimal (P,Q,R)-chains.
67.74/34.82	----------------------------------------
67.74/34.82	
67.74/34.82	(46) MNOCProof (EQUIVALENT)
67.74/34.82	We use the modular non-overlap check [FROCOS05] to decrease Q to the empty set.
67.74/34.82	----------------------------------------
67.74/34.82	
67.74/34.82	(47)
67.74/34.82	Obligation:
67.74/34.82	Q DP problem:
67.74/34.82	The TRS P consists of the following rules:
67.74/34.82	
67.74/34.82	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.82	   new_gcd0Gcd'(vuz542, vuz549) -> new_gcd0Gcd'1(new_esEs(new_rem(vuz549, vuz542)), vuz542, vuz549)
67.74/34.82	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.82	
67.74/34.82	The TRS R consists of the following rules:
67.74/34.82	
67.74/34.82	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.82	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.82	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.82	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.82	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.82	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.82	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.82	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.82	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.82	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.82	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.82	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.82	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.82	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.82	   new_error -> error([])
67.74/34.82	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.82	   new_primEqInt2 -> True
67.74/34.82	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.82	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.82	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.82	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.82	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.82	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.82	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.82	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.82	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.82	   new_primMinusNatS1 -> Zero
67.74/34.82	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.82	   new_primEqInt1 -> True
67.74/34.82	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.82	   new_primEqInt0(vuz3260) -> False
67.74/34.82	   new_primEqInt(vuz3250) -> False
67.74/34.82	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.82	
67.74/34.82	Q is empty.
67.74/34.82	We have to consider all (P,Q,R)-chains.
67.74/34.82	----------------------------------------
67.74/34.82	
67.74/34.82	(48) InductionCalculusProof (EQUIVALENT)
67.74/34.82	Note that final constraints are written in bold face.
67.74/34.82	
67.74/34.82	
67.74/34.82	
67.74/34.82	For Pair new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542) the following chains were created:
67.74/34.82	*We consider the chain new_gcd0Gcd'0(x2, x3) -> new_gcd0Gcd'(x3, x2), new_gcd0Gcd'(x4, x5) -> new_gcd0Gcd'1(new_esEs(new_rem(x5, x4)), x4, x5) which results in the following constraint:
67.74/34.82	
67.74/34.82	(1)    (new_gcd0Gcd'(x3, x2)=new_gcd0Gcd'(x4, x5)  ==>  new_gcd0Gcd'0(x2, x3)_>=_new_gcd0Gcd'(x3, x2))
67.74/34.82	
67.74/34.82	
67.74/34.82	
67.74/34.82	We simplified constraint (1) using rules (I), (II), (IV) which results in the following new constraint:
67.74/34.82	
67.74/34.82	(2)    (new_gcd0Gcd'0(x2, x3)_>=_new_gcd0Gcd'(x3, x2))
67.74/34.82	
67.74/34.82	
67.74/34.82	
67.74/34.82	
67.74/34.82	
67.74/34.82	
67.74/34.82	
67.74/34.82	
67.74/34.82	For Pair new_gcd0Gcd'(vuz542, vuz549) -> new_gcd0Gcd'1(new_esEs(new_rem(vuz549, vuz542)), vuz542, vuz549) the following chains were created:
67.74/34.82	*We consider the chain new_gcd0Gcd'(x12, x13) -> new_gcd0Gcd'1(new_esEs(new_rem(x13, x12)), x12, x13), new_gcd0Gcd'1(False, x14, x15) -> new_gcd0Gcd'0(x14, new_rem(x15, x14)) which results in the following constraint:
67.74/34.82	
67.74/34.82	(1)    (new_gcd0Gcd'1(new_esEs(new_rem(x13, x12)), x12, x13)=new_gcd0Gcd'1(False, x14, x15)  ==>  new_gcd0Gcd'(x12, x13)_>=_new_gcd0Gcd'1(new_esEs(new_rem(x13, x12)), x12, x13))
67.74/34.82	
67.74/34.82	
67.74/34.82	
67.74/34.82	We simplified constraint (1) using rules (I), (II), (IV), (VII) which results in the following new constraint:
67.74/34.82	
67.74/34.82	(2)    (new_rem(x13, x12)=x24 & new_esEs(x24)=False  ==>  new_gcd0Gcd'(x12, x13)_>=_new_gcd0Gcd'1(new_esEs(new_rem(x13, x12)), x12, x13))
67.74/34.82	
67.74/34.82	
67.74/34.82	
67.74/34.82	We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_esEs(x24)=False which results in the following new constraints:
67.74/34.82	
67.74/34.82	(3)    (new_primEqInt2=False & new_rem(x13, x12)=Neg(Zero)  ==>  new_gcd0Gcd'(x12, x13)_>=_new_gcd0Gcd'1(new_esEs(new_rem(x13, x12)), x12, x13))
67.74/34.82	
67.74/34.82	(4)    (new_primEqInt1=False & new_rem(x13, x12)=Pos(Zero)  ==>  new_gcd0Gcd'(x12, x13)_>=_new_gcd0Gcd'1(new_esEs(new_rem(x13, x12)), x12, x13))
67.74/34.82	
67.74/34.82	(5)    (new_primEqInt(x25)=False & new_rem(x13, x12)=Pos(Succ(x25))  ==>  new_gcd0Gcd'(x12, x13)_>=_new_gcd0Gcd'1(new_esEs(new_rem(x13, x12)), x12, x13))
67.74/34.82	
67.74/34.82	(6)    (new_primEqInt0(x26)=False & new_rem(x13, x12)=Neg(Succ(x26))  ==>  new_gcd0Gcd'(x12, x13)_>=_new_gcd0Gcd'1(new_esEs(new_rem(x13, x12)), x12, x13))
67.74/34.82	
67.74/34.82	
67.74/34.82	
67.74/34.82	We solved constraint (3) using rule (V) (with possible (I) afterwards).We solved constraint (4) using rule (V) (with possible (I) afterwards).We simplified constraint (5) using rule (V) (with possible (I) afterwards) using induction on new_primEqInt(x25)=False which results in the following new constraint:
67.74/34.82	
67.74/34.82	(7)    (False=False & new_rem(x13, x12)=Pos(Succ(x27))  ==>  new_gcd0Gcd'(x12, x13)_>=_new_gcd0Gcd'1(new_esEs(new_rem(x13, x12)), x12, x13))
67.74/34.82	
67.74/34.82	
67.74/34.82	
67.74/34.82	We simplified constraint (6) using rule (V) (with possible (I) afterwards) using induction on new_primEqInt0(x26)=False which results in the following new constraint:
67.74/34.82	
67.74/34.82	(8)    (False=False & new_rem(x13, x12)=Neg(Succ(x62))  ==>  new_gcd0Gcd'(x12, x13)_>=_new_gcd0Gcd'1(new_esEs(new_rem(x13, x12)), x12, x13))
67.74/34.82	
67.74/34.82	
67.74/34.82	
67.74/34.82	We simplified constraint (7) using rules (I), (II) which results in the following new constraint:
67.74/34.82	
67.74/34.82	(9)    (new_rem(x13, x12)=Pos(Succ(x27))  ==>  new_gcd0Gcd'(x12, x13)_>=_new_gcd0Gcd'1(new_esEs(new_rem(x13, x12)), x12, x13))
67.74/34.82	
67.74/34.82	
67.74/34.82	
67.74/34.82	We simplified constraint (9) using rule (V) (with possible (I) afterwards) using induction on new_rem(x13, x12)=Pos(Succ(x27)) which results in the following new constraints:
67.74/34.82	
67.74/34.82	(10)    (Pos(new_primModNatS1(x31, x30))=Pos(Succ(x27))  ==>  new_gcd0Gcd'(Pos(Succ(x30)), Pos(x31))_>=_new_gcd0Gcd'1(new_esEs(new_rem(Pos(x31), Pos(Succ(x30)))), Pos(Succ(x30)), Pos(x31)))
67.74/34.82	
67.74/34.82	(11)    (new_error=Pos(Succ(x27))  ==>  new_gcd0Gcd'(Neg(Zero), Neg(x32))_>=_new_gcd0Gcd'1(new_esEs(new_rem(Neg(x32), Neg(Zero))), Neg(Zero), Neg(x32)))
67.74/34.82	
67.74/34.82	(12)    (new_error=Pos(Succ(x27))  ==>  new_gcd0Gcd'(Neg(Zero), Pos(x33))_>=_new_gcd0Gcd'1(new_esEs(new_rem(Pos(x33), Neg(Zero))), Neg(Zero), Pos(x33)))
67.74/34.82	
67.74/34.82	(13)    (new_error=Pos(Succ(x27))  ==>  new_gcd0Gcd'(Pos(Zero), Neg(x34))_>=_new_gcd0Gcd'1(new_esEs(new_rem(Neg(x34), Pos(Zero))), Pos(Zero), Neg(x34)))
67.74/34.82	
67.74/34.82	(14)    (Pos(new_primModNatS1(x36, x35))=Pos(Succ(x27))  ==>  new_gcd0Gcd'(Neg(Succ(x35)), Pos(x36))_>=_new_gcd0Gcd'1(new_esEs(new_rem(Pos(x36), Neg(Succ(x35)))), Neg(Succ(x35)), Pos(x36)))
67.74/34.82	
67.74/34.82	(15)    (new_error=Pos(Succ(x27))  ==>  new_gcd0Gcd'(Pos(Zero), Pos(x39))_>=_new_gcd0Gcd'1(new_esEs(new_rem(Pos(x39), Pos(Zero))), Pos(Zero), Pos(x39)))
67.74/34.82	
67.74/34.82	
67.74/34.82	
67.74/34.82	We simplified constraint (10) using rules (I), (II) which results in the following new constraint:
67.74/34.82	
67.74/34.82	(16)    (new_primModNatS1(x31, x30)=Succ(x27)  ==>  new_gcd0Gcd'(Pos(Succ(x30)), Pos(x31))_>=_new_gcd0Gcd'1(new_esEs(new_rem(Pos(x31), Pos(Succ(x30)))), Pos(Succ(x30)), Pos(x31)))
67.74/34.82	
67.74/34.82	
67.74/34.82	
67.74/34.82	We solved constraint (11) using rule (V) (with possible (I) afterwards).We solved constraint (12) using rule (V) (with possible (I) afterwards).We solved constraint (13) using rule (V) (with possible (I) afterwards).We simplified constraint (14) using rules (I), (II) which results in the following new constraint:
67.74/34.82	
67.74/34.82	(17)    (new_primModNatS1(x36, x35)=Succ(x27)  ==>  new_gcd0Gcd'(Neg(Succ(x35)), Pos(x36))_>=_new_gcd0Gcd'1(new_esEs(new_rem(Pos(x36), Neg(Succ(x35)))), Neg(Succ(x35)), Pos(x36)))
67.74/34.82	
67.74/34.82	
67.74/34.82	
67.74/34.82	We solved constraint (15) using rule (V) (with possible (I) afterwards).We simplified constraint (16) using rule (V) (with possible (I) afterwards) using induction on new_primModNatS1(x31, x30)=Succ(x27) which results in the following new constraints:
67.74/34.82	
67.74/34.82	(18)    (new_primModNatS1(new_primMinusNatS0(x40), Zero)=Succ(x27)  ==>  new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(x40))))_>=_new_gcd0Gcd'1(new_esEs(new_rem(Pos(Succ(Succ(x40))), Pos(Succ(Zero)))), Pos(Succ(Zero)), Pos(Succ(Succ(x40)))))
67.74/34.82	
67.74/34.82	(19)    (Succ(Zero)=Succ(x27)  ==>  new_gcd0Gcd'(Pos(Succ(Succ(x41))), Pos(Succ(Zero)))_>=_new_gcd0Gcd'1(new_esEs(new_rem(Pos(Succ(Zero)), Pos(Succ(Succ(x41))))), Pos(Succ(Succ(x41))), Pos(Succ(Zero))))
67.74/34.82	
67.74/34.82	(20)    (new_primModNatS01(x43, x42, x43, x42)=Succ(x27)  ==>  new_gcd0Gcd'(Pos(Succ(Succ(x42))), Pos(Succ(Succ(x43))))_>=_new_gcd0Gcd'1(new_esEs(new_rem(Pos(Succ(Succ(x43))), Pos(Succ(Succ(x42))))), Pos(Succ(Succ(x42))), Pos(Succ(Succ(x43)))))
67.74/34.82	
67.74/34.82	(21)    (new_primModNatS1(new_primMinusNatS1, Zero)=Succ(x27)  ==>  new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Zero)))_>=_new_gcd0Gcd'1(new_esEs(new_rem(Pos(Succ(Zero)), Pos(Succ(Zero)))), Pos(Succ(Zero)), Pos(Succ(Zero))))
67.74/34.82	
67.74/34.82	
67.74/34.82	
67.74/34.82	We simplified constraint (18) using rules (III), (IV), (VII) which results in the following new constraint:
67.74/34.82	
67.74/34.82	(22)    (new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(x40))))_>=_new_gcd0Gcd'1(new_esEs(new_rem(Pos(Succ(Succ(x40))), Pos(Succ(Zero)))), Pos(Succ(Zero)), Pos(Succ(Succ(x40)))))
67.74/34.82	
67.74/34.82	
67.74/34.82	
67.74/34.82	We simplified constraint (19) using rules (I), (II), (IV) which results in the following new constraint:
67.74/34.82	
67.74/34.82	(23)    (new_gcd0Gcd'(Pos(Succ(Succ(x41))), Pos(Succ(Zero)))_>=_new_gcd0Gcd'1(new_esEs(new_rem(Pos(Succ(Zero)), Pos(Succ(Succ(x41))))), Pos(Succ(Succ(x41))), Pos(Succ(Zero))))
67.74/34.82	
67.74/34.82	
67.74/34.82	
67.74/34.82	We simplified constraint (20) using rules (III), (IV), (VII) which results in the following new constraint:
67.74/34.82	
67.74/34.82	(24)    (new_gcd0Gcd'(Pos(Succ(Succ(x48))), Pos(Succ(Succ(x47))))_>=_new_gcd0Gcd'1(new_esEs(new_rem(Pos(Succ(Succ(x47))), Pos(Succ(Succ(x48))))), Pos(Succ(Succ(x48))), Pos(Succ(Succ(x47)))))
67.74/34.82	
67.74/34.82	
67.74/34.82	
67.74/34.82	We simplified constraint (21) using rules (III), (IV), (VII) which results in the following new constraint:
67.74/34.82	
67.74/34.82	(25)    (new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Zero)))_>=_new_gcd0Gcd'1(new_esEs(new_rem(Pos(Succ(Zero)), Pos(Succ(Zero)))), Pos(Succ(Zero)), Pos(Succ(Zero))))
67.74/34.82	
67.74/34.82	
67.74/34.82	
67.74/34.82	We simplified constraint (17) using rule (V) (with possible (I) afterwards) using induction on new_primModNatS1(x36, x35)=Succ(x27) which results in the following new constraints:
67.74/34.82	
67.74/34.82	(26)    (new_primModNatS1(new_primMinusNatS0(x51), Zero)=Succ(x27)  ==>  new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x51))))_>=_new_gcd0Gcd'1(new_esEs(new_rem(Pos(Succ(Succ(x51))), Neg(Succ(Zero)))), Neg(Succ(Zero)), Pos(Succ(Succ(x51)))))
67.74/34.82	
67.74/34.82	(27)    (Succ(Zero)=Succ(x27)  ==>  new_gcd0Gcd'(Neg(Succ(Succ(x52))), Pos(Succ(Zero)))_>=_new_gcd0Gcd'1(new_esEs(new_rem(Pos(Succ(Zero)), Neg(Succ(Succ(x52))))), Neg(Succ(Succ(x52))), Pos(Succ(Zero))))
67.74/34.82	
67.74/34.82	(28)    (new_primModNatS01(x54, x53, x54, x53)=Succ(x27)  ==>  new_gcd0Gcd'(Neg(Succ(Succ(x53))), Pos(Succ(Succ(x54))))_>=_new_gcd0Gcd'1(new_esEs(new_rem(Pos(Succ(Succ(x54))), Neg(Succ(Succ(x53))))), Neg(Succ(Succ(x53))), Pos(Succ(Succ(x54)))))
67.74/34.82	
67.74/34.82	(29)    (new_primModNatS1(new_primMinusNatS1, Zero)=Succ(x27)  ==>  new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Zero)))_>=_new_gcd0Gcd'1(new_esEs(new_rem(Pos(Succ(Zero)), Neg(Succ(Zero)))), Neg(Succ(Zero)), Pos(Succ(Zero))))
67.74/34.82	
67.74/34.82	
67.74/34.82	
67.74/34.82	We simplified constraint (26) using rules (III), (IV), (VII) which results in the following new constraint:
67.74/34.82	
67.74/34.82	(30)    (new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x51))))_>=_new_gcd0Gcd'1(new_esEs(new_rem(Pos(Succ(Succ(x51))), Neg(Succ(Zero)))), Neg(Succ(Zero)), Pos(Succ(Succ(x51)))))
67.74/34.82	
67.74/34.82	
67.74/34.82	
67.74/34.82	We simplified constraint (27) using rules (I), (II), (IV) which results in the following new constraint:
67.74/34.82	
67.74/34.82	(31)    (new_gcd0Gcd'(Neg(Succ(Succ(x52))), Pos(Succ(Zero)))_>=_new_gcd0Gcd'1(new_esEs(new_rem(Pos(Succ(Zero)), Neg(Succ(Succ(x52))))), Neg(Succ(Succ(x52))), Pos(Succ(Zero))))
67.74/34.82	
67.74/34.82	
67.74/34.82	
67.74/34.82	We simplified constraint (28) using rules (III), (IV), (VII) which results in the following new constraint:
67.74/34.82	
67.74/34.82	(32)    (new_gcd0Gcd'(Neg(Succ(Succ(x59))), Pos(Succ(Succ(x58))))_>=_new_gcd0Gcd'1(new_esEs(new_rem(Pos(Succ(Succ(x58))), Neg(Succ(Succ(x59))))), Neg(Succ(Succ(x59))), Pos(Succ(Succ(x58)))))
67.74/34.82	
67.74/34.82	
67.74/34.82	
67.74/34.82	We simplified constraint (29) using rules (III), (IV), (VII) which results in the following new constraint:
67.74/34.82	
67.74/34.82	(33)    (new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Zero)))_>=_new_gcd0Gcd'1(new_esEs(new_rem(Pos(Succ(Zero)), Neg(Succ(Zero)))), Neg(Succ(Zero)), Pos(Succ(Zero))))
67.74/34.82	
67.74/34.82	
67.74/34.82	
67.74/34.82	We simplified constraint (8) using rules (I), (II) which results in the following new constraint:
67.74/34.82	
67.74/34.82	(34)    (new_rem(x13, x12)=Neg(Succ(x62))  ==>  new_gcd0Gcd'(x12, x13)_>=_new_gcd0Gcd'1(new_esEs(new_rem(x13, x12)), x12, x13))
67.74/34.82	
67.74/34.82	
67.74/34.82	
67.74/34.82	We simplified constraint (34) using rule (V) (with possible (I) afterwards) using induction on new_rem(x13, x12)=Neg(Succ(x62)) which results in the following new constraints:
67.74/34.82	
67.74/34.82	(35)    (Neg(new_primModNatS1(x64, x63))=Neg(Succ(x62))  ==>  new_gcd0Gcd'(Neg(Succ(x63)), Neg(x64))_>=_new_gcd0Gcd'1(new_esEs(new_rem(Neg(x64), Neg(Succ(x63)))), Neg(Succ(x63)), Neg(x64)))
67.74/34.82	
67.74/34.82	(36)    (new_error=Neg(Succ(x62))  ==>  new_gcd0Gcd'(Neg(Zero), Neg(x67))_>=_new_gcd0Gcd'1(new_esEs(new_rem(Neg(x67), Neg(Zero))), Neg(Zero), Neg(x67)))
67.74/34.82	
67.74/34.82	(37)    (new_error=Neg(Succ(x62))  ==>  new_gcd0Gcd'(Neg(Zero), Pos(x68))_>=_new_gcd0Gcd'1(new_esEs(new_rem(Pos(x68), Neg(Zero))), Neg(Zero), Pos(x68)))
67.74/34.82	
67.74/34.82	(38)    (new_error=Neg(Succ(x62))  ==>  new_gcd0Gcd'(Pos(Zero), Neg(x69))_>=_new_gcd0Gcd'1(new_esEs(new_rem(Neg(x69), Pos(Zero))), Pos(Zero), Neg(x69)))
67.74/34.82	
67.74/34.82	(39)    (Neg(new_primModNatS1(x73, x72))=Neg(Succ(x62))  ==>  new_gcd0Gcd'(Pos(Succ(x72)), Neg(x73))_>=_new_gcd0Gcd'1(new_esEs(new_rem(Neg(x73), Pos(Succ(x72)))), Pos(Succ(x72)), Neg(x73)))
67.74/34.82	
67.74/34.82	(40)    (new_error=Neg(Succ(x62))  ==>  new_gcd0Gcd'(Pos(Zero), Pos(x74))_>=_new_gcd0Gcd'1(new_esEs(new_rem(Pos(x74), Pos(Zero))), Pos(Zero), Pos(x74)))
67.74/34.82	
67.74/34.82	
67.74/34.82	
67.74/34.82	We simplified constraint (35) using rules (I), (II) which results in the following new constraint:
67.74/34.82	
67.74/34.82	(41)    (new_primModNatS1(x64, x63)=Succ(x62)  ==>  new_gcd0Gcd'(Neg(Succ(x63)), Neg(x64))_>=_new_gcd0Gcd'1(new_esEs(new_rem(Neg(x64), Neg(Succ(x63)))), Neg(Succ(x63)), Neg(x64)))
67.74/34.82	
67.74/34.82	
67.74/34.82	
67.74/34.82	We solved constraint (36) using rule (V) (with possible (I) afterwards).We solved constraint (37) using rule (V) (with possible (I) afterwards).We solved constraint (38) using rule (V) (with possible (I) afterwards).We simplified constraint (39) using rules (I), (II) which results in the following new constraint:
67.74/34.82	
67.74/34.82	(42)    (new_primModNatS1(x73, x72)=Succ(x62)  ==>  new_gcd0Gcd'(Pos(Succ(x72)), Neg(x73))_>=_new_gcd0Gcd'1(new_esEs(new_rem(Neg(x73), Pos(Succ(x72)))), Pos(Succ(x72)), Neg(x73)))
67.74/34.82	
67.74/34.82	
67.74/34.82	
67.74/34.82	We solved constraint (40) using rule (V) (with possible (I) afterwards).We simplified constraint (41) using rule (V) (with possible (I) afterwards) using induction on new_primModNatS1(x64, x63)=Succ(x62) which results in the following new constraints:
67.74/34.82	
67.74/34.82	(43)    (new_primModNatS1(new_primMinusNatS0(x75), Zero)=Succ(x62)  ==>  new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(x75))))_>=_new_gcd0Gcd'1(new_esEs(new_rem(Neg(Succ(Succ(x75))), Neg(Succ(Zero)))), Neg(Succ(Zero)), Neg(Succ(Succ(x75)))))
67.74/34.82	
67.74/34.82	(44)    (Succ(Zero)=Succ(x62)  ==>  new_gcd0Gcd'(Neg(Succ(Succ(x76))), Neg(Succ(Zero)))_>=_new_gcd0Gcd'1(new_esEs(new_rem(Neg(Succ(Zero)), Neg(Succ(Succ(x76))))), Neg(Succ(Succ(x76))), Neg(Succ(Zero))))
67.74/34.82	
67.74/34.82	(45)    (new_primModNatS01(x78, x77, x78, x77)=Succ(x62)  ==>  new_gcd0Gcd'(Neg(Succ(Succ(x77))), Neg(Succ(Succ(x78))))_>=_new_gcd0Gcd'1(new_esEs(new_rem(Neg(Succ(Succ(x78))), Neg(Succ(Succ(x77))))), Neg(Succ(Succ(x77))), Neg(Succ(Succ(x78)))))
67.74/34.82	
67.74/34.82	(46)    (new_primModNatS1(new_primMinusNatS1, Zero)=Succ(x62)  ==>  new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Zero)))_>=_new_gcd0Gcd'1(new_esEs(new_rem(Neg(Succ(Zero)), Neg(Succ(Zero)))), Neg(Succ(Zero)), Neg(Succ(Zero))))
67.74/34.82	
67.74/34.82	
67.74/34.82	
67.74/34.82	We simplified constraint (43) using rules (III), (IV), (VII) which results in the following new constraint:
67.74/34.82	
67.74/34.82	(47)    (new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(x75))))_>=_new_gcd0Gcd'1(new_esEs(new_rem(Neg(Succ(Succ(x75))), Neg(Succ(Zero)))), Neg(Succ(Zero)), Neg(Succ(Succ(x75)))))
67.74/34.82	
67.74/34.82	
67.74/34.82	
67.74/34.82	We simplified constraint (44) using rules (I), (II), (IV) which results in the following new constraint:
67.74/34.82	
67.74/34.82	(48)    (new_gcd0Gcd'(Neg(Succ(Succ(x76))), Neg(Succ(Zero)))_>=_new_gcd0Gcd'1(new_esEs(new_rem(Neg(Succ(Zero)), Neg(Succ(Succ(x76))))), Neg(Succ(Succ(x76))), Neg(Succ(Zero))))
67.74/34.82	
67.74/34.82	
67.74/34.82	
67.74/34.82	We simplified constraint (45) using rules (III), (IV), (VII) which results in the following new constraint:
67.74/34.82	
67.74/34.82	(49)    (new_gcd0Gcd'(Neg(Succ(Succ(x83))), Neg(Succ(Succ(x82))))_>=_new_gcd0Gcd'1(new_esEs(new_rem(Neg(Succ(Succ(x82))), Neg(Succ(Succ(x83))))), Neg(Succ(Succ(x83))), Neg(Succ(Succ(x82)))))
67.74/34.82	
67.74/34.82	
67.74/34.82	
67.74/34.82	We simplified constraint (46) using rules (III), (IV), (VII) which results in the following new constraint:
67.74/34.82	
67.74/34.82	(50)    (new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Zero)))_>=_new_gcd0Gcd'1(new_esEs(new_rem(Neg(Succ(Zero)), Neg(Succ(Zero)))), Neg(Succ(Zero)), Neg(Succ(Zero))))
67.74/34.82	
67.74/34.82	
67.74/34.82	
67.74/34.82	We simplified constraint (42) using rule (V) (with possible (I) afterwards) using induction on new_primModNatS1(x73, x72)=Succ(x62) which results in the following new constraints:
67.74/34.82	
67.74/34.82	(51)    (new_primModNatS1(new_primMinusNatS0(x86), Zero)=Succ(x62)  ==>  new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x86))))_>=_new_gcd0Gcd'1(new_esEs(new_rem(Neg(Succ(Succ(x86))), Pos(Succ(Zero)))), Pos(Succ(Zero)), Neg(Succ(Succ(x86)))))
67.74/34.82	
67.74/34.82	(52)    (Succ(Zero)=Succ(x62)  ==>  new_gcd0Gcd'(Pos(Succ(Succ(x87))), Neg(Succ(Zero)))_>=_new_gcd0Gcd'1(new_esEs(new_rem(Neg(Succ(Zero)), Pos(Succ(Succ(x87))))), Pos(Succ(Succ(x87))), Neg(Succ(Zero))))
67.74/34.82	
67.74/34.82	(53)    (new_primModNatS01(x89, x88, x89, x88)=Succ(x62)  ==>  new_gcd0Gcd'(Pos(Succ(Succ(x88))), Neg(Succ(Succ(x89))))_>=_new_gcd0Gcd'1(new_esEs(new_rem(Neg(Succ(Succ(x89))), Pos(Succ(Succ(x88))))), Pos(Succ(Succ(x88))), Neg(Succ(Succ(x89)))))
67.74/34.82	
67.74/34.82	(54)    (new_primModNatS1(new_primMinusNatS1, Zero)=Succ(x62)  ==>  new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Zero)))_>=_new_gcd0Gcd'1(new_esEs(new_rem(Neg(Succ(Zero)), Pos(Succ(Zero)))), Pos(Succ(Zero)), Neg(Succ(Zero))))
67.74/34.82	
67.74/34.82	
67.74/34.82	
67.74/34.82	We simplified constraint (51) using rules (III), (IV), (VII) which results in the following new constraint:
67.74/34.82	
67.74/34.82	(55)    (new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x86))))_>=_new_gcd0Gcd'1(new_esEs(new_rem(Neg(Succ(Succ(x86))), Pos(Succ(Zero)))), Pos(Succ(Zero)), Neg(Succ(Succ(x86)))))
67.74/34.82	
67.74/34.82	
67.74/34.82	
67.74/34.82	We simplified constraint (52) using rules (I), (II), (IV) which results in the following new constraint:
67.74/34.82	
67.74/34.82	(56)    (new_gcd0Gcd'(Pos(Succ(Succ(x87))), Neg(Succ(Zero)))_>=_new_gcd0Gcd'1(new_esEs(new_rem(Neg(Succ(Zero)), Pos(Succ(Succ(x87))))), Pos(Succ(Succ(x87))), Neg(Succ(Zero))))
67.74/34.82	
67.74/34.82	
67.74/34.82	
67.74/34.82	We simplified constraint (53) using rules (III), (IV), (VII) which results in the following new constraint:
67.74/34.82	
67.74/34.82	(57)    (new_gcd0Gcd'(Pos(Succ(Succ(x94))), Neg(Succ(Succ(x93))))_>=_new_gcd0Gcd'1(new_esEs(new_rem(Neg(Succ(Succ(x93))), Pos(Succ(Succ(x94))))), Pos(Succ(Succ(x94))), Neg(Succ(Succ(x93)))))
67.74/34.82	
67.74/34.82	
67.74/34.82	
67.74/34.82	We simplified constraint (54) using rules (III), (IV), (VII) which results in the following new constraint:
67.74/34.82	
67.74/34.82	(58)    (new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Zero)))_>=_new_gcd0Gcd'1(new_esEs(new_rem(Neg(Succ(Zero)), Pos(Succ(Zero)))), Pos(Succ(Zero)), Neg(Succ(Zero))))
67.74/34.82	
67.74/34.82	
67.74/34.82	
67.74/34.82	
67.74/34.82	
67.74/34.82	
67.74/34.82	
67.74/34.82	
67.74/34.82	For Pair new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542)) the following chains were created:
67.74/34.82	*We consider the chain new_gcd0Gcd'1(False, x16, x17) -> new_gcd0Gcd'0(x16, new_rem(x17, x16)), new_gcd0Gcd'0(x18, x19) -> new_gcd0Gcd'(x19, x18) which results in the following constraint:
67.74/34.82	
67.74/34.82	(1)    (new_gcd0Gcd'0(x16, new_rem(x17, x16))=new_gcd0Gcd'0(x18, x19)  ==>  new_gcd0Gcd'1(False, x16, x17)_>=_new_gcd0Gcd'0(x16, new_rem(x17, x16)))
67.74/34.82	
67.74/34.82	
67.74/34.82	
67.74/34.82	We simplified constraint (1) using rules (I), (II), (IV) which results in the following new constraint:
67.74/34.82	
67.74/34.82	(2)    (new_gcd0Gcd'1(False, x16, x17)_>=_new_gcd0Gcd'0(x16, new_rem(x17, x16)))
67.74/34.82	
67.74/34.82	
67.74/34.82	
67.74/34.82	
67.74/34.82	
67.74/34.82	
67.74/34.82	
67.74/34.82	
67.74/34.82	To summarize, we get the following constraints P__>=_ for the following pairs.
67.74/34.82	
67.74/34.82	*new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.82	
67.74/34.82	*(new_gcd0Gcd'0(x2, x3)_>=_new_gcd0Gcd'(x3, x2))
67.74/34.82	
67.74/34.82	
67.74/34.82	
67.74/34.82	
67.74/34.82	*new_gcd0Gcd'(vuz542, vuz549) -> new_gcd0Gcd'1(new_esEs(new_rem(vuz549, vuz542)), vuz542, vuz549)
67.74/34.82	
67.74/34.82	*(new_gcd0Gcd'(Pos(Succ(Succ(x41))), Pos(Succ(Zero)))_>=_new_gcd0Gcd'1(new_esEs(new_rem(Pos(Succ(Zero)), Pos(Succ(Succ(x41))))), Pos(Succ(Succ(x41))), Pos(Succ(Zero))))
67.74/34.82	
67.74/34.82	
67.74/34.82	*(new_gcd0Gcd'(Neg(Succ(Succ(x52))), Pos(Succ(Zero)))_>=_new_gcd0Gcd'1(new_esEs(new_rem(Pos(Succ(Zero)), Neg(Succ(Succ(x52))))), Neg(Succ(Succ(x52))), Pos(Succ(Zero))))
67.74/34.82	
67.74/34.82	
67.74/34.82	*(new_gcd0Gcd'(Neg(Succ(Succ(x76))), Neg(Succ(Zero)))_>=_new_gcd0Gcd'1(new_esEs(new_rem(Neg(Succ(Zero)), Neg(Succ(Succ(x76))))), Neg(Succ(Succ(x76))), Neg(Succ(Zero))))
67.74/34.82	
67.74/34.82	
67.74/34.82	*(new_gcd0Gcd'(Pos(Succ(Succ(x87))), Neg(Succ(Zero)))_>=_new_gcd0Gcd'1(new_esEs(new_rem(Neg(Succ(Zero)), Pos(Succ(Succ(x87))))), Pos(Succ(Succ(x87))), Neg(Succ(Zero))))
67.74/34.82	
67.74/34.82	
67.74/34.82	*(new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(x40))))_>=_new_gcd0Gcd'1(new_esEs(new_rem(Pos(Succ(Succ(x40))), Pos(Succ(Zero)))), Pos(Succ(Zero)), Pos(Succ(Succ(x40)))))
67.74/34.82	
67.74/34.82	
67.74/34.82	*(new_gcd0Gcd'(Pos(Succ(Succ(x48))), Pos(Succ(Succ(x47))))_>=_new_gcd0Gcd'1(new_esEs(new_rem(Pos(Succ(Succ(x47))), Pos(Succ(Succ(x48))))), Pos(Succ(Succ(x48))), Pos(Succ(Succ(x47)))))
67.74/34.82	
67.74/34.82	
67.74/34.82	*(new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Zero)))_>=_new_gcd0Gcd'1(new_esEs(new_rem(Pos(Succ(Zero)), Pos(Succ(Zero)))), Pos(Succ(Zero)), Pos(Succ(Zero))))
67.74/34.82	
67.74/34.82	
67.74/34.82	*(new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x51))))_>=_new_gcd0Gcd'1(new_esEs(new_rem(Pos(Succ(Succ(x51))), Neg(Succ(Zero)))), Neg(Succ(Zero)), Pos(Succ(Succ(x51)))))
67.74/34.82	
67.74/34.82	
67.74/34.82	*(new_gcd0Gcd'(Neg(Succ(Succ(x59))), Pos(Succ(Succ(x58))))_>=_new_gcd0Gcd'1(new_esEs(new_rem(Pos(Succ(Succ(x58))), Neg(Succ(Succ(x59))))), Neg(Succ(Succ(x59))), Pos(Succ(Succ(x58)))))
67.74/34.82	
67.74/34.82	
67.74/34.82	*(new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Zero)))_>=_new_gcd0Gcd'1(new_esEs(new_rem(Pos(Succ(Zero)), Neg(Succ(Zero)))), Neg(Succ(Zero)), Pos(Succ(Zero))))
67.74/34.82	
67.74/34.82	
67.74/34.82	*(new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(x75))))_>=_new_gcd0Gcd'1(new_esEs(new_rem(Neg(Succ(Succ(x75))), Neg(Succ(Zero)))), Neg(Succ(Zero)), Neg(Succ(Succ(x75)))))
67.74/34.82	
67.74/34.82	
67.74/34.82	*(new_gcd0Gcd'(Neg(Succ(Succ(x83))), Neg(Succ(Succ(x82))))_>=_new_gcd0Gcd'1(new_esEs(new_rem(Neg(Succ(Succ(x82))), Neg(Succ(Succ(x83))))), Neg(Succ(Succ(x83))), Neg(Succ(Succ(x82)))))
67.74/34.82	
67.74/34.82	
67.74/34.82	*(new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Zero)))_>=_new_gcd0Gcd'1(new_esEs(new_rem(Neg(Succ(Zero)), Neg(Succ(Zero)))), Neg(Succ(Zero)), Neg(Succ(Zero))))
67.74/34.82	
67.74/34.82	
67.74/34.82	*(new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x86))))_>=_new_gcd0Gcd'1(new_esEs(new_rem(Neg(Succ(Succ(x86))), Pos(Succ(Zero)))), Pos(Succ(Zero)), Neg(Succ(Succ(x86)))))
67.74/34.82	
67.74/34.82	
67.74/34.82	*(new_gcd0Gcd'(Pos(Succ(Succ(x94))), Neg(Succ(Succ(x93))))_>=_new_gcd0Gcd'1(new_esEs(new_rem(Neg(Succ(Succ(x93))), Pos(Succ(Succ(x94))))), Pos(Succ(Succ(x94))), Neg(Succ(Succ(x93)))))
67.74/34.82	
67.74/34.82	
67.74/34.82	*(new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Zero)))_>=_new_gcd0Gcd'1(new_esEs(new_rem(Neg(Succ(Zero)), Pos(Succ(Zero)))), Pos(Succ(Zero)), Neg(Succ(Zero))))
67.74/34.82	
67.74/34.82	
67.74/34.82	
67.74/34.82	
67.74/34.82	*new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.82	
67.74/34.82	*(new_gcd0Gcd'1(False, x16, x17)_>=_new_gcd0Gcd'0(x16, new_rem(x17, x16)))
67.74/34.82	
67.74/34.82	
67.74/34.82	
67.74/34.82	
67.74/34.82	
67.74/34.82	
67.74/34.82	
67.74/34.82	
67.74/34.82	The constraints for P_> respective P_bound are constructed from P__>=_ where we just replace every occurence of "t _>=_ s" in P__>=_ by  "t > s" respective "t _>=_ c". Here c stands for the fresh constant used for P_bound. 
67.74/34.82	----------------------------------------
67.74/34.82	
67.74/34.82	(49)
67.74/34.82	Obligation:
67.74/34.82	Q DP problem:
67.74/34.82	The TRS P consists of the following rules:
67.74/34.82	
67.74/34.82	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.82	   new_gcd0Gcd'(vuz542, vuz549) -> new_gcd0Gcd'1(new_esEs(new_rem(vuz549, vuz542)), vuz542, vuz549)
67.74/34.82	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.82	
67.74/34.82	The TRS R consists of the following rules:
67.74/34.82	
67.74/34.82	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.82	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.82	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.82	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.82	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.82	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.82	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.82	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.82	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.82	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.82	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.82	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.82	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.82	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.82	   new_error -> error([])
67.74/34.82	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.82	   new_primEqInt2 -> True
67.74/34.82	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.82	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.82	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.82	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.82	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.82	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.82	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.82	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.82	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.82	   new_primMinusNatS1 -> Zero
67.74/34.82	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.82	   new_primEqInt1 -> True
67.74/34.82	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.82	   new_primEqInt0(vuz3260) -> False
67.74/34.82	   new_primEqInt(vuz3250) -> False
67.74/34.82	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.82	
67.74/34.82	The set Q consists of the following terms:
67.74/34.82	
67.74/34.82	   new_rem(Neg(x0), Neg(Zero))
67.74/34.82	   new_primEqInt1
67.74/34.82	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.82	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.82	   new_primMinusNatS1
67.74/34.82	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.82	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.82	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.82	   new_primMinusNatS2(Zero, Zero)
67.74/34.82	   new_error
67.74/34.82	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.82	   new_rem(Pos(x0), Pos(Zero))
67.74/34.82	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.82	   new_primEqInt0(x0)
67.74/34.82	   new_esEs(Pos(Zero))
67.74/34.82	   new_esEs(Pos(Succ(x0)))
67.74/34.82	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.82	   new_primModNatS02(x0, x1)
67.74/34.82	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.82	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.82	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.82	   new_primModNatS1(Zero, x0)
67.74/34.82	   new_primEqInt(x0)
67.74/34.82	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.82	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.82	   new_rem(Pos(x0), Neg(Zero))
67.74/34.82	   new_rem(Neg(x0), Pos(Zero))
67.74/34.82	   new_primMinusNatS0(x0)
67.74/34.82	   new_primEqInt2
67.74/34.82	   new_esEs(Neg(Zero))
67.74/34.82	   new_esEs(Neg(Succ(x0)))
67.74/34.82	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.82	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.82	
67.74/34.82	We have to consider all minimal (P,Q,R)-chains.
67.74/34.82	----------------------------------------
67.74/34.82	
67.74/34.82	(50) TransformationProof (EQUIVALENT)
67.74/34.82	By narrowing [LPAR04] the rule new_gcd0Gcd'(vuz542, vuz549) -> new_gcd0Gcd'1(new_esEs(new_rem(vuz549, vuz542)), vuz542, vuz549) at position [0] we obtained the following new rules [LPAR04]:
67.74/34.82	
67.74/34.82	   (new_gcd0Gcd'(Neg(Succ(x1)), Neg(x0)) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(x0, x1))), Neg(Succ(x1)), Neg(x0)),new_gcd0Gcd'(Neg(Succ(x1)), Neg(x0)) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(x0, x1))), Neg(Succ(x1)), Neg(x0)))
67.74/34.82	   (new_gcd0Gcd'(Pos(Succ(x1)), Pos(x0)) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(x0, x1))), Pos(Succ(x1)), Pos(x0)),new_gcd0Gcd'(Pos(Succ(x1)), Pos(x0)) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(x0, x1))), Pos(Succ(x1)), Pos(x0)))
67.74/34.82	   (new_gcd0Gcd'(Neg(Zero), Neg(x0)) -> new_gcd0Gcd'1(new_esEs(new_error), Neg(Zero), Neg(x0)),new_gcd0Gcd'(Neg(Zero), Neg(x0)) -> new_gcd0Gcd'1(new_esEs(new_error), Neg(Zero), Neg(x0)))
67.74/34.82	   (new_gcd0Gcd'(Neg(Zero), Pos(x0)) -> new_gcd0Gcd'1(new_esEs(new_error), Neg(Zero), Pos(x0)),new_gcd0Gcd'(Neg(Zero), Pos(x0)) -> new_gcd0Gcd'1(new_esEs(new_error), Neg(Zero), Pos(x0)))
67.74/34.82	   (new_gcd0Gcd'(Pos(Zero), Neg(x0)) -> new_gcd0Gcd'1(new_esEs(new_error), Pos(Zero), Neg(x0)),new_gcd0Gcd'(Pos(Zero), Neg(x0)) -> new_gcd0Gcd'1(new_esEs(new_error), Pos(Zero), Neg(x0)))
67.74/34.82	   (new_gcd0Gcd'(Neg(Succ(x1)), Pos(x0)) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(x0, x1))), Neg(Succ(x1)), Pos(x0)),new_gcd0Gcd'(Neg(Succ(x1)), Pos(x0)) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(x0, x1))), Neg(Succ(x1)), Pos(x0)))
67.74/34.82	   (new_gcd0Gcd'(Pos(Succ(x1)), Neg(x0)) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(x0, x1))), Pos(Succ(x1)), Neg(x0)),new_gcd0Gcd'(Pos(Succ(x1)), Neg(x0)) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(x0, x1))), Pos(Succ(x1)), Neg(x0)))
67.74/34.82	   (new_gcd0Gcd'(Pos(Zero), Pos(x0)) -> new_gcd0Gcd'1(new_esEs(new_error), Pos(Zero), Pos(x0)),new_gcd0Gcd'(Pos(Zero), Pos(x0)) -> new_gcd0Gcd'1(new_esEs(new_error), Pos(Zero), Pos(x0)))
67.74/34.82	
67.74/34.82	
67.74/34.82	----------------------------------------
67.74/34.82	
67.74/34.82	(51)
67.74/34.82	Obligation:
67.74/34.82	Q DP problem:
67.74/34.82	The TRS P consists of the following rules:
67.74/34.82	
67.74/34.82	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.82	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.82	   new_gcd0Gcd'(Neg(Succ(x1)), Neg(x0)) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(x0, x1))), Neg(Succ(x1)), Neg(x0))
67.74/34.82	   new_gcd0Gcd'(Pos(Succ(x1)), Pos(x0)) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(x0, x1))), Pos(Succ(x1)), Pos(x0))
67.74/34.82	   new_gcd0Gcd'(Neg(Zero), Neg(x0)) -> new_gcd0Gcd'1(new_esEs(new_error), Neg(Zero), Neg(x0))
67.74/34.82	   new_gcd0Gcd'(Neg(Zero), Pos(x0)) -> new_gcd0Gcd'1(new_esEs(new_error), Neg(Zero), Pos(x0))
67.74/34.82	   new_gcd0Gcd'(Pos(Zero), Neg(x0)) -> new_gcd0Gcd'1(new_esEs(new_error), Pos(Zero), Neg(x0))
67.74/34.82	   new_gcd0Gcd'(Neg(Succ(x1)), Pos(x0)) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(x0, x1))), Neg(Succ(x1)), Pos(x0))
67.74/34.82	   new_gcd0Gcd'(Pos(Succ(x1)), Neg(x0)) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(x0, x1))), Pos(Succ(x1)), Neg(x0))
67.74/34.82	   new_gcd0Gcd'(Pos(Zero), Pos(x0)) -> new_gcd0Gcd'1(new_esEs(new_error), Pos(Zero), Pos(x0))
67.74/34.82	
67.74/34.82	The TRS R consists of the following rules:
67.74/34.82	
67.74/34.82	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.82	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.82	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.82	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.82	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.82	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.82	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.82	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.82	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.82	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.82	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.82	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.82	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.82	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.82	   new_error -> error([])
67.74/34.82	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.82	   new_primEqInt2 -> True
67.74/34.82	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.82	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.82	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.82	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.82	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.82	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.82	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.82	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.82	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.82	   new_primMinusNatS1 -> Zero
67.74/34.82	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.82	   new_primEqInt1 -> True
67.74/34.82	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.82	   new_primEqInt0(vuz3260) -> False
67.74/34.82	   new_primEqInt(vuz3250) -> False
67.74/34.82	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.82	
67.74/34.82	The set Q consists of the following terms:
67.74/34.82	
67.74/34.82	   new_rem(Neg(x0), Neg(Zero))
67.74/34.82	   new_primEqInt1
67.74/34.82	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.82	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.82	   new_primMinusNatS1
67.74/34.82	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.82	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.82	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.82	   new_primMinusNatS2(Zero, Zero)
67.74/34.82	   new_error
67.74/34.82	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.82	   new_rem(Pos(x0), Pos(Zero))
67.74/34.82	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.82	   new_primEqInt0(x0)
67.74/34.82	   new_esEs(Pos(Zero))
67.74/34.82	   new_esEs(Pos(Succ(x0)))
67.74/34.82	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.82	   new_primModNatS02(x0, x1)
67.74/34.82	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.82	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.82	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.82	   new_primModNatS1(Zero, x0)
67.74/34.82	   new_primEqInt(x0)
67.74/34.82	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.82	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.82	   new_rem(Pos(x0), Neg(Zero))
67.74/34.82	   new_rem(Neg(x0), Pos(Zero))
67.74/34.82	   new_primMinusNatS0(x0)
67.74/34.82	   new_primEqInt2
67.74/34.82	   new_esEs(Neg(Zero))
67.74/34.82	   new_esEs(Neg(Succ(x0)))
67.74/34.82	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.82	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.82	
67.74/34.82	We have to consider all minimal (P,Q,R)-chains.
67.74/34.82	----------------------------------------
67.74/34.82	
67.74/34.82	(52) TransformationProof (EQUIVALENT)
67.74/34.82	By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Zero), Neg(x0)) -> new_gcd0Gcd'1(new_esEs(new_error), Neg(Zero), Neg(x0)) at position [0,0] we obtained the following new rules [LPAR04]:
67.74/34.82	
67.74/34.82	   (new_gcd0Gcd'(Neg(Zero), Neg(x0)) -> new_gcd0Gcd'1(new_esEs(error([])), Neg(Zero), Neg(x0)),new_gcd0Gcd'(Neg(Zero), Neg(x0)) -> new_gcd0Gcd'1(new_esEs(error([])), Neg(Zero), Neg(x0)))
67.74/34.82	
67.74/34.82	
67.74/34.82	----------------------------------------
67.74/34.82	
67.74/34.82	(53)
67.74/34.82	Obligation:
67.74/34.82	Q DP problem:
67.74/34.82	The TRS P consists of the following rules:
67.74/34.82	
67.74/34.82	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.82	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.82	   new_gcd0Gcd'(Neg(Succ(x1)), Neg(x0)) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(x0, x1))), Neg(Succ(x1)), Neg(x0))
67.74/34.82	   new_gcd0Gcd'(Pos(Succ(x1)), Pos(x0)) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(x0, x1))), Pos(Succ(x1)), Pos(x0))
67.74/34.82	   new_gcd0Gcd'(Neg(Zero), Pos(x0)) -> new_gcd0Gcd'1(new_esEs(new_error), Neg(Zero), Pos(x0))
67.74/34.82	   new_gcd0Gcd'(Pos(Zero), Neg(x0)) -> new_gcd0Gcd'1(new_esEs(new_error), Pos(Zero), Neg(x0))
67.74/34.82	   new_gcd0Gcd'(Neg(Succ(x1)), Pos(x0)) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(x0, x1))), Neg(Succ(x1)), Pos(x0))
67.74/34.82	   new_gcd0Gcd'(Pos(Succ(x1)), Neg(x0)) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(x0, x1))), Pos(Succ(x1)), Neg(x0))
67.74/34.82	   new_gcd0Gcd'(Pos(Zero), Pos(x0)) -> new_gcd0Gcd'1(new_esEs(new_error), Pos(Zero), Pos(x0))
67.74/34.82	   new_gcd0Gcd'(Neg(Zero), Neg(x0)) -> new_gcd0Gcd'1(new_esEs(error([])), Neg(Zero), Neg(x0))
67.74/34.82	
67.74/34.82	The TRS R consists of the following rules:
67.74/34.82	
67.74/34.82	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.82	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.82	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.82	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.82	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.82	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.82	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.82	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.82	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.82	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.82	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.82	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.82	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.82	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.82	   new_error -> error([])
67.74/34.82	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.82	   new_primEqInt2 -> True
67.74/34.82	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.82	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.82	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.82	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.82	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.82	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.82	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.82	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.82	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.82	   new_primMinusNatS1 -> Zero
67.74/34.82	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.82	   new_primEqInt1 -> True
67.74/34.82	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.82	   new_primEqInt0(vuz3260) -> False
67.74/34.82	   new_primEqInt(vuz3250) -> False
67.74/34.82	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.82	
67.74/34.82	The set Q consists of the following terms:
67.74/34.82	
67.74/34.82	   new_rem(Neg(x0), Neg(Zero))
67.74/34.82	   new_primEqInt1
67.74/34.82	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.82	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.82	   new_primMinusNatS1
67.74/34.82	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.82	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.82	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.82	   new_primMinusNatS2(Zero, Zero)
67.74/34.82	   new_error
67.74/34.82	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.82	   new_rem(Pos(x0), Pos(Zero))
67.74/34.82	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.82	   new_primEqInt0(x0)
67.74/34.82	   new_esEs(Pos(Zero))
67.74/34.82	   new_esEs(Pos(Succ(x0)))
67.74/34.82	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.82	   new_primModNatS02(x0, x1)
67.74/34.82	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.82	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.82	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.82	   new_primModNatS1(Zero, x0)
67.74/34.82	   new_primEqInt(x0)
67.74/34.82	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.82	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.82	   new_rem(Pos(x0), Neg(Zero))
67.74/34.82	   new_rem(Neg(x0), Pos(Zero))
67.74/34.82	   new_primMinusNatS0(x0)
67.74/34.82	   new_primEqInt2
67.74/34.82	   new_esEs(Neg(Zero))
67.74/34.82	   new_esEs(Neg(Succ(x0)))
67.74/34.82	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.82	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.82	
67.74/34.82	We have to consider all minimal (P,Q,R)-chains.
67.74/34.82	----------------------------------------
67.74/34.82	
67.74/34.82	(54) DependencyGraphProof (EQUIVALENT)
67.74/34.82	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
67.74/34.82	----------------------------------------
67.74/34.82	
67.74/34.82	(55)
67.74/34.82	Obligation:
67.74/34.82	Q DP problem:
67.74/34.82	The TRS P consists of the following rules:
67.74/34.82	
67.74/34.82	   new_gcd0Gcd'(Neg(Succ(x1)), Neg(x0)) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(x0, x1))), Neg(Succ(x1)), Neg(x0))
67.74/34.82	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.82	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.82	   new_gcd0Gcd'(Pos(Succ(x1)), Pos(x0)) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(x0, x1))), Pos(Succ(x1)), Pos(x0))
67.74/34.82	   new_gcd0Gcd'(Neg(Zero), Pos(x0)) -> new_gcd0Gcd'1(new_esEs(new_error), Neg(Zero), Pos(x0))
67.74/34.82	   new_gcd0Gcd'(Pos(Zero), Neg(x0)) -> new_gcd0Gcd'1(new_esEs(new_error), Pos(Zero), Neg(x0))
67.74/34.82	   new_gcd0Gcd'(Neg(Succ(x1)), Pos(x0)) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(x0, x1))), Neg(Succ(x1)), Pos(x0))
67.74/34.82	   new_gcd0Gcd'(Pos(Succ(x1)), Neg(x0)) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(x0, x1))), Pos(Succ(x1)), Neg(x0))
67.74/34.82	   new_gcd0Gcd'(Pos(Zero), Pos(x0)) -> new_gcd0Gcd'1(new_esEs(new_error), Pos(Zero), Pos(x0))
67.74/34.82	
67.74/34.82	The TRS R consists of the following rules:
67.74/34.82	
67.74/34.82	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.82	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.82	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.82	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.82	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.82	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.82	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.82	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.82	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.82	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.82	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.82	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.82	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.82	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.82	   new_error -> error([])
67.74/34.82	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.82	   new_primEqInt2 -> True
67.74/34.82	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.82	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.82	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.82	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.82	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.82	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.82	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.82	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.82	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.82	   new_primMinusNatS1 -> Zero
67.74/34.82	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.82	   new_primEqInt1 -> True
67.74/34.82	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.82	   new_primEqInt0(vuz3260) -> False
67.74/34.82	   new_primEqInt(vuz3250) -> False
67.74/34.82	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.82	
67.74/34.82	The set Q consists of the following terms:
67.74/34.82	
67.74/34.82	   new_rem(Neg(x0), Neg(Zero))
67.74/34.82	   new_primEqInt1
67.74/34.82	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.82	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.82	   new_primMinusNatS1
67.74/34.82	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.82	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.82	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.82	   new_primMinusNatS2(Zero, Zero)
67.74/34.82	   new_error
67.74/34.82	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.82	   new_rem(Pos(x0), Pos(Zero))
67.74/34.82	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.82	   new_primEqInt0(x0)
67.74/34.82	   new_esEs(Pos(Zero))
67.74/34.82	   new_esEs(Pos(Succ(x0)))
67.74/34.82	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.82	   new_primModNatS02(x0, x1)
67.74/34.82	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.82	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.82	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.82	   new_primModNatS1(Zero, x0)
67.74/34.82	   new_primEqInt(x0)
67.74/34.82	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.82	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.82	   new_rem(Pos(x0), Neg(Zero))
67.74/34.82	   new_rem(Neg(x0), Pos(Zero))
67.74/34.82	   new_primMinusNatS0(x0)
67.74/34.82	   new_primEqInt2
67.74/34.82	   new_esEs(Neg(Zero))
67.74/34.82	   new_esEs(Neg(Succ(x0)))
67.74/34.82	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.82	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.82	
67.74/34.82	We have to consider all minimal (P,Q,R)-chains.
67.74/34.82	----------------------------------------
67.74/34.82	
67.74/34.82	(56) TransformationProof (EQUIVALENT)
67.74/34.82	By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Zero), Pos(x0)) -> new_gcd0Gcd'1(new_esEs(new_error), Neg(Zero), Pos(x0)) at position [0,0] we obtained the following new rules [LPAR04]:
67.74/34.82	
67.74/34.82	   (new_gcd0Gcd'(Neg(Zero), Pos(x0)) -> new_gcd0Gcd'1(new_esEs(error([])), Neg(Zero), Pos(x0)),new_gcd0Gcd'(Neg(Zero), Pos(x0)) -> new_gcd0Gcd'1(new_esEs(error([])), Neg(Zero), Pos(x0)))
67.74/34.82	
67.74/34.82	
67.74/34.82	----------------------------------------
67.74/34.82	
67.74/34.82	(57)
67.74/34.82	Obligation:
67.74/34.82	Q DP problem:
67.74/34.82	The TRS P consists of the following rules:
67.74/34.82	
67.74/34.82	   new_gcd0Gcd'(Neg(Succ(x1)), Neg(x0)) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(x0, x1))), Neg(Succ(x1)), Neg(x0))
67.74/34.82	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.82	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.82	   new_gcd0Gcd'(Pos(Succ(x1)), Pos(x0)) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(x0, x1))), Pos(Succ(x1)), Pos(x0))
67.74/34.82	   new_gcd0Gcd'(Pos(Zero), Neg(x0)) -> new_gcd0Gcd'1(new_esEs(new_error), Pos(Zero), Neg(x0))
67.74/34.82	   new_gcd0Gcd'(Neg(Succ(x1)), Pos(x0)) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(x0, x1))), Neg(Succ(x1)), Pos(x0))
67.74/34.82	   new_gcd0Gcd'(Pos(Succ(x1)), Neg(x0)) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(x0, x1))), Pos(Succ(x1)), Neg(x0))
67.74/34.82	   new_gcd0Gcd'(Pos(Zero), Pos(x0)) -> new_gcd0Gcd'1(new_esEs(new_error), Pos(Zero), Pos(x0))
67.74/34.82	   new_gcd0Gcd'(Neg(Zero), Pos(x0)) -> new_gcd0Gcd'1(new_esEs(error([])), Neg(Zero), Pos(x0))
67.74/34.82	
67.74/34.82	The TRS R consists of the following rules:
67.74/34.82	
67.74/34.82	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.82	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.82	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.82	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.82	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.82	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.82	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.82	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.82	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.82	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.82	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.82	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.82	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.82	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.82	   new_error -> error([])
67.74/34.82	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.82	   new_primEqInt2 -> True
67.74/34.82	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.82	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.82	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.82	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.82	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.82	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.82	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.82	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.82	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.82	   new_primMinusNatS1 -> Zero
67.74/34.82	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.82	   new_primEqInt1 -> True
67.74/34.82	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.82	   new_primEqInt0(vuz3260) -> False
67.74/34.82	   new_primEqInt(vuz3250) -> False
67.74/34.82	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.82	
67.74/34.82	The set Q consists of the following terms:
67.74/34.82	
67.74/34.82	   new_rem(Neg(x0), Neg(Zero))
67.74/34.82	   new_primEqInt1
67.74/34.82	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.82	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.82	   new_primMinusNatS1
67.74/34.82	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.82	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.82	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.82	   new_primMinusNatS2(Zero, Zero)
67.74/34.82	   new_error
67.74/34.82	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.82	   new_rem(Pos(x0), Pos(Zero))
67.74/34.82	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.82	   new_primEqInt0(x0)
67.74/34.82	   new_esEs(Pos(Zero))
67.74/34.82	   new_esEs(Pos(Succ(x0)))
67.74/34.82	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.82	   new_primModNatS02(x0, x1)
67.74/34.82	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.82	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.82	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.82	   new_primModNatS1(Zero, x0)
67.74/34.82	   new_primEqInt(x0)
67.74/34.82	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.82	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.82	   new_rem(Pos(x0), Neg(Zero))
67.74/34.82	   new_rem(Neg(x0), Pos(Zero))
67.74/34.82	   new_primMinusNatS0(x0)
67.74/34.82	   new_primEqInt2
67.74/34.82	   new_esEs(Neg(Zero))
67.74/34.82	   new_esEs(Neg(Succ(x0)))
67.74/34.82	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.82	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.82	
67.74/34.82	We have to consider all minimal (P,Q,R)-chains.
67.74/34.82	----------------------------------------
67.74/34.82	
67.74/34.82	(58) DependencyGraphProof (EQUIVALENT)
67.74/34.82	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
67.74/34.82	----------------------------------------
67.74/34.82	
67.74/34.82	(59)
67.74/34.82	Obligation:
67.74/34.82	Q DP problem:
67.74/34.82	The TRS P consists of the following rules:
67.74/34.82	
67.74/34.82	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.82	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.82	   new_gcd0Gcd'(Neg(Succ(x1)), Neg(x0)) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(x0, x1))), Neg(Succ(x1)), Neg(x0))
67.74/34.82	   new_gcd0Gcd'(Pos(Succ(x1)), Pos(x0)) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(x0, x1))), Pos(Succ(x1)), Pos(x0))
67.74/34.82	   new_gcd0Gcd'(Pos(Zero), Neg(x0)) -> new_gcd0Gcd'1(new_esEs(new_error), Pos(Zero), Neg(x0))
67.74/34.82	   new_gcd0Gcd'(Neg(Succ(x1)), Pos(x0)) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(x0, x1))), Neg(Succ(x1)), Pos(x0))
67.74/34.82	   new_gcd0Gcd'(Pos(Succ(x1)), Neg(x0)) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(x0, x1))), Pos(Succ(x1)), Neg(x0))
67.74/34.82	   new_gcd0Gcd'(Pos(Zero), Pos(x0)) -> new_gcd0Gcd'1(new_esEs(new_error), Pos(Zero), Pos(x0))
67.74/34.82	
67.74/34.82	The TRS R consists of the following rules:
67.74/34.82	
67.74/34.82	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.82	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.82	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.82	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.82	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.82	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.82	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.82	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.82	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.82	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.82	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.82	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.82	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.82	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.82	   new_error -> error([])
67.74/34.82	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.82	   new_primEqInt2 -> True
67.74/34.82	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.82	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.82	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.82	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.82	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.82	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.82	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.82	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.82	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.82	   new_primMinusNatS1 -> Zero
67.74/34.82	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.82	   new_primEqInt1 -> True
67.74/34.82	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.82	   new_primEqInt0(vuz3260) -> False
67.74/34.82	   new_primEqInt(vuz3250) -> False
67.74/34.82	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.82	
67.74/34.82	The set Q consists of the following terms:
67.74/34.82	
67.74/34.82	   new_rem(Neg(x0), Neg(Zero))
67.74/34.82	   new_primEqInt1
67.74/34.82	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.82	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.82	   new_primMinusNatS1
67.74/34.82	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.82	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.82	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.82	   new_primMinusNatS2(Zero, Zero)
67.74/34.82	   new_error
67.74/34.82	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.82	   new_rem(Pos(x0), Pos(Zero))
67.74/34.82	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.82	   new_primEqInt0(x0)
67.74/34.82	   new_esEs(Pos(Zero))
67.74/34.82	   new_esEs(Pos(Succ(x0)))
67.74/34.82	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.82	   new_primModNatS02(x0, x1)
67.74/34.82	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.82	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.82	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.82	   new_primModNatS1(Zero, x0)
67.74/34.82	   new_primEqInt(x0)
67.74/34.82	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.82	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.82	   new_rem(Pos(x0), Neg(Zero))
67.74/34.82	   new_rem(Neg(x0), Pos(Zero))
67.74/34.82	   new_primMinusNatS0(x0)
67.74/34.82	   new_primEqInt2
67.74/34.82	   new_esEs(Neg(Zero))
67.74/34.82	   new_esEs(Neg(Succ(x0)))
67.74/34.82	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.82	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.82	
67.74/34.82	We have to consider all minimal (P,Q,R)-chains.
67.74/34.82	----------------------------------------
67.74/34.82	
67.74/34.82	(60) TransformationProof (EQUIVALENT)
67.74/34.82	By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Zero), Neg(x0)) -> new_gcd0Gcd'1(new_esEs(new_error), Pos(Zero), Neg(x0)) at position [0,0] we obtained the following new rules [LPAR04]:
67.74/34.82	
67.74/34.82	   (new_gcd0Gcd'(Pos(Zero), Neg(x0)) -> new_gcd0Gcd'1(new_esEs(error([])), Pos(Zero), Neg(x0)),new_gcd0Gcd'(Pos(Zero), Neg(x0)) -> new_gcd0Gcd'1(new_esEs(error([])), Pos(Zero), Neg(x0)))
67.74/34.82	
67.74/34.82	
67.74/34.82	----------------------------------------
67.74/34.82	
67.74/34.82	(61)
67.74/34.82	Obligation:
67.74/34.82	Q DP problem:
67.74/34.82	The TRS P consists of the following rules:
67.74/34.82	
67.74/34.82	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.82	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.82	   new_gcd0Gcd'(Neg(Succ(x1)), Neg(x0)) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(x0, x1))), Neg(Succ(x1)), Neg(x0))
67.74/34.82	   new_gcd0Gcd'(Pos(Succ(x1)), Pos(x0)) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(x0, x1))), Pos(Succ(x1)), Pos(x0))
67.74/34.82	   new_gcd0Gcd'(Neg(Succ(x1)), Pos(x0)) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(x0, x1))), Neg(Succ(x1)), Pos(x0))
67.74/34.82	   new_gcd0Gcd'(Pos(Succ(x1)), Neg(x0)) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(x0, x1))), Pos(Succ(x1)), Neg(x0))
67.74/34.82	   new_gcd0Gcd'(Pos(Zero), Pos(x0)) -> new_gcd0Gcd'1(new_esEs(new_error), Pos(Zero), Pos(x0))
67.74/34.82	   new_gcd0Gcd'(Pos(Zero), Neg(x0)) -> new_gcd0Gcd'1(new_esEs(error([])), Pos(Zero), Neg(x0))
67.74/34.82	
67.74/34.82	The TRS R consists of the following rules:
67.74/34.82	
67.74/34.82	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.82	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.82	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.82	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.82	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.82	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.82	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.82	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.82	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.82	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.82	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.82	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.82	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.82	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.82	   new_error -> error([])
67.74/34.82	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.82	   new_primEqInt2 -> True
67.74/34.82	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.82	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.82	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.82	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.82	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.82	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.82	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.82	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.82	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.82	   new_primMinusNatS1 -> Zero
67.74/34.82	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.82	   new_primEqInt1 -> True
67.74/34.82	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.82	   new_primEqInt0(vuz3260) -> False
67.74/34.82	   new_primEqInt(vuz3250) -> False
67.74/34.82	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.82	
67.74/34.82	The set Q consists of the following terms:
67.74/34.82	
67.74/34.82	   new_rem(Neg(x0), Neg(Zero))
67.74/34.82	   new_primEqInt1
67.74/34.82	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.82	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.82	   new_primMinusNatS1
67.74/34.82	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.82	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.82	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.82	   new_primMinusNatS2(Zero, Zero)
67.74/34.82	   new_error
67.74/34.82	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.82	   new_rem(Pos(x0), Pos(Zero))
67.74/34.82	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.82	   new_primEqInt0(x0)
67.74/34.82	   new_esEs(Pos(Zero))
67.74/34.82	   new_esEs(Pos(Succ(x0)))
67.74/34.82	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.82	   new_primModNatS02(x0, x1)
67.74/34.82	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.82	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.82	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.82	   new_primModNatS1(Zero, x0)
67.74/34.82	   new_primEqInt(x0)
67.74/34.82	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.82	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.82	   new_rem(Pos(x0), Neg(Zero))
67.74/34.82	   new_rem(Neg(x0), Pos(Zero))
67.74/34.82	   new_primMinusNatS0(x0)
67.74/34.82	   new_primEqInt2
67.74/34.82	   new_esEs(Neg(Zero))
67.74/34.82	   new_esEs(Neg(Succ(x0)))
67.74/34.82	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.82	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.82	
67.74/34.82	We have to consider all minimal (P,Q,R)-chains.
67.74/34.82	----------------------------------------
67.74/34.82	
67.74/34.82	(62) DependencyGraphProof (EQUIVALENT)
67.74/34.82	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
67.74/34.82	----------------------------------------
67.74/34.82	
67.74/34.82	(63)
67.74/34.82	Obligation:
67.74/34.82	Q DP problem:
67.74/34.82	The TRS P consists of the following rules:
67.74/34.82	
67.74/34.82	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.82	   new_gcd0Gcd'(Neg(Succ(x1)), Neg(x0)) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(x0, x1))), Neg(Succ(x1)), Neg(x0))
67.74/34.82	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.82	   new_gcd0Gcd'(Pos(Succ(x1)), Pos(x0)) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(x0, x1))), Pos(Succ(x1)), Pos(x0))
67.74/34.82	   new_gcd0Gcd'(Neg(Succ(x1)), Pos(x0)) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(x0, x1))), Neg(Succ(x1)), Pos(x0))
67.74/34.82	   new_gcd0Gcd'(Pos(Succ(x1)), Neg(x0)) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(x0, x1))), Pos(Succ(x1)), Neg(x0))
67.74/34.82	   new_gcd0Gcd'(Pos(Zero), Pos(x0)) -> new_gcd0Gcd'1(new_esEs(new_error), Pos(Zero), Pos(x0))
67.74/34.82	
67.74/34.82	The TRS R consists of the following rules:
67.74/34.82	
67.74/34.82	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.82	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.82	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.82	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.82	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.82	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.82	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.82	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.82	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.82	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.82	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.82	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.82	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.82	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.82	   new_error -> error([])
67.74/34.82	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.82	   new_primEqInt2 -> True
67.74/34.82	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.82	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.82	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.82	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.82	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.82	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.82	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.82	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.82	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.82	   new_primMinusNatS1 -> Zero
67.74/34.82	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.82	   new_primEqInt1 -> True
67.74/34.82	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.82	   new_primEqInt0(vuz3260) -> False
67.74/34.82	   new_primEqInt(vuz3250) -> False
67.74/34.82	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.82	
67.74/34.82	The set Q consists of the following terms:
67.74/34.82	
67.74/34.82	   new_rem(Neg(x0), Neg(Zero))
67.74/34.82	   new_primEqInt1
67.74/34.82	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.82	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.82	   new_primMinusNatS1
67.74/34.82	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.82	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.82	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.82	   new_primMinusNatS2(Zero, Zero)
67.74/34.82	   new_error
67.74/34.82	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.82	   new_rem(Pos(x0), Pos(Zero))
67.74/34.82	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.82	   new_primEqInt0(x0)
67.74/34.82	   new_esEs(Pos(Zero))
67.74/34.82	   new_esEs(Pos(Succ(x0)))
67.74/34.82	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.82	   new_primModNatS02(x0, x1)
67.74/34.82	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.82	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.82	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.82	   new_primModNatS1(Zero, x0)
67.74/34.82	   new_primEqInt(x0)
67.74/34.82	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.82	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.82	   new_rem(Pos(x0), Neg(Zero))
67.74/34.82	   new_rem(Neg(x0), Pos(Zero))
67.74/34.82	   new_primMinusNatS0(x0)
67.74/34.82	   new_primEqInt2
67.74/34.82	   new_esEs(Neg(Zero))
67.74/34.82	   new_esEs(Neg(Succ(x0)))
67.74/34.82	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.82	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.82	
67.74/34.82	We have to consider all minimal (P,Q,R)-chains.
67.74/34.82	----------------------------------------
67.74/34.82	
67.74/34.82	(64) TransformationProof (EQUIVALENT)
67.74/34.82	By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Zero), Pos(x0)) -> new_gcd0Gcd'1(new_esEs(new_error), Pos(Zero), Pos(x0)) at position [0,0] we obtained the following new rules [LPAR04]:
67.74/34.82	
67.74/34.82	   (new_gcd0Gcd'(Pos(Zero), Pos(x0)) -> new_gcd0Gcd'1(new_esEs(error([])), Pos(Zero), Pos(x0)),new_gcd0Gcd'(Pos(Zero), Pos(x0)) -> new_gcd0Gcd'1(new_esEs(error([])), Pos(Zero), Pos(x0)))
67.74/34.82	
67.74/34.82	
67.74/34.82	----------------------------------------
67.74/34.82	
67.74/34.82	(65)
67.74/34.82	Obligation:
67.74/34.82	Q DP problem:
67.74/34.82	The TRS P consists of the following rules:
67.74/34.82	
67.74/34.82	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.82	   new_gcd0Gcd'(Neg(Succ(x1)), Neg(x0)) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(x0, x1))), Neg(Succ(x1)), Neg(x0))
67.74/34.82	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.82	   new_gcd0Gcd'(Pos(Succ(x1)), Pos(x0)) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(x0, x1))), Pos(Succ(x1)), Pos(x0))
67.74/34.82	   new_gcd0Gcd'(Neg(Succ(x1)), Pos(x0)) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(x0, x1))), Neg(Succ(x1)), Pos(x0))
67.74/34.82	   new_gcd0Gcd'(Pos(Succ(x1)), Neg(x0)) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(x0, x1))), Pos(Succ(x1)), Neg(x0))
67.74/34.82	   new_gcd0Gcd'(Pos(Zero), Pos(x0)) -> new_gcd0Gcd'1(new_esEs(error([])), Pos(Zero), Pos(x0))
67.74/34.82	
67.74/34.82	The TRS R consists of the following rules:
67.74/34.82	
67.74/34.82	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.82	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.82	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.82	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.82	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.82	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.82	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.82	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.82	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.82	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.82	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.82	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.82	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.82	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.82	   new_error -> error([])
67.74/34.82	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.82	   new_primEqInt2 -> True
67.74/34.82	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.82	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.82	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.82	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.82	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.82	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.82	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.82	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.82	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.82	   new_primMinusNatS1 -> Zero
67.74/34.82	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.82	   new_primEqInt1 -> True
67.74/34.82	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.82	   new_primEqInt0(vuz3260) -> False
67.74/34.82	   new_primEqInt(vuz3250) -> False
67.74/34.82	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.82	
67.74/34.82	The set Q consists of the following terms:
67.74/34.82	
67.74/34.82	   new_rem(Neg(x0), Neg(Zero))
67.74/34.82	   new_primEqInt1
67.74/34.82	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.82	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.82	   new_primMinusNatS1
67.74/34.82	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.82	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.82	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.82	   new_primMinusNatS2(Zero, Zero)
67.74/34.82	   new_error
67.74/34.82	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.82	   new_rem(Pos(x0), Pos(Zero))
67.74/34.82	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.82	   new_primEqInt0(x0)
67.74/34.82	   new_esEs(Pos(Zero))
67.74/34.82	   new_esEs(Pos(Succ(x0)))
67.74/34.82	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.82	   new_primModNatS02(x0, x1)
67.74/34.82	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.82	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.82	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.82	   new_primModNatS1(Zero, x0)
67.74/34.82	   new_primEqInt(x0)
67.74/34.82	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.82	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.82	   new_rem(Pos(x0), Neg(Zero))
67.74/34.82	   new_rem(Neg(x0), Pos(Zero))
67.74/34.82	   new_primMinusNatS0(x0)
67.74/34.82	   new_primEqInt2
67.74/34.82	   new_esEs(Neg(Zero))
67.74/34.82	   new_esEs(Neg(Succ(x0)))
67.74/34.82	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.82	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.82	
67.74/34.82	We have to consider all minimal (P,Q,R)-chains.
67.74/34.82	----------------------------------------
67.74/34.82	
67.74/34.82	(66) DependencyGraphProof (EQUIVALENT)
67.74/34.82	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
67.74/34.82	----------------------------------------
67.74/34.82	
67.74/34.82	(67)
67.74/34.82	Obligation:
67.74/34.82	Q DP problem:
67.74/34.82	The TRS P consists of the following rules:
67.74/34.82	
67.74/34.82	   new_gcd0Gcd'(Neg(Succ(x1)), Neg(x0)) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(x0, x1))), Neg(Succ(x1)), Neg(x0))
67.74/34.82	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.82	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.82	   new_gcd0Gcd'(Pos(Succ(x1)), Pos(x0)) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(x0, x1))), Pos(Succ(x1)), Pos(x0))
67.74/34.82	   new_gcd0Gcd'(Neg(Succ(x1)), Pos(x0)) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(x0, x1))), Neg(Succ(x1)), Pos(x0))
67.74/34.82	   new_gcd0Gcd'(Pos(Succ(x1)), Neg(x0)) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(x0, x1))), Pos(Succ(x1)), Neg(x0))
67.74/34.82	
67.74/34.82	The TRS R consists of the following rules:
67.74/34.82	
67.74/34.82	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.82	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.82	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.82	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.82	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.82	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.82	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.82	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.82	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.82	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.82	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.82	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.82	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.82	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.82	   new_error -> error([])
67.74/34.82	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.82	   new_primEqInt2 -> True
67.74/34.82	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.82	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.82	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.82	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.82	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.82	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.82	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.82	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.82	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.82	   new_primMinusNatS1 -> Zero
67.74/34.82	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.82	   new_primEqInt1 -> True
67.74/34.82	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.82	   new_primEqInt0(vuz3260) -> False
67.74/34.82	   new_primEqInt(vuz3250) -> False
67.74/34.82	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.82	
67.74/34.82	The set Q consists of the following terms:
67.74/34.82	
67.74/34.82	   new_rem(Neg(x0), Neg(Zero))
67.74/34.82	   new_primEqInt1
67.74/34.82	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.82	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.82	   new_primMinusNatS1
67.74/34.82	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.82	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.82	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.82	   new_primMinusNatS2(Zero, Zero)
67.74/34.82	   new_error
67.74/34.82	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.82	   new_rem(Pos(x0), Pos(Zero))
67.74/34.82	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.82	   new_primEqInt0(x0)
67.74/34.82	   new_esEs(Pos(Zero))
67.74/34.82	   new_esEs(Pos(Succ(x0)))
67.74/34.82	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.82	   new_primModNatS02(x0, x1)
67.74/34.82	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.82	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.82	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.82	   new_primModNatS1(Zero, x0)
67.74/34.82	   new_primEqInt(x0)
67.74/34.82	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.82	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.82	   new_rem(Pos(x0), Neg(Zero))
67.74/34.82	   new_rem(Neg(x0), Pos(Zero))
67.74/34.82	   new_primMinusNatS0(x0)
67.74/34.82	   new_primEqInt2
67.74/34.82	   new_esEs(Neg(Zero))
67.74/34.82	   new_esEs(Neg(Succ(x0)))
67.74/34.82	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.82	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.82	
67.74/34.82	We have to consider all minimal (P,Q,R)-chains.
67.74/34.82	----------------------------------------
67.74/34.82	
67.74/34.82	(68) TransformationProof (EQUIVALENT)
67.74/34.82	By narrowing [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(x1)), Neg(x0)) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(x0, x1))), Neg(Succ(x1)), Neg(x0)) at position [0] we obtained the following new rules [LPAR04]:
67.74/34.82	
67.74/34.82	   (new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS0(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(x0)))),new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS0(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(x0)))))
67.74/34.82	   (new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(new_esEs(Neg(Succ(Zero))), Neg(Succ(Succ(x0))), Neg(Succ(Zero))),new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(new_esEs(Neg(Succ(Zero))), Neg(Succ(Succ(x0))), Neg(Succ(Zero))))
67.74/34.82	   (new_gcd0Gcd'(Neg(Succ(Succ(x1))), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, x1, x0, x1))), Neg(Succ(Succ(x1))), Neg(Succ(Succ(x0)))),new_gcd0Gcd'(Neg(Succ(Succ(x1))), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, x1, x0, x1))), Neg(Succ(Succ(x1))), Neg(Succ(Succ(x0)))))
67.74/34.82	   (new_gcd0Gcd'(Neg(Succ(x0)), Neg(Zero)) -> new_gcd0Gcd'1(new_esEs(Neg(Zero)), Neg(Succ(x0)), Neg(Zero)),new_gcd0Gcd'(Neg(Succ(x0)), Neg(Zero)) -> new_gcd0Gcd'1(new_esEs(Neg(Zero)), Neg(Succ(x0)), Neg(Zero)))
67.74/34.82	   (new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Zero))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS1, Zero))), Neg(Succ(Zero)), Neg(Succ(Zero))),new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Zero))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS1, Zero))), Neg(Succ(Zero)), Neg(Succ(Zero))))
67.74/34.82	
67.74/34.82	
67.74/34.82	----------------------------------------
67.74/34.82	
67.74/34.82	(69)
67.74/34.82	Obligation:
67.74/34.82	Q DP problem:
67.74/34.82	The TRS P consists of the following rules:
67.74/34.82	
67.74/34.82	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.82	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.82	   new_gcd0Gcd'(Pos(Succ(x1)), Pos(x0)) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(x0, x1))), Pos(Succ(x1)), Pos(x0))
67.74/34.82	   new_gcd0Gcd'(Neg(Succ(x1)), Pos(x0)) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(x0, x1))), Neg(Succ(x1)), Pos(x0))
67.74/34.82	   new_gcd0Gcd'(Pos(Succ(x1)), Neg(x0)) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(x0, x1))), Pos(Succ(x1)), Neg(x0))
67.74/34.82	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS0(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.82	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(new_esEs(Neg(Succ(Zero))), Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.82	   new_gcd0Gcd'(Neg(Succ(Succ(x1))), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, x1, x0, x1))), Neg(Succ(Succ(x1))), Neg(Succ(Succ(x0))))
67.74/34.82	   new_gcd0Gcd'(Neg(Succ(x0)), Neg(Zero)) -> new_gcd0Gcd'1(new_esEs(Neg(Zero)), Neg(Succ(x0)), Neg(Zero))
67.74/34.82	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Zero))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS1, Zero))), Neg(Succ(Zero)), Neg(Succ(Zero)))
67.74/34.82	
67.74/34.82	The TRS R consists of the following rules:
67.74/34.82	
67.74/34.82	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.82	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.82	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.82	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.82	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.82	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.82	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.82	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.82	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.82	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.82	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.82	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.82	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.82	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.82	   new_error -> error([])
67.74/34.82	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.82	   new_primEqInt2 -> True
67.74/34.82	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.82	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.82	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.82	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.82	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.82	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.82	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.82	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.82	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.82	   new_primMinusNatS1 -> Zero
67.74/34.82	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.82	   new_primEqInt1 -> True
67.74/34.82	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.82	   new_primEqInt0(vuz3260) -> False
67.74/34.82	   new_primEqInt(vuz3250) -> False
67.74/34.82	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.82	
67.74/34.82	The set Q consists of the following terms:
67.74/34.82	
67.74/34.82	   new_rem(Neg(x0), Neg(Zero))
67.74/34.82	   new_primEqInt1
67.74/34.82	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.82	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.82	   new_primMinusNatS1
67.74/34.82	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.82	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.82	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.82	   new_primMinusNatS2(Zero, Zero)
67.74/34.82	   new_error
67.74/34.82	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.82	   new_rem(Pos(x0), Pos(Zero))
67.74/34.82	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.82	   new_primEqInt0(x0)
67.74/34.82	   new_esEs(Pos(Zero))
67.74/34.82	   new_esEs(Pos(Succ(x0)))
67.74/34.82	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.82	   new_primModNatS02(x0, x1)
67.74/34.82	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.82	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.82	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.82	   new_primModNatS1(Zero, x0)
67.74/34.82	   new_primEqInt(x0)
67.74/34.82	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.82	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.82	   new_rem(Pos(x0), Neg(Zero))
67.74/34.82	   new_rem(Neg(x0), Pos(Zero))
67.74/34.82	   new_primMinusNatS0(x0)
67.74/34.82	   new_primEqInt2
67.74/34.82	   new_esEs(Neg(Zero))
67.74/34.82	   new_esEs(Neg(Succ(x0)))
67.74/34.82	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.82	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.82	
67.74/34.82	We have to consider all minimal (P,Q,R)-chains.
67.74/34.82	----------------------------------------
67.74/34.82	
67.74/34.82	(70) DependencyGraphProof (EQUIVALENT)
67.74/34.82	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
67.74/34.82	----------------------------------------
67.74/34.82	
67.74/34.82	(71)
67.74/34.82	Obligation:
67.74/34.82	Q DP problem:
67.74/34.82	The TRS P consists of the following rules:
67.74/34.82	
67.74/34.82	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.82	   new_gcd0Gcd'(Pos(Succ(x1)), Pos(x0)) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(x0, x1))), Pos(Succ(x1)), Pos(x0))
67.74/34.82	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.82	   new_gcd0Gcd'(Neg(Succ(x1)), Pos(x0)) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(x0, x1))), Neg(Succ(x1)), Pos(x0))
67.74/34.82	   new_gcd0Gcd'(Pos(Succ(x1)), Neg(x0)) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(x0, x1))), Pos(Succ(x1)), Neg(x0))
67.74/34.82	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS0(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.82	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(new_esEs(Neg(Succ(Zero))), Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.82	   new_gcd0Gcd'(Neg(Succ(Succ(x1))), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, x1, x0, x1))), Neg(Succ(Succ(x1))), Neg(Succ(Succ(x0))))
67.74/34.82	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Zero))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS1, Zero))), Neg(Succ(Zero)), Neg(Succ(Zero)))
67.74/34.82	
67.74/34.82	The TRS R consists of the following rules:
67.74/34.82	
67.74/34.82	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.82	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.82	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.82	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.82	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.82	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.82	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.82	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.82	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.82	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.82	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.82	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.82	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.82	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.82	   new_error -> error([])
67.74/34.82	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.82	   new_primEqInt2 -> True
67.74/34.82	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.82	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.82	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.82	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.82	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.82	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.82	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.82	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.82	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.82	   new_primMinusNatS1 -> Zero
67.74/34.82	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.82	   new_primEqInt1 -> True
67.74/34.82	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.82	   new_primEqInt0(vuz3260) -> False
67.74/34.82	   new_primEqInt(vuz3250) -> False
67.74/34.82	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.82	
67.74/34.82	The set Q consists of the following terms:
67.74/34.82	
67.74/34.82	   new_rem(Neg(x0), Neg(Zero))
67.74/34.82	   new_primEqInt1
67.74/34.82	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.82	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.82	   new_primMinusNatS1
67.74/34.82	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.82	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.82	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.82	   new_primMinusNatS2(Zero, Zero)
67.74/34.82	   new_error
67.74/34.82	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.82	   new_rem(Pos(x0), Pos(Zero))
67.74/34.82	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.82	   new_primEqInt0(x0)
67.74/34.82	   new_esEs(Pos(Zero))
67.74/34.82	   new_esEs(Pos(Succ(x0)))
67.74/34.82	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.82	   new_primModNatS02(x0, x1)
67.74/34.82	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.82	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.82	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.82	   new_primModNatS1(Zero, x0)
67.74/34.82	   new_primEqInt(x0)
67.74/34.82	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.82	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.82	   new_rem(Pos(x0), Neg(Zero))
67.74/34.82	   new_rem(Neg(x0), Pos(Zero))
67.74/34.82	   new_primMinusNatS0(x0)
67.74/34.82	   new_primEqInt2
67.74/34.82	   new_esEs(Neg(Zero))
67.74/34.82	   new_esEs(Neg(Succ(x0)))
67.74/34.82	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.82	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.82	
67.74/34.82	We have to consider all minimal (P,Q,R)-chains.
67.74/34.82	----------------------------------------
67.74/34.82	
67.74/34.82	(72) TransformationProof (EQUIVALENT)
67.74/34.82	By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS0(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(x0)))) at position [0,0,0,0] we obtained the following new rules [LPAR04]:
67.74/34.82	
67.74/34.82	   (new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(x0)))),new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(x0)))))
67.74/34.82	
67.74/34.82	
67.74/34.82	----------------------------------------
67.74/34.82	
67.74/34.82	(73)
67.74/34.82	Obligation:
67.74/34.82	Q DP problem:
67.74/34.82	The TRS P consists of the following rules:
67.74/34.82	
67.74/34.82	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.82	   new_gcd0Gcd'(Pos(Succ(x1)), Pos(x0)) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(x0, x1))), Pos(Succ(x1)), Pos(x0))
67.74/34.82	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.82	   new_gcd0Gcd'(Neg(Succ(x1)), Pos(x0)) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(x0, x1))), Neg(Succ(x1)), Pos(x0))
67.74/34.82	   new_gcd0Gcd'(Pos(Succ(x1)), Neg(x0)) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(x0, x1))), Pos(Succ(x1)), Neg(x0))
67.74/34.82	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(new_esEs(Neg(Succ(Zero))), Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.82	   new_gcd0Gcd'(Neg(Succ(Succ(x1))), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, x1, x0, x1))), Neg(Succ(Succ(x1))), Neg(Succ(Succ(x0))))
67.74/34.82	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Zero))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS1, Zero))), Neg(Succ(Zero)), Neg(Succ(Zero)))
67.74/34.82	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.82	
67.74/34.82	The TRS R consists of the following rules:
67.74/34.82	
67.74/34.82	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.82	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.82	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.82	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.82	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.82	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.82	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.82	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.82	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.82	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.82	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.82	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.82	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.82	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.82	   new_error -> error([])
67.74/34.82	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.82	   new_primEqInt2 -> True
67.74/34.82	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.82	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.82	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.82	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.82	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.82	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.82	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.82	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.82	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.82	   new_primMinusNatS1 -> Zero
67.74/34.82	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.82	   new_primEqInt1 -> True
67.74/34.82	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.82	   new_primEqInt0(vuz3260) -> False
67.74/34.82	   new_primEqInt(vuz3250) -> False
67.74/34.82	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.82	
67.74/34.82	The set Q consists of the following terms:
67.74/34.82	
67.74/34.82	   new_rem(Neg(x0), Neg(Zero))
67.74/34.82	   new_primEqInt1
67.74/34.82	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.82	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.82	   new_primMinusNatS1
67.74/34.82	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.82	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.82	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.82	   new_primMinusNatS2(Zero, Zero)
67.74/34.82	   new_error
67.74/34.82	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.82	   new_rem(Pos(x0), Pos(Zero))
67.74/34.82	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.82	   new_primEqInt0(x0)
67.74/34.82	   new_esEs(Pos(Zero))
67.74/34.82	   new_esEs(Pos(Succ(x0)))
67.74/34.82	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.82	   new_primModNatS02(x0, x1)
67.74/34.82	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.82	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.82	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.82	   new_primModNatS1(Zero, x0)
67.74/34.82	   new_primEqInt(x0)
67.74/34.82	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.82	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.82	   new_rem(Pos(x0), Neg(Zero))
67.74/34.82	   new_rem(Neg(x0), Pos(Zero))
67.74/34.82	   new_primMinusNatS0(x0)
67.74/34.82	   new_primEqInt2
67.74/34.82	   new_esEs(Neg(Zero))
67.74/34.82	   new_esEs(Neg(Succ(x0)))
67.74/34.82	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.82	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.82	
67.74/34.82	We have to consider all minimal (P,Q,R)-chains.
67.74/34.82	----------------------------------------
67.74/34.82	
67.74/34.82	(74) TransformationProof (EQUIVALENT)
67.74/34.82	By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(new_esEs(Neg(Succ(Zero))), Neg(Succ(Succ(x0))), Neg(Succ(Zero))) at position [0] we obtained the following new rules [LPAR04]:
67.74/34.82	
67.74/34.82	   (new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(new_primEqInt0(Zero), Neg(Succ(Succ(x0))), Neg(Succ(Zero))),new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(new_primEqInt0(Zero), Neg(Succ(Succ(x0))), Neg(Succ(Zero))))
67.74/34.82	
67.74/34.82	
67.74/34.82	----------------------------------------
67.74/34.82	
67.74/34.82	(75)
67.74/34.82	Obligation:
67.74/34.82	Q DP problem:
67.74/34.82	The TRS P consists of the following rules:
67.74/34.82	
67.74/34.82	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.82	   new_gcd0Gcd'(Pos(Succ(x1)), Pos(x0)) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(x0, x1))), Pos(Succ(x1)), Pos(x0))
67.74/34.82	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.82	   new_gcd0Gcd'(Neg(Succ(x1)), Pos(x0)) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(x0, x1))), Neg(Succ(x1)), Pos(x0))
67.74/34.82	   new_gcd0Gcd'(Pos(Succ(x1)), Neg(x0)) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(x0, x1))), Pos(Succ(x1)), Neg(x0))
67.74/34.82	   new_gcd0Gcd'(Neg(Succ(Succ(x1))), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, x1, x0, x1))), Neg(Succ(Succ(x1))), Neg(Succ(Succ(x0))))
67.74/34.82	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Zero))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS1, Zero))), Neg(Succ(Zero)), Neg(Succ(Zero)))
67.74/34.82	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.82	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(new_primEqInt0(Zero), Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.82	
67.74/34.82	The TRS R consists of the following rules:
67.74/34.82	
67.74/34.82	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.82	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.82	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.82	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.82	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.82	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.82	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.82	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.82	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.82	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.82	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.82	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.82	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.82	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.82	   new_error -> error([])
67.74/34.82	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.82	   new_primEqInt2 -> True
67.74/34.82	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.82	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.82	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.82	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.82	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.82	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.82	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.82	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.82	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.82	   new_primMinusNatS1 -> Zero
67.74/34.82	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.82	   new_primEqInt1 -> True
67.74/34.82	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.82	   new_primEqInt0(vuz3260) -> False
67.74/34.82	   new_primEqInt(vuz3250) -> False
67.74/34.82	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.82	
67.74/34.82	The set Q consists of the following terms:
67.74/34.82	
67.74/34.82	   new_rem(Neg(x0), Neg(Zero))
67.74/34.82	   new_primEqInt1
67.74/34.82	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.82	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.82	   new_primMinusNatS1
67.74/34.82	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.82	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.82	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.82	   new_primMinusNatS2(Zero, Zero)
67.74/34.82	   new_error
67.74/34.82	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.82	   new_rem(Pos(x0), Pos(Zero))
67.74/34.82	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.82	   new_primEqInt0(x0)
67.74/34.82	   new_esEs(Pos(Zero))
67.74/34.82	   new_esEs(Pos(Succ(x0)))
67.74/34.82	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.82	   new_primModNatS02(x0, x1)
67.74/34.82	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.82	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.82	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.82	   new_primModNatS1(Zero, x0)
67.74/34.82	   new_primEqInt(x0)
67.74/34.82	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.82	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.82	   new_rem(Pos(x0), Neg(Zero))
67.74/34.82	   new_rem(Neg(x0), Pos(Zero))
67.74/34.82	   new_primMinusNatS0(x0)
67.74/34.82	   new_primEqInt2
67.74/34.82	   new_esEs(Neg(Zero))
67.74/34.82	   new_esEs(Neg(Succ(x0)))
67.74/34.82	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.82	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.82	
67.74/34.82	We have to consider all minimal (P,Q,R)-chains.
67.74/34.82	----------------------------------------
67.74/34.82	
67.74/34.82	(76) TransformationProof (EQUIVALENT)
67.74/34.82	By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Zero))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS1, Zero))), Neg(Succ(Zero)), Neg(Succ(Zero))) at position [0,0,0,0] we obtained the following new rules [LPAR04]:
67.74/34.82	
67.74/34.82	   (new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Zero))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Zero, Zero))), Neg(Succ(Zero)), Neg(Succ(Zero))),new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Zero))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Zero, Zero))), Neg(Succ(Zero)), Neg(Succ(Zero))))
67.74/34.82	
67.74/34.82	
67.74/34.82	----------------------------------------
67.74/34.82	
67.74/34.82	(77)
67.74/34.82	Obligation:
67.74/34.82	Q DP problem:
67.74/34.82	The TRS P consists of the following rules:
67.74/34.82	
67.74/34.82	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.82	   new_gcd0Gcd'(Pos(Succ(x1)), Pos(x0)) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(x0, x1))), Pos(Succ(x1)), Pos(x0))
67.74/34.82	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.82	   new_gcd0Gcd'(Neg(Succ(x1)), Pos(x0)) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(x0, x1))), Neg(Succ(x1)), Pos(x0))
67.74/34.82	   new_gcd0Gcd'(Pos(Succ(x1)), Neg(x0)) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(x0, x1))), Pos(Succ(x1)), Neg(x0))
67.74/34.82	   new_gcd0Gcd'(Neg(Succ(Succ(x1))), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, x1, x0, x1))), Neg(Succ(Succ(x1))), Neg(Succ(Succ(x0))))
67.74/34.82	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.82	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(new_primEqInt0(Zero), Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.82	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Zero))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Zero, Zero))), Neg(Succ(Zero)), Neg(Succ(Zero)))
67.74/34.82	
67.74/34.82	The TRS R consists of the following rules:
67.74/34.82	
67.74/34.82	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.82	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.82	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.82	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.82	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.82	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.82	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.82	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.82	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.82	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.82	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.82	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.82	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.82	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.82	   new_error -> error([])
67.74/34.82	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.82	   new_primEqInt2 -> True
67.74/34.82	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.82	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.82	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.82	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.82	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.82	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.82	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.82	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.82	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.82	   new_primMinusNatS1 -> Zero
67.74/34.82	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.82	   new_primEqInt1 -> True
67.74/34.82	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.82	   new_primEqInt0(vuz3260) -> False
67.74/34.82	   new_primEqInt(vuz3250) -> False
67.74/34.82	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.82	
67.74/34.82	The set Q consists of the following terms:
67.74/34.82	
67.74/34.82	   new_rem(Neg(x0), Neg(Zero))
67.74/34.82	   new_primEqInt1
67.74/34.82	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.82	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.82	   new_primMinusNatS1
67.74/34.82	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.82	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.82	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.82	   new_primMinusNatS2(Zero, Zero)
67.74/34.82	   new_error
67.74/34.82	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.82	   new_rem(Pos(x0), Pos(Zero))
67.74/34.82	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.82	   new_primEqInt0(x0)
67.74/34.82	   new_esEs(Pos(Zero))
67.74/34.82	   new_esEs(Pos(Succ(x0)))
67.74/34.82	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.83	   new_primModNatS02(x0, x1)
67.74/34.83	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.83	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.83	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.83	   new_primModNatS1(Zero, x0)
67.74/34.83	   new_primEqInt(x0)
67.74/34.83	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.83	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.83	   new_rem(Pos(x0), Neg(Zero))
67.74/34.83	   new_rem(Neg(x0), Pos(Zero))
67.74/34.83	   new_primMinusNatS0(x0)
67.74/34.83	   new_primEqInt2
67.74/34.83	   new_esEs(Neg(Zero))
67.74/34.83	   new_esEs(Neg(Succ(x0)))
67.74/34.83	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.83	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.83	
67.74/34.83	We have to consider all minimal (P,Q,R)-chains.
67.74/34.83	----------------------------------------
67.74/34.83	
67.74/34.83	(78) TransformationProof (EQUIVALENT)
67.74/34.83	By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(new_primEqInt0(Zero), Neg(Succ(Succ(x0))), Neg(Succ(Zero))) at position [0] we obtained the following new rules [LPAR04]:
67.74/34.83	
67.74/34.83	   (new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero))),new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero))))
67.74/34.83	
67.74/34.83	
67.74/34.83	----------------------------------------
67.74/34.83	
67.74/34.83	(79)
67.74/34.83	Obligation:
67.74/34.83	Q DP problem:
67.74/34.83	The TRS P consists of the following rules:
67.74/34.83	
67.74/34.83	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.83	   new_gcd0Gcd'(Pos(Succ(x1)), Pos(x0)) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(x0, x1))), Pos(Succ(x1)), Pos(x0))
67.74/34.83	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.83	   new_gcd0Gcd'(Neg(Succ(x1)), Pos(x0)) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(x0, x1))), Neg(Succ(x1)), Pos(x0))
67.74/34.83	   new_gcd0Gcd'(Pos(Succ(x1)), Neg(x0)) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(x0, x1))), Pos(Succ(x1)), Neg(x0))
67.74/34.83	   new_gcd0Gcd'(Neg(Succ(Succ(x1))), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, x1, x0, x1))), Neg(Succ(Succ(x1))), Neg(Succ(Succ(x0))))
67.74/34.83	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.83	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Zero))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Zero, Zero))), Neg(Succ(Zero)), Neg(Succ(Zero)))
67.74/34.83	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.83	
67.74/34.83	The TRS R consists of the following rules:
67.74/34.83	
67.74/34.83	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.83	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.83	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.83	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.83	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.83	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.83	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.83	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.83	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.83	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.83	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.83	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.83	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.83	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.83	   new_error -> error([])
67.74/34.83	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.83	   new_primEqInt2 -> True
67.74/34.83	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.83	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.83	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.83	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.83	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.83	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.83	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.83	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.83	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.83	   new_primMinusNatS1 -> Zero
67.74/34.83	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.83	   new_primEqInt1 -> True
67.74/34.83	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.83	   new_primEqInt0(vuz3260) -> False
67.74/34.83	   new_primEqInt(vuz3250) -> False
67.74/34.83	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.83	
67.74/34.83	The set Q consists of the following terms:
67.74/34.83	
67.74/34.83	   new_rem(Neg(x0), Neg(Zero))
67.74/34.83	   new_primEqInt1
67.74/34.83	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.83	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.83	   new_primMinusNatS1
67.74/34.83	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.83	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.83	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.83	   new_primMinusNatS2(Zero, Zero)
67.74/34.83	   new_error
67.74/34.83	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.83	   new_rem(Pos(x0), Pos(Zero))
67.74/34.83	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.83	   new_primEqInt0(x0)
67.74/34.83	   new_esEs(Pos(Zero))
67.74/34.83	   new_esEs(Pos(Succ(x0)))
67.74/34.83	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.83	   new_primModNatS02(x0, x1)
67.74/34.83	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.83	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.83	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.83	   new_primModNatS1(Zero, x0)
67.74/34.83	   new_primEqInt(x0)
67.74/34.83	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.83	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.83	   new_rem(Pos(x0), Neg(Zero))
67.74/34.83	   new_rem(Neg(x0), Pos(Zero))
67.74/34.83	   new_primMinusNatS0(x0)
67.74/34.83	   new_primEqInt2
67.74/34.83	   new_esEs(Neg(Zero))
67.74/34.83	   new_esEs(Neg(Succ(x0)))
67.74/34.83	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.83	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.83	
67.74/34.83	We have to consider all minimal (P,Q,R)-chains.
67.74/34.83	----------------------------------------
67.74/34.83	
67.74/34.83	(80) TransformationProof (EQUIVALENT)
67.74/34.83	By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Zero))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Zero, Zero))), Neg(Succ(Zero)), Neg(Succ(Zero))) at position [0,0,0] we obtained the following new rules [LPAR04]:
67.74/34.83	
67.74/34.83	   (new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Zero))) -> new_gcd0Gcd'1(new_esEs(Neg(Zero)), Neg(Succ(Zero)), Neg(Succ(Zero))),new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Zero))) -> new_gcd0Gcd'1(new_esEs(Neg(Zero)), Neg(Succ(Zero)), Neg(Succ(Zero))))
67.74/34.83	
67.74/34.83	
67.74/34.83	----------------------------------------
67.74/34.83	
67.74/34.83	(81)
67.74/34.83	Obligation:
67.74/34.83	Q DP problem:
67.74/34.83	The TRS P consists of the following rules:
67.74/34.83	
67.74/34.83	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.83	   new_gcd0Gcd'(Pos(Succ(x1)), Pos(x0)) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(x0, x1))), Pos(Succ(x1)), Pos(x0))
67.74/34.83	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.83	   new_gcd0Gcd'(Neg(Succ(x1)), Pos(x0)) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(x0, x1))), Neg(Succ(x1)), Pos(x0))
67.74/34.83	   new_gcd0Gcd'(Pos(Succ(x1)), Neg(x0)) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(x0, x1))), Pos(Succ(x1)), Neg(x0))
67.74/34.83	   new_gcd0Gcd'(Neg(Succ(Succ(x1))), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, x1, x0, x1))), Neg(Succ(Succ(x1))), Neg(Succ(Succ(x0))))
67.74/34.83	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.83	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.83	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Zero))) -> new_gcd0Gcd'1(new_esEs(Neg(Zero)), Neg(Succ(Zero)), Neg(Succ(Zero)))
67.74/34.83	
67.74/34.83	The TRS R consists of the following rules:
67.74/34.83	
67.74/34.83	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.83	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.83	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.83	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.83	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.83	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.83	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.83	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.83	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.83	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.83	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.83	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.83	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.83	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.83	   new_error -> error([])
67.74/34.83	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.83	   new_primEqInt2 -> True
67.74/34.83	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.83	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.83	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.83	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.83	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.83	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.83	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.83	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.83	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.83	   new_primMinusNatS1 -> Zero
67.74/34.83	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.83	   new_primEqInt1 -> True
67.74/34.83	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.83	   new_primEqInt0(vuz3260) -> False
67.74/34.83	   new_primEqInt(vuz3250) -> False
67.74/34.83	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.83	
67.74/34.83	The set Q consists of the following terms:
67.74/34.83	
67.74/34.83	   new_rem(Neg(x0), Neg(Zero))
67.74/34.83	   new_primEqInt1
67.74/34.83	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.83	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.83	   new_primMinusNatS1
67.74/34.83	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.83	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.83	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.83	   new_primMinusNatS2(Zero, Zero)
67.74/34.83	   new_error
67.74/34.83	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.83	   new_rem(Pos(x0), Pos(Zero))
67.74/34.83	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.83	   new_primEqInt0(x0)
67.74/34.83	   new_esEs(Pos(Zero))
67.74/34.83	   new_esEs(Pos(Succ(x0)))
67.74/34.83	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.83	   new_primModNatS02(x0, x1)
67.74/34.83	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.83	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.83	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.83	   new_primModNatS1(Zero, x0)
67.74/34.83	   new_primEqInt(x0)
67.74/34.83	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.83	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.83	   new_rem(Pos(x0), Neg(Zero))
67.74/34.83	   new_rem(Neg(x0), Pos(Zero))
67.74/34.83	   new_primMinusNatS0(x0)
67.74/34.83	   new_primEqInt2
67.74/34.83	   new_esEs(Neg(Zero))
67.74/34.83	   new_esEs(Neg(Succ(x0)))
67.74/34.83	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.83	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.83	
67.74/34.83	We have to consider all minimal (P,Q,R)-chains.
67.74/34.83	----------------------------------------
67.74/34.83	
67.74/34.83	(82) DependencyGraphProof (EQUIVALENT)
67.74/34.83	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
67.74/34.83	----------------------------------------
67.74/34.83	
67.74/34.83	(83)
67.74/34.83	Obligation:
67.74/34.83	Q DP problem:
67.74/34.83	The TRS P consists of the following rules:
67.74/34.83	
67.74/34.83	   new_gcd0Gcd'(Pos(Succ(x1)), Pos(x0)) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(x0, x1))), Pos(Succ(x1)), Pos(x0))
67.74/34.83	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.83	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.83	   new_gcd0Gcd'(Neg(Succ(x1)), Pos(x0)) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(x0, x1))), Neg(Succ(x1)), Pos(x0))
67.74/34.83	   new_gcd0Gcd'(Pos(Succ(x1)), Neg(x0)) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(x0, x1))), Pos(Succ(x1)), Neg(x0))
67.74/34.83	   new_gcd0Gcd'(Neg(Succ(Succ(x1))), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, x1, x0, x1))), Neg(Succ(Succ(x1))), Neg(Succ(Succ(x0))))
67.74/34.83	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.83	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.83	
67.74/34.83	The TRS R consists of the following rules:
67.74/34.83	
67.74/34.83	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.83	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.83	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.83	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.83	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.83	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.83	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.83	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.83	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.83	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.83	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.83	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.83	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.83	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.83	   new_error -> error([])
67.74/34.83	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.83	   new_primEqInt2 -> True
67.74/34.83	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.83	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.83	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.83	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.83	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.83	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.83	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.83	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.83	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.83	   new_primMinusNatS1 -> Zero
67.74/34.83	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.83	   new_primEqInt1 -> True
67.74/34.83	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.83	   new_primEqInt0(vuz3260) -> False
67.74/34.83	   new_primEqInt(vuz3250) -> False
67.74/34.83	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.83	
67.74/34.83	The set Q consists of the following terms:
67.74/34.83	
67.74/34.83	   new_rem(Neg(x0), Neg(Zero))
67.74/34.83	   new_primEqInt1
67.74/34.83	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.83	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.83	   new_primMinusNatS1
67.74/34.83	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.83	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.83	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.83	   new_primMinusNatS2(Zero, Zero)
67.74/34.83	   new_error
67.74/34.83	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.83	   new_rem(Pos(x0), Pos(Zero))
67.74/34.83	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.83	   new_primEqInt0(x0)
67.74/34.83	   new_esEs(Pos(Zero))
67.74/34.83	   new_esEs(Pos(Succ(x0)))
67.74/34.83	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.83	   new_primModNatS02(x0, x1)
67.74/34.83	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.83	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.83	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.83	   new_primModNatS1(Zero, x0)
67.74/34.83	   new_primEqInt(x0)
67.74/34.83	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.83	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.83	   new_rem(Pos(x0), Neg(Zero))
67.74/34.83	   new_rem(Neg(x0), Pos(Zero))
67.74/34.83	   new_primMinusNatS0(x0)
67.74/34.83	   new_primEqInt2
67.74/34.83	   new_esEs(Neg(Zero))
67.74/34.83	   new_esEs(Neg(Succ(x0)))
67.74/34.83	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.83	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.83	
67.74/34.83	We have to consider all minimal (P,Q,R)-chains.
67.74/34.83	----------------------------------------
67.74/34.83	
67.74/34.83	(84) TransformationProof (EQUIVALENT)
67.74/34.83	By narrowing [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(x1)), Pos(x0)) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(x0, x1))), Pos(Succ(x1)), Pos(x0)) at position [0] we obtained the following new rules [LPAR04]:
67.74/34.83	
67.74/34.83	   (new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS0(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(x0)))),new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS0(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(x0)))))
67.74/34.83	   (new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(new_esEs(Pos(Succ(Zero))), Pos(Succ(Succ(x0))), Pos(Succ(Zero))),new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(new_esEs(Pos(Succ(Zero))), Pos(Succ(Succ(x0))), Pos(Succ(Zero))))
67.74/34.83	   (new_gcd0Gcd'(Pos(Succ(Succ(x1))), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, x1, x0, x1))), Pos(Succ(Succ(x1))), Pos(Succ(Succ(x0)))),new_gcd0Gcd'(Pos(Succ(Succ(x1))), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, x1, x0, x1))), Pos(Succ(Succ(x1))), Pos(Succ(Succ(x0)))))
67.74/34.83	   (new_gcd0Gcd'(Pos(Succ(x0)), Pos(Zero)) -> new_gcd0Gcd'1(new_esEs(Pos(Zero)), Pos(Succ(x0)), Pos(Zero)),new_gcd0Gcd'(Pos(Succ(x0)), Pos(Zero)) -> new_gcd0Gcd'1(new_esEs(Pos(Zero)), Pos(Succ(x0)), Pos(Zero)))
67.74/34.83	   (new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Zero))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS1, Zero))), Pos(Succ(Zero)), Pos(Succ(Zero))),new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Zero))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS1, Zero))), Pos(Succ(Zero)), Pos(Succ(Zero))))
67.74/34.83	
67.74/34.83	
67.74/34.83	----------------------------------------
67.74/34.83	
67.74/34.83	(85)
67.74/34.83	Obligation:
67.74/34.83	Q DP problem:
67.74/34.83	The TRS P consists of the following rules:
67.74/34.83	
67.74/34.83	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.83	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.83	   new_gcd0Gcd'(Neg(Succ(x1)), Pos(x0)) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(x0, x1))), Neg(Succ(x1)), Pos(x0))
67.74/34.83	   new_gcd0Gcd'(Pos(Succ(x1)), Neg(x0)) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(x0, x1))), Pos(Succ(x1)), Neg(x0))
67.74/34.83	   new_gcd0Gcd'(Neg(Succ(Succ(x1))), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, x1, x0, x1))), Neg(Succ(Succ(x1))), Neg(Succ(Succ(x0))))
67.74/34.83	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.83	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.83	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS0(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.83	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(new_esEs(Pos(Succ(Zero))), Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.83	   new_gcd0Gcd'(Pos(Succ(Succ(x1))), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, x1, x0, x1))), Pos(Succ(Succ(x1))), Pos(Succ(Succ(x0))))
67.74/34.83	   new_gcd0Gcd'(Pos(Succ(x0)), Pos(Zero)) -> new_gcd0Gcd'1(new_esEs(Pos(Zero)), Pos(Succ(x0)), Pos(Zero))
67.74/34.83	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Zero))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS1, Zero))), Pos(Succ(Zero)), Pos(Succ(Zero)))
67.74/34.83	
67.74/34.83	The TRS R consists of the following rules:
67.74/34.83	
67.74/34.83	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.83	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.83	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.83	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.83	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.83	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.83	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.83	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.83	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.83	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.83	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.83	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.83	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.83	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.83	   new_error -> error([])
67.74/34.83	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.83	   new_primEqInt2 -> True
67.74/34.83	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.83	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.83	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.83	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.83	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.83	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.83	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.83	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.83	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.83	   new_primMinusNatS1 -> Zero
67.74/34.83	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.83	   new_primEqInt1 -> True
67.74/34.83	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.83	   new_primEqInt0(vuz3260) -> False
67.74/34.83	   new_primEqInt(vuz3250) -> False
67.74/34.83	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.83	
67.74/34.83	The set Q consists of the following terms:
67.74/34.83	
67.74/34.83	   new_rem(Neg(x0), Neg(Zero))
67.74/34.83	   new_primEqInt1
67.74/34.83	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.83	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.83	   new_primMinusNatS1
67.74/34.83	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.83	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.83	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.83	   new_primMinusNatS2(Zero, Zero)
67.74/34.83	   new_error
67.74/34.83	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.83	   new_rem(Pos(x0), Pos(Zero))
67.74/34.83	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.83	   new_primEqInt0(x0)
67.74/34.83	   new_esEs(Pos(Zero))
67.74/34.83	   new_esEs(Pos(Succ(x0)))
67.74/34.83	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.83	   new_primModNatS02(x0, x1)
67.74/34.83	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.83	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.83	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.83	   new_primModNatS1(Zero, x0)
67.74/34.83	   new_primEqInt(x0)
67.74/34.83	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.83	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.83	   new_rem(Pos(x0), Neg(Zero))
67.74/34.83	   new_rem(Neg(x0), Pos(Zero))
67.74/34.83	   new_primMinusNatS0(x0)
67.74/34.83	   new_primEqInt2
67.74/34.83	   new_esEs(Neg(Zero))
67.74/34.83	   new_esEs(Neg(Succ(x0)))
67.74/34.83	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.83	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.83	
67.74/34.83	We have to consider all minimal (P,Q,R)-chains.
67.74/34.83	----------------------------------------
67.74/34.83	
67.74/34.83	(86) DependencyGraphProof (EQUIVALENT)
67.74/34.83	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
67.74/34.83	----------------------------------------
67.74/34.83	
67.74/34.83	(87)
67.74/34.83	Obligation:
67.74/34.83	Q DP problem:
67.74/34.83	The TRS P consists of the following rules:
67.74/34.83	
67.74/34.83	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.83	   new_gcd0Gcd'(Neg(Succ(x1)), Pos(x0)) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(x0, x1))), Neg(Succ(x1)), Pos(x0))
67.74/34.83	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.83	   new_gcd0Gcd'(Pos(Succ(x1)), Neg(x0)) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(x0, x1))), Pos(Succ(x1)), Neg(x0))
67.74/34.83	   new_gcd0Gcd'(Neg(Succ(Succ(x1))), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, x1, x0, x1))), Neg(Succ(Succ(x1))), Neg(Succ(Succ(x0))))
67.74/34.83	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.83	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.83	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS0(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.83	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(new_esEs(Pos(Succ(Zero))), Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.83	   new_gcd0Gcd'(Pos(Succ(Succ(x1))), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, x1, x0, x1))), Pos(Succ(Succ(x1))), Pos(Succ(Succ(x0))))
67.74/34.83	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Zero))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS1, Zero))), Pos(Succ(Zero)), Pos(Succ(Zero)))
67.74/34.83	
67.74/34.83	The TRS R consists of the following rules:
67.74/34.83	
67.74/34.83	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.83	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.83	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.83	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.83	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.83	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.83	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.83	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.83	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.83	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.83	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.83	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.83	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.83	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.83	   new_error -> error([])
67.74/34.83	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.83	   new_primEqInt2 -> True
67.74/34.83	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.83	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.83	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.83	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.83	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.83	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.83	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.83	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.83	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.83	   new_primMinusNatS1 -> Zero
67.74/34.83	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.83	   new_primEqInt1 -> True
67.74/34.83	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.83	   new_primEqInt0(vuz3260) -> False
67.74/34.83	   new_primEqInt(vuz3250) -> False
67.74/34.83	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.83	
67.74/34.83	The set Q consists of the following terms:
67.74/34.83	
67.74/34.83	   new_rem(Neg(x0), Neg(Zero))
67.74/34.83	   new_primEqInt1
67.74/34.83	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.83	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.83	   new_primMinusNatS1
67.74/34.83	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.83	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.83	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.83	   new_primMinusNatS2(Zero, Zero)
67.74/34.83	   new_error
67.74/34.83	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.83	   new_rem(Pos(x0), Pos(Zero))
67.74/34.83	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.83	   new_primEqInt0(x0)
67.74/34.83	   new_esEs(Pos(Zero))
67.74/34.83	   new_esEs(Pos(Succ(x0)))
67.74/34.83	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.83	   new_primModNatS02(x0, x1)
67.74/34.83	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.83	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.83	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.83	   new_primModNatS1(Zero, x0)
67.74/34.83	   new_primEqInt(x0)
67.74/34.83	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.83	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.83	   new_rem(Pos(x0), Neg(Zero))
67.74/34.83	   new_rem(Neg(x0), Pos(Zero))
67.74/34.83	   new_primMinusNatS0(x0)
67.74/34.83	   new_primEqInt2
67.74/34.83	   new_esEs(Neg(Zero))
67.74/34.83	   new_esEs(Neg(Succ(x0)))
67.74/34.83	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.83	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.83	
67.74/34.83	We have to consider all minimal (P,Q,R)-chains.
67.74/34.83	----------------------------------------
67.74/34.83	
67.74/34.83	(88) TransformationProof (EQUIVALENT)
67.74/34.83	By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS0(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(x0)))) at position [0,0,0,0] we obtained the following new rules [LPAR04]:
67.74/34.83	
67.74/34.83	   (new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(x0)))),new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(x0)))))
67.74/34.83	
67.74/34.83	
67.74/34.83	----------------------------------------
67.74/34.83	
67.74/34.83	(89)
67.74/34.83	Obligation:
67.74/34.83	Q DP problem:
67.74/34.83	The TRS P consists of the following rules:
67.74/34.83	
67.74/34.83	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.83	   new_gcd0Gcd'(Neg(Succ(x1)), Pos(x0)) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(x0, x1))), Neg(Succ(x1)), Pos(x0))
67.74/34.83	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.83	   new_gcd0Gcd'(Pos(Succ(x1)), Neg(x0)) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(x0, x1))), Pos(Succ(x1)), Neg(x0))
67.74/34.83	   new_gcd0Gcd'(Neg(Succ(Succ(x1))), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, x1, x0, x1))), Neg(Succ(Succ(x1))), Neg(Succ(Succ(x0))))
67.74/34.83	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.83	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.83	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(new_esEs(Pos(Succ(Zero))), Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.83	   new_gcd0Gcd'(Pos(Succ(Succ(x1))), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, x1, x0, x1))), Pos(Succ(Succ(x1))), Pos(Succ(Succ(x0))))
67.74/34.83	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Zero))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS1, Zero))), Pos(Succ(Zero)), Pos(Succ(Zero)))
67.74/34.83	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.83	
67.74/34.83	The TRS R consists of the following rules:
67.74/34.83	
67.74/34.83	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.83	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.83	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.83	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.83	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.83	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.83	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.83	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.83	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.83	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.83	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.83	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.83	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.83	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.83	   new_error -> error([])
67.74/34.83	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.83	   new_primEqInt2 -> True
67.74/34.83	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.83	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.83	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.83	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.83	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.83	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.83	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.83	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.83	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.83	   new_primMinusNatS1 -> Zero
67.74/34.83	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.83	   new_primEqInt1 -> True
67.74/34.83	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.83	   new_primEqInt0(vuz3260) -> False
67.74/34.83	   new_primEqInt(vuz3250) -> False
67.74/34.83	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.83	
67.74/34.83	The set Q consists of the following terms:
67.74/34.83	
67.74/34.83	   new_rem(Neg(x0), Neg(Zero))
67.74/34.83	   new_primEqInt1
67.74/34.83	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.83	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.83	   new_primMinusNatS1
67.74/34.83	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.83	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.83	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.83	   new_primMinusNatS2(Zero, Zero)
67.74/34.83	   new_error
67.74/34.83	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.83	   new_rem(Pos(x0), Pos(Zero))
67.74/34.83	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.83	   new_primEqInt0(x0)
67.74/34.83	   new_esEs(Pos(Zero))
67.74/34.83	   new_esEs(Pos(Succ(x0)))
67.74/34.83	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.83	   new_primModNatS02(x0, x1)
67.74/34.83	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.83	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.83	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.83	   new_primModNatS1(Zero, x0)
67.74/34.83	   new_primEqInt(x0)
67.74/34.83	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.83	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.83	   new_rem(Pos(x0), Neg(Zero))
67.74/34.83	   new_rem(Neg(x0), Pos(Zero))
67.74/34.83	   new_primMinusNatS0(x0)
67.74/34.83	   new_primEqInt2
67.74/34.83	   new_esEs(Neg(Zero))
67.74/34.83	   new_esEs(Neg(Succ(x0)))
67.74/34.83	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.83	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.83	
67.74/34.83	We have to consider all minimal (P,Q,R)-chains.
67.74/34.83	----------------------------------------
67.74/34.83	
67.74/34.83	(90) TransformationProof (EQUIVALENT)
67.74/34.83	By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(new_esEs(Pos(Succ(Zero))), Pos(Succ(Succ(x0))), Pos(Succ(Zero))) at position [0] we obtained the following new rules [LPAR04]:
67.74/34.83	
67.74/34.83	   (new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(new_primEqInt(Zero), Pos(Succ(Succ(x0))), Pos(Succ(Zero))),new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(new_primEqInt(Zero), Pos(Succ(Succ(x0))), Pos(Succ(Zero))))
67.74/34.83	
67.74/34.83	
67.74/34.83	----------------------------------------
67.74/34.83	
67.74/34.83	(91)
67.74/34.83	Obligation:
67.74/34.83	Q DP problem:
67.74/34.83	The TRS P consists of the following rules:
67.74/34.83	
67.74/34.83	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.83	   new_gcd0Gcd'(Neg(Succ(x1)), Pos(x0)) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(x0, x1))), Neg(Succ(x1)), Pos(x0))
67.74/34.83	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.83	   new_gcd0Gcd'(Pos(Succ(x1)), Neg(x0)) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(x0, x1))), Pos(Succ(x1)), Neg(x0))
67.74/34.83	   new_gcd0Gcd'(Neg(Succ(Succ(x1))), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, x1, x0, x1))), Neg(Succ(Succ(x1))), Neg(Succ(Succ(x0))))
67.74/34.83	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.83	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.83	   new_gcd0Gcd'(Pos(Succ(Succ(x1))), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, x1, x0, x1))), Pos(Succ(Succ(x1))), Pos(Succ(Succ(x0))))
67.74/34.83	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Zero))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS1, Zero))), Pos(Succ(Zero)), Pos(Succ(Zero)))
67.74/34.83	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.83	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(new_primEqInt(Zero), Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.83	
67.74/34.83	The TRS R consists of the following rules:
67.74/34.83	
67.74/34.83	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.83	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.83	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.83	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.83	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.83	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.83	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.83	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.83	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.83	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.83	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.83	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.83	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.83	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.83	   new_error -> error([])
67.74/34.83	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.83	   new_primEqInt2 -> True
67.74/34.83	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.83	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.83	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.83	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.83	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.83	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.83	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.83	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.83	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.83	   new_primMinusNatS1 -> Zero
67.74/34.83	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.83	   new_primEqInt1 -> True
67.74/34.83	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.83	   new_primEqInt0(vuz3260) -> False
67.74/34.83	   new_primEqInt(vuz3250) -> False
67.74/34.83	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.83	
67.74/34.83	The set Q consists of the following terms:
67.74/34.83	
67.74/34.83	   new_rem(Neg(x0), Neg(Zero))
67.74/34.83	   new_primEqInt1
67.74/34.83	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.83	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.83	   new_primMinusNatS1
67.74/34.83	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.83	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.83	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.83	   new_primMinusNatS2(Zero, Zero)
67.74/34.83	   new_error
67.74/34.83	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.83	   new_rem(Pos(x0), Pos(Zero))
67.74/34.83	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.83	   new_primEqInt0(x0)
67.74/34.83	   new_esEs(Pos(Zero))
67.74/34.83	   new_esEs(Pos(Succ(x0)))
67.74/34.83	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.83	   new_primModNatS02(x0, x1)
67.74/34.83	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.83	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.83	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.83	   new_primModNatS1(Zero, x0)
67.74/34.83	   new_primEqInt(x0)
67.74/34.83	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.83	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.83	   new_rem(Pos(x0), Neg(Zero))
67.74/34.83	   new_rem(Neg(x0), Pos(Zero))
67.74/34.83	   new_primMinusNatS0(x0)
67.74/34.83	   new_primEqInt2
67.74/34.83	   new_esEs(Neg(Zero))
67.74/34.83	   new_esEs(Neg(Succ(x0)))
67.74/34.83	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.83	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.83	
67.74/34.83	We have to consider all minimal (P,Q,R)-chains.
67.74/34.83	----------------------------------------
67.74/34.83	
67.74/34.83	(92) TransformationProof (EQUIVALENT)
67.74/34.83	By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Zero))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS1, Zero))), Pos(Succ(Zero)), Pos(Succ(Zero))) at position [0,0,0,0] we obtained the following new rules [LPAR04]:
67.74/34.83	
67.74/34.83	   (new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Zero))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Zero, Zero))), Pos(Succ(Zero)), Pos(Succ(Zero))),new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Zero))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Zero, Zero))), Pos(Succ(Zero)), Pos(Succ(Zero))))
67.74/34.83	
67.74/34.83	
67.74/34.83	----------------------------------------
67.74/34.83	
67.74/34.83	(93)
67.74/34.83	Obligation:
67.74/34.83	Q DP problem:
67.74/34.83	The TRS P consists of the following rules:
67.74/34.83	
67.74/34.83	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.83	   new_gcd0Gcd'(Neg(Succ(x1)), Pos(x0)) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(x0, x1))), Neg(Succ(x1)), Pos(x0))
67.74/34.83	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.83	   new_gcd0Gcd'(Pos(Succ(x1)), Neg(x0)) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(x0, x1))), Pos(Succ(x1)), Neg(x0))
67.74/34.83	   new_gcd0Gcd'(Neg(Succ(Succ(x1))), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, x1, x0, x1))), Neg(Succ(Succ(x1))), Neg(Succ(Succ(x0))))
67.74/34.83	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.83	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.83	   new_gcd0Gcd'(Pos(Succ(Succ(x1))), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, x1, x0, x1))), Pos(Succ(Succ(x1))), Pos(Succ(Succ(x0))))
67.74/34.83	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.83	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(new_primEqInt(Zero), Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.83	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Zero))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Zero, Zero))), Pos(Succ(Zero)), Pos(Succ(Zero)))
67.74/34.83	
67.74/34.83	The TRS R consists of the following rules:
67.74/34.83	
67.74/34.83	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.83	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.83	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.83	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.83	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.83	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.83	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.83	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.83	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.83	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.83	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.83	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.83	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.83	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.83	   new_error -> error([])
67.74/34.83	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.83	   new_primEqInt2 -> True
67.74/34.83	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.83	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.83	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.83	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.83	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.83	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.83	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.83	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.83	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.83	   new_primMinusNatS1 -> Zero
67.74/34.83	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.83	   new_primEqInt1 -> True
67.74/34.83	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.83	   new_primEqInt0(vuz3260) -> False
67.74/34.83	   new_primEqInt(vuz3250) -> False
67.74/34.83	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.83	
67.74/34.83	The set Q consists of the following terms:
67.74/34.83	
67.74/34.83	   new_rem(Neg(x0), Neg(Zero))
67.74/34.83	   new_primEqInt1
67.74/34.83	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.83	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.83	   new_primMinusNatS1
67.74/34.83	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.83	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.83	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.83	   new_primMinusNatS2(Zero, Zero)
67.74/34.83	   new_error
67.74/34.83	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.83	   new_rem(Pos(x0), Pos(Zero))
67.74/34.83	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.83	   new_primEqInt0(x0)
67.74/34.83	   new_esEs(Pos(Zero))
67.74/34.83	   new_esEs(Pos(Succ(x0)))
67.74/34.83	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.83	   new_primModNatS02(x0, x1)
67.74/34.83	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.83	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.83	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.83	   new_primModNatS1(Zero, x0)
67.74/34.83	   new_primEqInt(x0)
67.74/34.83	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.83	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.83	   new_rem(Pos(x0), Neg(Zero))
67.74/34.83	   new_rem(Neg(x0), Pos(Zero))
67.74/34.83	   new_primMinusNatS0(x0)
67.74/34.83	   new_primEqInt2
67.74/34.83	   new_esEs(Neg(Zero))
67.74/34.83	   new_esEs(Neg(Succ(x0)))
67.74/34.83	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.83	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.83	
67.74/34.83	We have to consider all minimal (P,Q,R)-chains.
67.74/34.83	----------------------------------------
67.74/34.83	
67.74/34.83	(94) TransformationProof (EQUIVALENT)
67.74/34.83	By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(new_primEqInt(Zero), Pos(Succ(Succ(x0))), Pos(Succ(Zero))) at position [0] we obtained the following new rules [LPAR04]:
67.74/34.83	
67.74/34.83	   (new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero))),new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero))))
67.74/34.83	
67.74/34.83	
67.74/34.83	----------------------------------------
67.74/34.83	
67.74/34.83	(95)
67.74/34.83	Obligation:
67.74/34.83	Q DP problem:
67.74/34.83	The TRS P consists of the following rules:
67.74/34.83	
67.74/34.83	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.83	   new_gcd0Gcd'(Neg(Succ(x1)), Pos(x0)) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(x0, x1))), Neg(Succ(x1)), Pos(x0))
67.74/34.83	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.83	   new_gcd0Gcd'(Pos(Succ(x1)), Neg(x0)) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(x0, x1))), Pos(Succ(x1)), Neg(x0))
67.74/34.83	   new_gcd0Gcd'(Neg(Succ(Succ(x1))), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, x1, x0, x1))), Neg(Succ(Succ(x1))), Neg(Succ(Succ(x0))))
67.74/34.83	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.83	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.83	   new_gcd0Gcd'(Pos(Succ(Succ(x1))), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, x1, x0, x1))), Pos(Succ(Succ(x1))), Pos(Succ(Succ(x0))))
67.74/34.83	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.83	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Zero))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Zero, Zero))), Pos(Succ(Zero)), Pos(Succ(Zero)))
67.74/34.83	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.83	
67.74/34.83	The TRS R consists of the following rules:
67.74/34.83	
67.74/34.83	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.83	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.83	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.83	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.83	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.83	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.83	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.83	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.83	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.83	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.83	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.83	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.83	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.83	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.83	   new_error -> error([])
67.74/34.83	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.83	   new_primEqInt2 -> True
67.74/34.83	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.83	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.83	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.83	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.83	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.83	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.83	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.83	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.83	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.83	   new_primMinusNatS1 -> Zero
67.74/34.83	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.83	   new_primEqInt1 -> True
67.74/34.83	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.83	   new_primEqInt0(vuz3260) -> False
67.74/34.83	   new_primEqInt(vuz3250) -> False
67.74/34.83	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.83	
67.74/34.83	The set Q consists of the following terms:
67.74/34.83	
67.74/34.83	   new_rem(Neg(x0), Neg(Zero))
67.74/34.83	   new_primEqInt1
67.74/34.83	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.83	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.83	   new_primMinusNatS1
67.74/34.83	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.83	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.83	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.83	   new_primMinusNatS2(Zero, Zero)
67.74/34.83	   new_error
67.74/34.83	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.83	   new_rem(Pos(x0), Pos(Zero))
67.74/34.83	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.83	   new_primEqInt0(x0)
67.74/34.83	   new_esEs(Pos(Zero))
67.74/34.83	   new_esEs(Pos(Succ(x0)))
67.74/34.83	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.83	   new_primModNatS02(x0, x1)
67.74/34.83	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.83	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.83	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.83	   new_primModNatS1(Zero, x0)
67.74/34.83	   new_primEqInt(x0)
67.74/34.83	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.83	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.83	   new_rem(Pos(x0), Neg(Zero))
67.74/34.83	   new_rem(Neg(x0), Pos(Zero))
67.74/34.83	   new_primMinusNatS0(x0)
67.74/34.83	   new_primEqInt2
67.74/34.83	   new_esEs(Neg(Zero))
67.74/34.83	   new_esEs(Neg(Succ(x0)))
67.74/34.83	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.83	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.83	
67.74/34.83	We have to consider all minimal (P,Q,R)-chains.
67.74/34.83	----------------------------------------
67.74/34.83	
67.74/34.83	(96) TransformationProof (EQUIVALENT)
67.74/34.83	By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Zero))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Zero, Zero))), Pos(Succ(Zero)), Pos(Succ(Zero))) at position [0,0,0] we obtained the following new rules [LPAR04]:
67.74/34.83	
67.74/34.83	   (new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Zero))) -> new_gcd0Gcd'1(new_esEs(Pos(Zero)), Pos(Succ(Zero)), Pos(Succ(Zero))),new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Zero))) -> new_gcd0Gcd'1(new_esEs(Pos(Zero)), Pos(Succ(Zero)), Pos(Succ(Zero))))
67.74/34.83	
67.74/34.83	
67.74/34.83	----------------------------------------
67.74/34.83	
67.74/34.83	(97)
67.74/34.83	Obligation:
67.74/34.83	Q DP problem:
67.74/34.83	The TRS P consists of the following rules:
67.74/34.83	
67.74/34.83	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.83	   new_gcd0Gcd'(Neg(Succ(x1)), Pos(x0)) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(x0, x1))), Neg(Succ(x1)), Pos(x0))
67.74/34.83	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.83	   new_gcd0Gcd'(Pos(Succ(x1)), Neg(x0)) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(x0, x1))), Pos(Succ(x1)), Neg(x0))
67.74/34.83	   new_gcd0Gcd'(Neg(Succ(Succ(x1))), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, x1, x0, x1))), Neg(Succ(Succ(x1))), Neg(Succ(Succ(x0))))
67.74/34.83	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.83	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.83	   new_gcd0Gcd'(Pos(Succ(Succ(x1))), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, x1, x0, x1))), Pos(Succ(Succ(x1))), Pos(Succ(Succ(x0))))
67.74/34.83	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.83	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.83	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Zero))) -> new_gcd0Gcd'1(new_esEs(Pos(Zero)), Pos(Succ(Zero)), Pos(Succ(Zero)))
67.74/34.83	
67.74/34.83	The TRS R consists of the following rules:
67.74/34.83	
67.74/34.83	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.83	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.83	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.83	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.83	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.83	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.83	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.83	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.83	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.83	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.83	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.83	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.83	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.83	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.83	   new_error -> error([])
67.74/34.83	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.83	   new_primEqInt2 -> True
67.74/34.83	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.83	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.83	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.83	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.83	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.83	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.83	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.83	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.83	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.83	   new_primMinusNatS1 -> Zero
67.74/34.83	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.83	   new_primEqInt1 -> True
67.74/34.83	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.83	   new_primEqInt0(vuz3260) -> False
67.74/34.83	   new_primEqInt(vuz3250) -> False
67.74/34.83	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.83	
67.74/34.83	The set Q consists of the following terms:
67.74/34.83	
67.74/34.83	   new_rem(Neg(x0), Neg(Zero))
67.74/34.83	   new_primEqInt1
67.74/34.83	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.83	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.83	   new_primMinusNatS1
67.74/34.83	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.83	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.83	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.83	   new_primMinusNatS2(Zero, Zero)
67.74/34.83	   new_error
67.74/34.83	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.83	   new_rem(Pos(x0), Pos(Zero))
67.74/34.83	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.83	   new_primEqInt0(x0)
67.74/34.83	   new_esEs(Pos(Zero))
67.74/34.83	   new_esEs(Pos(Succ(x0)))
67.74/34.83	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.83	   new_primModNatS02(x0, x1)
67.74/34.83	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.83	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.83	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.83	   new_primModNatS1(Zero, x0)
67.74/34.83	   new_primEqInt(x0)
67.74/34.83	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.83	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.83	   new_rem(Pos(x0), Neg(Zero))
67.74/34.83	   new_rem(Neg(x0), Pos(Zero))
67.74/34.83	   new_primMinusNatS0(x0)
67.74/34.83	   new_primEqInt2
67.74/34.83	   new_esEs(Neg(Zero))
67.74/34.83	   new_esEs(Neg(Succ(x0)))
67.74/34.83	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.83	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.83	
67.74/34.83	We have to consider all minimal (P,Q,R)-chains.
67.74/34.83	----------------------------------------
67.74/34.83	
67.74/34.83	(98) DependencyGraphProof (EQUIVALENT)
67.74/34.83	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
67.74/34.83	----------------------------------------
67.74/34.83	
67.74/34.83	(99)
67.74/34.83	Obligation:
67.74/34.83	Q DP problem:
67.74/34.83	The TRS P consists of the following rules:
67.74/34.83	
67.74/34.83	   new_gcd0Gcd'(Neg(Succ(x1)), Pos(x0)) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(x0, x1))), Neg(Succ(x1)), Pos(x0))
67.74/34.83	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.83	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.83	   new_gcd0Gcd'(Pos(Succ(x1)), Neg(x0)) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(x0, x1))), Pos(Succ(x1)), Neg(x0))
67.74/34.83	   new_gcd0Gcd'(Neg(Succ(Succ(x1))), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, x1, x0, x1))), Neg(Succ(Succ(x1))), Neg(Succ(Succ(x0))))
67.74/34.83	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.83	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.83	   new_gcd0Gcd'(Pos(Succ(Succ(x1))), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, x1, x0, x1))), Pos(Succ(Succ(x1))), Pos(Succ(Succ(x0))))
67.74/34.83	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.83	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.83	
67.74/34.83	The TRS R consists of the following rules:
67.74/34.83	
67.74/34.83	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.83	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.83	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.83	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.83	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.83	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.83	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.83	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.83	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.83	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.83	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.83	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.83	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.83	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.83	   new_error -> error([])
67.74/34.83	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.83	   new_primEqInt2 -> True
67.74/34.83	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.83	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.83	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.83	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.83	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.83	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.83	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.83	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.83	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.83	   new_primMinusNatS1 -> Zero
67.74/34.83	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.83	   new_primEqInt1 -> True
67.74/34.83	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.83	   new_primEqInt0(vuz3260) -> False
67.74/34.83	   new_primEqInt(vuz3250) -> False
67.74/34.83	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.83	
67.74/34.83	The set Q consists of the following terms:
67.74/34.83	
67.74/34.83	   new_rem(Neg(x0), Neg(Zero))
67.74/34.83	   new_primEqInt1
67.74/34.83	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.83	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.83	   new_primMinusNatS1
67.74/34.83	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.83	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.83	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.83	   new_primMinusNatS2(Zero, Zero)
67.74/34.83	   new_error
67.74/34.83	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.83	   new_rem(Pos(x0), Pos(Zero))
67.74/34.83	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.83	   new_primEqInt0(x0)
67.74/34.83	   new_esEs(Pos(Zero))
67.74/34.83	   new_esEs(Pos(Succ(x0)))
67.74/34.83	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.83	   new_primModNatS02(x0, x1)
67.74/34.83	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.83	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.83	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.83	   new_primModNatS1(Zero, x0)
67.74/34.83	   new_primEqInt(x0)
67.74/34.83	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.83	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.83	   new_rem(Pos(x0), Neg(Zero))
67.74/34.83	   new_rem(Neg(x0), Pos(Zero))
67.74/34.83	   new_primMinusNatS0(x0)
67.74/34.83	   new_primEqInt2
67.74/34.83	   new_esEs(Neg(Zero))
67.74/34.83	   new_esEs(Neg(Succ(x0)))
67.74/34.83	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.83	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.83	
67.74/34.83	We have to consider all minimal (P,Q,R)-chains.
67.74/34.83	----------------------------------------
67.74/34.83	
67.74/34.83	(100) TransformationProof (EQUIVALENT)
67.74/34.83	By narrowing [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(x1)), Pos(x0)) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(x0, x1))), Neg(Succ(x1)), Pos(x0)) at position [0] we obtained the following new rules [LPAR04]:
67.74/34.83	
67.74/34.83	   (new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS0(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(x0)))),new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS0(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(x0)))))
67.74/34.83	   (new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(new_esEs(Pos(Succ(Zero))), Neg(Succ(Succ(x0))), Pos(Succ(Zero))),new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(new_esEs(Pos(Succ(Zero))), Neg(Succ(Succ(x0))), Pos(Succ(Zero))))
67.74/34.83	   (new_gcd0Gcd'(Neg(Succ(Succ(x1))), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, x1, x0, x1))), Neg(Succ(Succ(x1))), Pos(Succ(Succ(x0)))),new_gcd0Gcd'(Neg(Succ(Succ(x1))), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, x1, x0, x1))), Neg(Succ(Succ(x1))), Pos(Succ(Succ(x0)))))
67.74/34.83	   (new_gcd0Gcd'(Neg(Succ(x0)), Pos(Zero)) -> new_gcd0Gcd'1(new_esEs(Pos(Zero)), Neg(Succ(x0)), Pos(Zero)),new_gcd0Gcd'(Neg(Succ(x0)), Pos(Zero)) -> new_gcd0Gcd'1(new_esEs(Pos(Zero)), Neg(Succ(x0)), Pos(Zero)))
67.74/34.83	   (new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Zero))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS1, Zero))), Neg(Succ(Zero)), Pos(Succ(Zero))),new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Zero))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS1, Zero))), Neg(Succ(Zero)), Pos(Succ(Zero))))
67.74/34.83	
67.74/34.83	
67.74/34.83	----------------------------------------
67.74/34.83	
67.74/34.83	(101)
67.74/34.83	Obligation:
67.74/34.83	Q DP problem:
67.74/34.83	The TRS P consists of the following rules:
67.74/34.83	
67.74/34.83	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.83	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.83	   new_gcd0Gcd'(Pos(Succ(x1)), Neg(x0)) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(x0, x1))), Pos(Succ(x1)), Neg(x0))
67.74/34.83	   new_gcd0Gcd'(Neg(Succ(Succ(x1))), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, x1, x0, x1))), Neg(Succ(Succ(x1))), Neg(Succ(Succ(x0))))
67.74/34.83	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.83	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.83	   new_gcd0Gcd'(Pos(Succ(Succ(x1))), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, x1, x0, x1))), Pos(Succ(Succ(x1))), Pos(Succ(Succ(x0))))
67.74/34.83	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.83	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.83	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS0(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.83	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(new_esEs(Pos(Succ(Zero))), Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.83	   new_gcd0Gcd'(Neg(Succ(Succ(x1))), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, x1, x0, x1))), Neg(Succ(Succ(x1))), Pos(Succ(Succ(x0))))
67.74/34.83	   new_gcd0Gcd'(Neg(Succ(x0)), Pos(Zero)) -> new_gcd0Gcd'1(new_esEs(Pos(Zero)), Neg(Succ(x0)), Pos(Zero))
67.74/34.83	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Zero))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS1, Zero))), Neg(Succ(Zero)), Pos(Succ(Zero)))
67.74/34.83	
67.74/34.83	The TRS R consists of the following rules:
67.74/34.83	
67.74/34.83	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.83	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.83	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.83	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.83	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.83	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.83	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.83	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.83	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.83	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.83	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.83	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.83	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.83	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.83	   new_error -> error([])
67.74/34.83	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.83	   new_primEqInt2 -> True
67.74/34.83	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.83	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.83	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.83	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.83	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.83	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.83	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.83	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.83	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.83	   new_primMinusNatS1 -> Zero
67.74/34.83	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.83	   new_primEqInt1 -> True
67.74/34.83	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.83	   new_primEqInt0(vuz3260) -> False
67.74/34.83	   new_primEqInt(vuz3250) -> False
67.74/34.83	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.83	
67.74/34.83	The set Q consists of the following terms:
67.74/34.83	
67.74/34.83	   new_rem(Neg(x0), Neg(Zero))
67.74/34.83	   new_primEqInt1
67.74/34.83	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.83	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.83	   new_primMinusNatS1
67.74/34.83	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.83	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.83	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.83	   new_primMinusNatS2(Zero, Zero)
67.74/34.83	   new_error
67.74/34.83	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.83	   new_rem(Pos(x0), Pos(Zero))
67.74/34.83	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.83	   new_primEqInt0(x0)
67.74/34.83	   new_esEs(Pos(Zero))
67.74/34.83	   new_esEs(Pos(Succ(x0)))
67.74/34.83	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.83	   new_primModNatS02(x0, x1)
67.74/34.83	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.83	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.83	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.83	   new_primModNatS1(Zero, x0)
67.74/34.83	   new_primEqInt(x0)
67.74/34.83	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.83	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.83	   new_rem(Pos(x0), Neg(Zero))
67.74/34.83	   new_rem(Neg(x0), Pos(Zero))
67.74/34.83	   new_primMinusNatS0(x0)
67.74/34.83	   new_primEqInt2
67.74/34.83	   new_esEs(Neg(Zero))
67.74/34.83	   new_esEs(Neg(Succ(x0)))
67.74/34.83	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.83	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.83	
67.74/34.83	We have to consider all minimal (P,Q,R)-chains.
67.74/34.83	----------------------------------------
67.74/34.83	
67.74/34.83	(102) DependencyGraphProof (EQUIVALENT)
67.74/34.83	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
67.74/34.83	----------------------------------------
67.74/34.83	
67.74/34.83	(103)
67.74/34.83	Obligation:
67.74/34.83	Q DP problem:
67.74/34.83	The TRS P consists of the following rules:
67.74/34.83	
67.74/34.83	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.83	   new_gcd0Gcd'(Pos(Succ(x1)), Neg(x0)) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(x0, x1))), Pos(Succ(x1)), Neg(x0))
67.74/34.83	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.83	   new_gcd0Gcd'(Neg(Succ(Succ(x1))), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, x1, x0, x1))), Neg(Succ(Succ(x1))), Neg(Succ(Succ(x0))))
67.74/34.83	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.83	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.83	   new_gcd0Gcd'(Pos(Succ(Succ(x1))), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, x1, x0, x1))), Pos(Succ(Succ(x1))), Pos(Succ(Succ(x0))))
67.74/34.83	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.83	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.83	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS0(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.83	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(new_esEs(Pos(Succ(Zero))), Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.83	   new_gcd0Gcd'(Neg(Succ(Succ(x1))), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, x1, x0, x1))), Neg(Succ(Succ(x1))), Pos(Succ(Succ(x0))))
67.74/34.83	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Zero))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS1, Zero))), Neg(Succ(Zero)), Pos(Succ(Zero)))
67.74/34.83	
67.74/34.83	The TRS R consists of the following rules:
67.74/34.83	
67.74/34.83	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.83	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.83	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.83	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.83	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.83	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.83	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.83	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.83	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.83	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.83	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.83	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.83	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.83	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.83	   new_error -> error([])
67.74/34.83	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.83	   new_primEqInt2 -> True
67.74/34.83	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.83	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.83	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.83	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.83	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.83	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.83	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.83	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.83	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.83	   new_primMinusNatS1 -> Zero
67.74/34.83	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.83	   new_primEqInt1 -> True
67.74/34.83	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.83	   new_primEqInt0(vuz3260) -> False
67.74/34.83	   new_primEqInt(vuz3250) -> False
67.74/34.83	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.83	
67.74/34.83	The set Q consists of the following terms:
67.74/34.83	
67.74/34.83	   new_rem(Neg(x0), Neg(Zero))
67.74/34.83	   new_primEqInt1
67.74/34.83	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.83	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.83	   new_primMinusNatS1
67.74/34.83	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.83	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.83	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.83	   new_primMinusNatS2(Zero, Zero)
67.74/34.83	   new_error
67.74/34.83	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.83	   new_rem(Pos(x0), Pos(Zero))
67.74/34.83	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.83	   new_primEqInt0(x0)
67.74/34.83	   new_esEs(Pos(Zero))
67.74/34.83	   new_esEs(Pos(Succ(x0)))
67.74/34.83	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.83	   new_primModNatS02(x0, x1)
67.74/34.83	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.83	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.83	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.83	   new_primModNatS1(Zero, x0)
67.74/34.83	   new_primEqInt(x0)
67.74/34.83	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.83	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.83	   new_rem(Pos(x0), Neg(Zero))
67.74/34.83	   new_rem(Neg(x0), Pos(Zero))
67.74/34.83	   new_primMinusNatS0(x0)
67.74/34.83	   new_primEqInt2
67.74/34.83	   new_esEs(Neg(Zero))
67.74/34.83	   new_esEs(Neg(Succ(x0)))
67.74/34.83	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.83	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.83	
67.74/34.83	We have to consider all minimal (P,Q,R)-chains.
67.74/34.83	----------------------------------------
67.74/34.83	
67.74/34.83	(104) TransformationProof (EQUIVALENT)
67.74/34.83	By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS0(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(x0)))) at position [0,0,0,0] we obtained the following new rules [LPAR04]:
67.74/34.83	
67.74/34.83	   (new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(x0)))),new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(x0)))))
67.74/34.83	
67.74/34.83	
67.74/34.83	----------------------------------------
67.74/34.83	
67.74/34.83	(105)
67.74/34.83	Obligation:
67.74/34.83	Q DP problem:
67.74/34.83	The TRS P consists of the following rules:
67.74/34.83	
67.74/34.83	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.83	   new_gcd0Gcd'(Pos(Succ(x1)), Neg(x0)) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(x0, x1))), Pos(Succ(x1)), Neg(x0))
67.74/34.83	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.83	   new_gcd0Gcd'(Neg(Succ(Succ(x1))), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, x1, x0, x1))), Neg(Succ(Succ(x1))), Neg(Succ(Succ(x0))))
67.74/34.83	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.83	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.83	   new_gcd0Gcd'(Pos(Succ(Succ(x1))), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, x1, x0, x1))), Pos(Succ(Succ(x1))), Pos(Succ(Succ(x0))))
67.74/34.83	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.83	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.83	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(new_esEs(Pos(Succ(Zero))), Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.83	   new_gcd0Gcd'(Neg(Succ(Succ(x1))), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, x1, x0, x1))), Neg(Succ(Succ(x1))), Pos(Succ(Succ(x0))))
67.74/34.83	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Zero))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS1, Zero))), Neg(Succ(Zero)), Pos(Succ(Zero)))
67.74/34.83	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.83	
67.74/34.83	The TRS R consists of the following rules:
67.74/34.83	
67.74/34.83	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.83	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.83	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.83	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.83	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.83	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.83	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.83	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.83	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.83	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.83	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.83	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.83	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.83	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.83	   new_error -> error([])
67.74/34.83	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.83	   new_primEqInt2 -> True
67.74/34.83	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.83	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.83	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.83	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.83	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.83	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.83	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.83	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.83	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.83	   new_primMinusNatS1 -> Zero
67.74/34.83	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.83	   new_primEqInt1 -> True
67.74/34.83	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.83	   new_primEqInt0(vuz3260) -> False
67.74/34.83	   new_primEqInt(vuz3250) -> False
67.74/34.83	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.83	
67.74/34.83	The set Q consists of the following terms:
67.74/34.83	
67.74/34.83	   new_rem(Neg(x0), Neg(Zero))
67.74/34.83	   new_primEqInt1
67.74/34.83	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.83	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.83	   new_primMinusNatS1
67.74/34.83	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.83	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.83	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.83	   new_primMinusNatS2(Zero, Zero)
67.74/34.83	   new_error
67.74/34.83	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.83	   new_rem(Pos(x0), Pos(Zero))
67.74/34.83	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.83	   new_primEqInt0(x0)
67.74/34.83	   new_esEs(Pos(Zero))
67.74/34.83	   new_esEs(Pos(Succ(x0)))
67.74/34.83	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.83	   new_primModNatS02(x0, x1)
67.74/34.83	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.83	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.83	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.83	   new_primModNatS1(Zero, x0)
67.74/34.83	   new_primEqInt(x0)
67.74/34.83	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.83	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.83	   new_rem(Pos(x0), Neg(Zero))
67.74/34.83	   new_rem(Neg(x0), Pos(Zero))
67.74/34.83	   new_primMinusNatS0(x0)
67.74/34.83	   new_primEqInt2
67.74/34.83	   new_esEs(Neg(Zero))
67.74/34.83	   new_esEs(Neg(Succ(x0)))
67.74/34.83	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.83	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.83	
67.74/34.83	We have to consider all minimal (P,Q,R)-chains.
67.74/34.83	----------------------------------------
67.74/34.83	
67.74/34.83	(106) TransformationProof (EQUIVALENT)
67.74/34.83	By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(new_esEs(Pos(Succ(Zero))), Neg(Succ(Succ(x0))), Pos(Succ(Zero))) at position [0] we obtained the following new rules [LPAR04]:
67.74/34.83	
67.74/34.83	   (new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(new_primEqInt(Zero), Neg(Succ(Succ(x0))), Pos(Succ(Zero))),new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(new_primEqInt(Zero), Neg(Succ(Succ(x0))), Pos(Succ(Zero))))
67.74/34.83	
67.74/34.83	
67.74/34.83	----------------------------------------
67.74/34.83	
67.74/34.83	(107)
67.74/34.83	Obligation:
67.74/34.83	Q DP problem:
67.74/34.83	The TRS P consists of the following rules:
67.74/34.83	
67.74/34.83	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.83	   new_gcd0Gcd'(Pos(Succ(x1)), Neg(x0)) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(x0, x1))), Pos(Succ(x1)), Neg(x0))
67.74/34.83	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.83	   new_gcd0Gcd'(Neg(Succ(Succ(x1))), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, x1, x0, x1))), Neg(Succ(Succ(x1))), Neg(Succ(Succ(x0))))
67.74/34.83	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.83	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.83	   new_gcd0Gcd'(Pos(Succ(Succ(x1))), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, x1, x0, x1))), Pos(Succ(Succ(x1))), Pos(Succ(Succ(x0))))
67.74/34.83	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.83	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.83	   new_gcd0Gcd'(Neg(Succ(Succ(x1))), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, x1, x0, x1))), Neg(Succ(Succ(x1))), Pos(Succ(Succ(x0))))
67.74/34.83	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Zero))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS1, Zero))), Neg(Succ(Zero)), Pos(Succ(Zero)))
67.74/34.83	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.83	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(new_primEqInt(Zero), Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.83	
67.74/34.83	The TRS R consists of the following rules:
67.74/34.83	
67.74/34.83	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.83	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.83	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.83	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.83	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.83	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.83	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.83	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.83	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.83	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.83	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.83	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.83	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.83	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.83	   new_error -> error([])
67.74/34.83	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.83	   new_primEqInt2 -> True
67.74/34.83	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.83	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.83	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.83	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.83	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.83	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.83	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.83	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.83	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.83	   new_primMinusNatS1 -> Zero
67.74/34.83	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.83	   new_primEqInt1 -> True
67.74/34.83	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.83	   new_primEqInt0(vuz3260) -> False
67.74/34.83	   new_primEqInt(vuz3250) -> False
67.74/34.83	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.83	
67.74/34.83	The set Q consists of the following terms:
67.74/34.83	
67.74/34.83	   new_rem(Neg(x0), Neg(Zero))
67.74/34.83	   new_primEqInt1
67.74/34.83	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.83	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.83	   new_primMinusNatS1
67.74/34.83	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.83	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.83	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.83	   new_primMinusNatS2(Zero, Zero)
67.74/34.83	   new_error
67.74/34.83	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.83	   new_rem(Pos(x0), Pos(Zero))
67.74/34.83	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.83	   new_primEqInt0(x0)
67.74/34.83	   new_esEs(Pos(Zero))
67.74/34.83	   new_esEs(Pos(Succ(x0)))
67.74/34.83	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.83	   new_primModNatS02(x0, x1)
67.74/34.83	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.83	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.83	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.83	   new_primModNatS1(Zero, x0)
67.74/34.83	   new_primEqInt(x0)
67.74/34.83	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.83	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.83	   new_rem(Pos(x0), Neg(Zero))
67.74/34.83	   new_rem(Neg(x0), Pos(Zero))
67.74/34.83	   new_primMinusNatS0(x0)
67.74/34.83	   new_primEqInt2
67.74/34.83	   new_esEs(Neg(Zero))
67.74/34.83	   new_esEs(Neg(Succ(x0)))
67.74/34.83	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.83	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.83	
67.74/34.83	We have to consider all minimal (P,Q,R)-chains.
67.74/34.83	----------------------------------------
67.74/34.83	
67.74/34.83	(108) TransformationProof (EQUIVALENT)
67.74/34.83	By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Zero))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS1, Zero))), Neg(Succ(Zero)), Pos(Succ(Zero))) at position [0,0,0,0] we obtained the following new rules [LPAR04]:
67.74/34.83	
67.74/34.83	   (new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Zero))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Zero, Zero))), Neg(Succ(Zero)), Pos(Succ(Zero))),new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Zero))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Zero, Zero))), Neg(Succ(Zero)), Pos(Succ(Zero))))
67.74/34.83	
67.74/34.83	
67.74/34.83	----------------------------------------
67.74/34.83	
67.74/34.83	(109)
67.74/34.83	Obligation:
67.74/34.83	Q DP problem:
67.74/34.83	The TRS P consists of the following rules:
67.74/34.83	
67.74/34.83	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.83	   new_gcd0Gcd'(Pos(Succ(x1)), Neg(x0)) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(x0, x1))), Pos(Succ(x1)), Neg(x0))
67.74/34.83	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.83	   new_gcd0Gcd'(Neg(Succ(Succ(x1))), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, x1, x0, x1))), Neg(Succ(Succ(x1))), Neg(Succ(Succ(x0))))
67.74/34.83	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.83	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.83	   new_gcd0Gcd'(Pos(Succ(Succ(x1))), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, x1, x0, x1))), Pos(Succ(Succ(x1))), Pos(Succ(Succ(x0))))
67.74/34.83	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.83	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.83	   new_gcd0Gcd'(Neg(Succ(Succ(x1))), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, x1, x0, x1))), Neg(Succ(Succ(x1))), Pos(Succ(Succ(x0))))
67.74/34.83	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.83	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(new_primEqInt(Zero), Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.83	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Zero))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Zero, Zero))), Neg(Succ(Zero)), Pos(Succ(Zero)))
67.74/34.83	
67.74/34.83	The TRS R consists of the following rules:
67.74/34.83	
67.74/34.83	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.83	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.83	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.83	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.83	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.83	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.83	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.83	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.83	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.83	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.83	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.83	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.83	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.83	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.83	   new_error -> error([])
67.74/34.83	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.83	   new_primEqInt2 -> True
67.74/34.83	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.83	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.83	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.83	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.83	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.83	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.83	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.83	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.83	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.83	   new_primMinusNatS1 -> Zero
67.74/34.83	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.83	   new_primEqInt1 -> True
67.74/34.83	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.83	   new_primEqInt0(vuz3260) -> False
67.74/34.83	   new_primEqInt(vuz3250) -> False
67.74/34.83	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.83	
67.74/34.83	The set Q consists of the following terms:
67.74/34.83	
67.74/34.83	   new_rem(Neg(x0), Neg(Zero))
67.74/34.83	   new_primEqInt1
67.74/34.83	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.83	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.83	   new_primMinusNatS1
67.74/34.83	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.83	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.83	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.83	   new_primMinusNatS2(Zero, Zero)
67.74/34.83	   new_error
67.74/34.83	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.83	   new_rem(Pos(x0), Pos(Zero))
67.74/34.83	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.83	   new_primEqInt0(x0)
67.74/34.83	   new_esEs(Pos(Zero))
67.74/34.83	   new_esEs(Pos(Succ(x0)))
67.74/34.83	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.83	   new_primModNatS02(x0, x1)
67.74/34.83	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.83	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.83	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.83	   new_primModNatS1(Zero, x0)
67.74/34.83	   new_primEqInt(x0)
67.74/34.83	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.83	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.83	   new_rem(Pos(x0), Neg(Zero))
67.74/34.83	   new_rem(Neg(x0), Pos(Zero))
67.74/34.83	   new_primMinusNatS0(x0)
67.74/34.83	   new_primEqInt2
67.74/34.83	   new_esEs(Neg(Zero))
67.74/34.83	   new_esEs(Neg(Succ(x0)))
67.74/34.83	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.83	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.83	
67.74/34.83	We have to consider all minimal (P,Q,R)-chains.
67.74/34.83	----------------------------------------
67.74/34.83	
67.74/34.83	(110) TransformationProof (EQUIVALENT)
67.74/34.83	By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(new_primEqInt(Zero), Neg(Succ(Succ(x0))), Pos(Succ(Zero))) at position [0] we obtained the following new rules [LPAR04]:
67.74/34.83	
67.74/34.83	   (new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero))),new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero))))
67.74/34.83	
67.74/34.83	
67.74/34.83	----------------------------------------
67.74/34.83	
67.74/34.83	(111)
67.74/34.83	Obligation:
67.74/34.83	Q DP problem:
67.74/34.83	The TRS P consists of the following rules:
67.74/34.83	
67.74/34.83	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.83	   new_gcd0Gcd'(Pos(Succ(x1)), Neg(x0)) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(x0, x1))), Pos(Succ(x1)), Neg(x0))
67.74/34.83	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.83	   new_gcd0Gcd'(Neg(Succ(Succ(x1))), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, x1, x0, x1))), Neg(Succ(Succ(x1))), Neg(Succ(Succ(x0))))
67.74/34.83	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.83	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.83	   new_gcd0Gcd'(Pos(Succ(Succ(x1))), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, x1, x0, x1))), Pos(Succ(Succ(x1))), Pos(Succ(Succ(x0))))
67.74/34.83	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.83	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.83	   new_gcd0Gcd'(Neg(Succ(Succ(x1))), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, x1, x0, x1))), Neg(Succ(Succ(x1))), Pos(Succ(Succ(x0))))
67.74/34.83	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.83	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Zero))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Zero, Zero))), Neg(Succ(Zero)), Pos(Succ(Zero)))
67.74/34.83	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.83	
67.74/34.83	The TRS R consists of the following rules:
67.74/34.83	
67.74/34.83	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.83	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.83	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.83	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.83	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.83	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.83	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.83	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.83	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.83	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.83	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.83	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.83	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.83	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.83	   new_error -> error([])
67.74/34.83	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.83	   new_primEqInt2 -> True
67.74/34.83	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.83	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.83	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.83	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.83	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.83	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.83	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.83	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.83	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.83	   new_primMinusNatS1 -> Zero
67.74/34.83	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.83	   new_primEqInt1 -> True
67.74/34.83	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.83	   new_primEqInt0(vuz3260) -> False
67.74/34.83	   new_primEqInt(vuz3250) -> False
67.74/34.83	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.83	
67.74/34.83	The set Q consists of the following terms:
67.74/34.83	
67.74/34.83	   new_rem(Neg(x0), Neg(Zero))
67.74/34.83	   new_primEqInt1
67.74/34.83	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.83	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.83	   new_primMinusNatS1
67.74/34.83	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.83	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.83	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.83	   new_primMinusNatS2(Zero, Zero)
67.74/34.83	   new_error
67.74/34.83	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.83	   new_rem(Pos(x0), Pos(Zero))
67.74/34.83	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.83	   new_primEqInt0(x0)
67.74/34.83	   new_esEs(Pos(Zero))
67.74/34.83	   new_esEs(Pos(Succ(x0)))
67.74/34.83	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.83	   new_primModNatS02(x0, x1)
67.74/34.83	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.83	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.83	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.83	   new_primModNatS1(Zero, x0)
67.74/34.83	   new_primEqInt(x0)
67.74/34.83	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.83	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.83	   new_rem(Pos(x0), Neg(Zero))
67.74/34.83	   new_rem(Neg(x0), Pos(Zero))
67.74/34.83	   new_primMinusNatS0(x0)
67.74/34.83	   new_primEqInt2
67.74/34.83	   new_esEs(Neg(Zero))
67.74/34.83	   new_esEs(Neg(Succ(x0)))
67.74/34.83	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.83	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.83	
67.74/34.83	We have to consider all minimal (P,Q,R)-chains.
67.74/34.83	----------------------------------------
67.74/34.83	
67.74/34.83	(112) TransformationProof (EQUIVALENT)
67.74/34.83	By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Zero))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Zero, Zero))), Neg(Succ(Zero)), Pos(Succ(Zero))) at position [0,0,0] we obtained the following new rules [LPAR04]:
67.74/34.83	
67.74/34.83	   (new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Zero))) -> new_gcd0Gcd'1(new_esEs(Pos(Zero)), Neg(Succ(Zero)), Pos(Succ(Zero))),new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Zero))) -> new_gcd0Gcd'1(new_esEs(Pos(Zero)), Neg(Succ(Zero)), Pos(Succ(Zero))))
67.74/34.83	
67.74/34.83	
67.74/34.83	----------------------------------------
67.74/34.83	
67.74/34.83	(113)
67.74/34.83	Obligation:
67.74/34.83	Q DP problem:
67.74/34.83	The TRS P consists of the following rules:
67.74/34.83	
67.74/34.83	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.83	   new_gcd0Gcd'(Pos(Succ(x1)), Neg(x0)) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(x0, x1))), Pos(Succ(x1)), Neg(x0))
67.74/34.83	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.83	   new_gcd0Gcd'(Neg(Succ(Succ(x1))), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, x1, x0, x1))), Neg(Succ(Succ(x1))), Neg(Succ(Succ(x0))))
67.74/34.83	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.83	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.83	   new_gcd0Gcd'(Pos(Succ(Succ(x1))), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, x1, x0, x1))), Pos(Succ(Succ(x1))), Pos(Succ(Succ(x0))))
67.74/34.83	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.83	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.83	   new_gcd0Gcd'(Neg(Succ(Succ(x1))), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, x1, x0, x1))), Neg(Succ(Succ(x1))), Pos(Succ(Succ(x0))))
67.74/34.83	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.83	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.83	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Zero))) -> new_gcd0Gcd'1(new_esEs(Pos(Zero)), Neg(Succ(Zero)), Pos(Succ(Zero)))
67.74/34.83	
67.74/34.83	The TRS R consists of the following rules:
67.74/34.83	
67.74/34.83	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.83	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.83	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.83	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.83	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.83	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.83	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.83	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.83	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.83	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.83	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.83	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.83	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.83	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.83	   new_error -> error([])
67.74/34.83	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.83	   new_primEqInt2 -> True
67.74/34.83	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.83	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.83	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.83	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.83	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.83	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.83	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.83	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.83	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.83	   new_primMinusNatS1 -> Zero
67.74/34.83	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.83	   new_primEqInt1 -> True
67.74/34.83	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.83	   new_primEqInt0(vuz3260) -> False
67.74/34.83	   new_primEqInt(vuz3250) -> False
67.74/34.83	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.83	
67.74/34.83	The set Q consists of the following terms:
67.74/34.83	
67.74/34.83	   new_rem(Neg(x0), Neg(Zero))
67.74/34.83	   new_primEqInt1
67.74/34.83	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.83	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.83	   new_primMinusNatS1
67.74/34.83	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.83	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.83	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.83	   new_primMinusNatS2(Zero, Zero)
67.74/34.83	   new_error
67.74/34.83	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.83	   new_rem(Pos(x0), Pos(Zero))
67.74/34.83	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.83	   new_primEqInt0(x0)
67.74/34.83	   new_esEs(Pos(Zero))
67.74/34.83	   new_esEs(Pos(Succ(x0)))
67.74/34.83	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.83	   new_primModNatS02(x0, x1)
67.74/34.83	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.83	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.83	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.83	   new_primModNatS1(Zero, x0)
67.74/34.83	   new_primEqInt(x0)
67.74/34.83	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.83	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.83	   new_rem(Pos(x0), Neg(Zero))
67.74/34.83	   new_rem(Neg(x0), Pos(Zero))
67.74/34.83	   new_primMinusNatS0(x0)
67.74/34.83	   new_primEqInt2
67.74/34.83	   new_esEs(Neg(Zero))
67.74/34.83	   new_esEs(Neg(Succ(x0)))
67.74/34.83	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.83	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.83	
67.74/34.83	We have to consider all minimal (P,Q,R)-chains.
67.74/34.83	----------------------------------------
67.74/34.83	
67.74/34.83	(114) DependencyGraphProof (EQUIVALENT)
67.74/34.83	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
67.74/34.83	----------------------------------------
67.74/34.83	
67.74/34.83	(115)
67.74/34.83	Obligation:
67.74/34.83	Q DP problem:
67.74/34.83	The TRS P consists of the following rules:
67.74/34.83	
67.74/34.83	   new_gcd0Gcd'(Pos(Succ(x1)), Neg(x0)) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(x0, x1))), Pos(Succ(x1)), Neg(x0))
67.74/34.83	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.83	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.83	   new_gcd0Gcd'(Neg(Succ(Succ(x1))), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, x1, x0, x1))), Neg(Succ(Succ(x1))), Neg(Succ(Succ(x0))))
67.74/34.83	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.83	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.83	   new_gcd0Gcd'(Pos(Succ(Succ(x1))), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, x1, x0, x1))), Pos(Succ(Succ(x1))), Pos(Succ(Succ(x0))))
67.74/34.83	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.83	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.83	   new_gcd0Gcd'(Neg(Succ(Succ(x1))), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, x1, x0, x1))), Neg(Succ(Succ(x1))), Pos(Succ(Succ(x0))))
67.74/34.83	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.83	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.83	
67.74/34.83	The TRS R consists of the following rules:
67.74/34.83	
67.74/34.83	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.83	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.83	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.83	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.83	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.83	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.83	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.83	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.83	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.83	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.83	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.83	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.83	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.83	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.83	   new_error -> error([])
67.74/34.83	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.83	   new_primEqInt2 -> True
67.74/34.83	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.83	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.83	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.83	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.83	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.83	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.83	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.83	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.83	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.83	   new_primMinusNatS1 -> Zero
67.74/34.83	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.83	   new_primEqInt1 -> True
67.74/34.83	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.83	   new_primEqInt0(vuz3260) -> False
67.74/34.83	   new_primEqInt(vuz3250) -> False
67.74/34.83	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.83	
67.74/34.83	The set Q consists of the following terms:
67.74/34.83	
67.74/34.83	   new_rem(Neg(x0), Neg(Zero))
67.74/34.83	   new_primEqInt1
67.74/34.83	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.83	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.83	   new_primMinusNatS1
67.74/34.83	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.83	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.83	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.83	   new_primMinusNatS2(Zero, Zero)
67.74/34.83	   new_error
67.74/34.83	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.83	   new_rem(Pos(x0), Pos(Zero))
67.74/34.83	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.83	   new_primEqInt0(x0)
67.74/34.83	   new_esEs(Pos(Zero))
67.74/34.83	   new_esEs(Pos(Succ(x0)))
67.74/34.83	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.83	   new_primModNatS02(x0, x1)
67.74/34.83	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.83	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.83	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.83	   new_primModNatS1(Zero, x0)
67.74/34.84	   new_primEqInt(x0)
67.74/34.84	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.84	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.84	   new_rem(Pos(x0), Neg(Zero))
67.74/34.84	   new_rem(Neg(x0), Pos(Zero))
67.74/34.84	   new_primMinusNatS0(x0)
67.74/34.84	   new_primEqInt2
67.74/34.84	   new_esEs(Neg(Zero))
67.74/34.84	   new_esEs(Neg(Succ(x0)))
67.74/34.84	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.84	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.84	
67.74/34.84	We have to consider all minimal (P,Q,R)-chains.
67.74/34.84	----------------------------------------
67.74/34.84	
67.74/34.84	(116) TransformationProof (EQUIVALENT)
67.74/34.84	By narrowing [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(x1)), Neg(x0)) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(x0, x1))), Pos(Succ(x1)), Neg(x0)) at position [0] we obtained the following new rules [LPAR04]:
67.74/34.84	
67.74/34.84	   (new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS0(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(x0)))),new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS0(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(x0)))))
67.74/34.84	   (new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(new_esEs(Neg(Succ(Zero))), Pos(Succ(Succ(x0))), Neg(Succ(Zero))),new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(new_esEs(Neg(Succ(Zero))), Pos(Succ(Succ(x0))), Neg(Succ(Zero))))
67.74/34.84	   (new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, x1, x0, x1))), Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0)))),new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, x1, x0, x1))), Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0)))))
67.74/34.84	   (new_gcd0Gcd'(Pos(Succ(x0)), Neg(Zero)) -> new_gcd0Gcd'1(new_esEs(Neg(Zero)), Pos(Succ(x0)), Neg(Zero)),new_gcd0Gcd'(Pos(Succ(x0)), Neg(Zero)) -> new_gcd0Gcd'1(new_esEs(Neg(Zero)), Pos(Succ(x0)), Neg(Zero)))
67.74/34.84	   (new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Zero))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS1, Zero))), Pos(Succ(Zero)), Neg(Succ(Zero))),new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Zero))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS1, Zero))), Pos(Succ(Zero)), Neg(Succ(Zero))))
67.74/34.84	
67.74/34.84	
67.74/34.84	----------------------------------------
67.74/34.84	
67.74/34.84	(117)
67.74/34.84	Obligation:
67.74/34.84	Q DP problem:
67.74/34.84	The TRS P consists of the following rules:
67.74/34.84	
67.74/34.84	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.84	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Succ(x1))), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, x1, x0, x1))), Neg(Succ(Succ(x1))), Neg(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Succ(x1))), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, x1, x0, x1))), Pos(Succ(Succ(x1))), Pos(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Succ(x1))), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, x1, x0, x1))), Neg(Succ(Succ(x1))), Pos(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS0(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(new_esEs(Neg(Succ(Zero))), Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, x1, x0, x1))), Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(x0)), Neg(Zero)) -> new_gcd0Gcd'1(new_esEs(Neg(Zero)), Pos(Succ(x0)), Neg(Zero))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Zero))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS1, Zero))), Pos(Succ(Zero)), Neg(Succ(Zero)))
67.74/34.84	
67.74/34.84	The TRS R consists of the following rules:
67.74/34.84	
67.74/34.84	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.84	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.84	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.84	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.84	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.84	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.84	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.84	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.84	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.84	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.84	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.84	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.84	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.84	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.84	   new_error -> error([])
67.74/34.84	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.84	   new_primEqInt2 -> True
67.74/34.84	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.84	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.84	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.84	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.84	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.84	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.84	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.84	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.84	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.84	   new_primMinusNatS1 -> Zero
67.74/34.84	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.84	   new_primEqInt1 -> True
67.74/34.84	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.84	   new_primEqInt0(vuz3260) -> False
67.74/34.84	   new_primEqInt(vuz3250) -> False
67.74/34.84	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.84	
67.74/34.84	The set Q consists of the following terms:
67.74/34.84	
67.74/34.84	   new_rem(Neg(x0), Neg(Zero))
67.74/34.84	   new_primEqInt1
67.74/34.84	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.84	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.84	   new_primMinusNatS1
67.74/34.84	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.84	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.84	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.84	   new_primMinusNatS2(Zero, Zero)
67.74/34.84	   new_error
67.74/34.84	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.84	   new_rem(Pos(x0), Pos(Zero))
67.74/34.84	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.84	   new_primEqInt0(x0)
67.74/34.84	   new_esEs(Pos(Zero))
67.74/34.84	   new_esEs(Pos(Succ(x0)))
67.74/34.84	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.84	   new_primModNatS02(x0, x1)
67.74/34.84	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.84	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.84	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.84	   new_primModNatS1(Zero, x0)
67.74/34.84	   new_primEqInt(x0)
67.74/34.84	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.84	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.84	   new_rem(Pos(x0), Neg(Zero))
67.74/34.84	   new_rem(Neg(x0), Pos(Zero))
67.74/34.84	   new_primMinusNatS0(x0)
67.74/34.84	   new_primEqInt2
67.74/34.84	   new_esEs(Neg(Zero))
67.74/34.84	   new_esEs(Neg(Succ(x0)))
67.74/34.84	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.84	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.84	
67.74/34.84	We have to consider all minimal (P,Q,R)-chains.
67.74/34.84	----------------------------------------
67.74/34.84	
67.74/34.84	(118) DependencyGraphProof (EQUIVALENT)
67.74/34.84	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
67.74/34.84	----------------------------------------
67.74/34.84	
67.74/34.84	(119)
67.74/34.84	Obligation:
67.74/34.84	Q DP problem:
67.74/34.84	The TRS P consists of the following rules:
67.74/34.84	
67.74/34.84	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Succ(x1))), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, x1, x0, x1))), Neg(Succ(Succ(x1))), Neg(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Succ(x1))), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, x1, x0, x1))), Pos(Succ(Succ(x1))), Pos(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Succ(x1))), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, x1, x0, x1))), Neg(Succ(Succ(x1))), Pos(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS0(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(new_esEs(Neg(Succ(Zero))), Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, x1, x0, x1))), Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Zero))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS1, Zero))), Pos(Succ(Zero)), Neg(Succ(Zero)))
67.74/34.84	
67.74/34.84	The TRS R consists of the following rules:
67.74/34.84	
67.74/34.84	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.84	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.84	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.84	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.84	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.84	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.84	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.84	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.84	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.84	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.84	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.84	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.84	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.84	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.84	   new_error -> error([])
67.74/34.84	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.84	   new_primEqInt2 -> True
67.74/34.84	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.84	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.84	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.84	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.84	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.84	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.84	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.84	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.84	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.84	   new_primMinusNatS1 -> Zero
67.74/34.84	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.84	   new_primEqInt1 -> True
67.74/34.84	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.84	   new_primEqInt0(vuz3260) -> False
67.74/34.84	   new_primEqInt(vuz3250) -> False
67.74/34.84	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.84	
67.74/34.84	The set Q consists of the following terms:
67.74/34.84	
67.74/34.84	   new_rem(Neg(x0), Neg(Zero))
67.74/34.84	   new_primEqInt1
67.74/34.84	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.84	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.84	   new_primMinusNatS1
67.74/34.84	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.84	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.84	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.84	   new_primMinusNatS2(Zero, Zero)
67.74/34.84	   new_error
67.74/34.84	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.84	   new_rem(Pos(x0), Pos(Zero))
67.74/34.84	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.84	   new_primEqInt0(x0)
67.74/34.84	   new_esEs(Pos(Zero))
67.74/34.84	   new_esEs(Pos(Succ(x0)))
67.74/34.84	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.84	   new_primModNatS02(x0, x1)
67.74/34.84	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.84	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.84	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.84	   new_primModNatS1(Zero, x0)
67.74/34.84	   new_primEqInt(x0)
67.74/34.84	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.84	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.84	   new_rem(Pos(x0), Neg(Zero))
67.74/34.84	   new_rem(Neg(x0), Pos(Zero))
67.74/34.84	   new_primMinusNatS0(x0)
67.74/34.84	   new_primEqInt2
67.74/34.84	   new_esEs(Neg(Zero))
67.74/34.84	   new_esEs(Neg(Succ(x0)))
67.74/34.84	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.84	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.84	
67.74/34.84	We have to consider all minimal (P,Q,R)-chains.
67.74/34.84	----------------------------------------
67.74/34.84	
67.74/34.84	(120) TransformationProof (EQUIVALENT)
67.74/34.84	By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS0(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) at position [0,0,0,0] we obtained the following new rules [LPAR04]:
67.74/34.84	
67.74/34.84	   (new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(x0)))),new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(x0)))))
67.74/34.84	
67.74/34.84	
67.74/34.84	----------------------------------------
67.74/34.84	
67.74/34.84	(121)
67.74/34.84	Obligation:
67.74/34.84	Q DP problem:
67.74/34.84	The TRS P consists of the following rules:
67.74/34.84	
67.74/34.84	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Succ(x1))), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, x1, x0, x1))), Neg(Succ(Succ(x1))), Neg(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Succ(x1))), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, x1, x0, x1))), Pos(Succ(Succ(x1))), Pos(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Succ(x1))), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, x1, x0, x1))), Neg(Succ(Succ(x1))), Pos(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(new_esEs(Neg(Succ(Zero))), Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, x1, x0, x1))), Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Zero))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS1, Zero))), Pos(Succ(Zero)), Neg(Succ(Zero)))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.84	
67.74/34.84	The TRS R consists of the following rules:
67.74/34.84	
67.74/34.84	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.84	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.84	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.84	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.84	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.84	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.84	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.84	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.84	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.84	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.84	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.84	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.84	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.84	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.84	   new_error -> error([])
67.74/34.84	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.84	   new_primEqInt2 -> True
67.74/34.84	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.84	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.84	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.84	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.84	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.84	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.84	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.84	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.84	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.84	   new_primMinusNatS1 -> Zero
67.74/34.84	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.84	   new_primEqInt1 -> True
67.74/34.84	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.84	   new_primEqInt0(vuz3260) -> False
67.74/34.84	   new_primEqInt(vuz3250) -> False
67.74/34.84	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.84	
67.74/34.84	The set Q consists of the following terms:
67.74/34.84	
67.74/34.84	   new_rem(Neg(x0), Neg(Zero))
67.74/34.84	   new_primEqInt1
67.74/34.84	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.84	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.84	   new_primMinusNatS1
67.74/34.84	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.84	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.84	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.84	   new_primMinusNatS2(Zero, Zero)
67.74/34.84	   new_error
67.74/34.84	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.84	   new_rem(Pos(x0), Pos(Zero))
67.74/34.84	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.84	   new_primEqInt0(x0)
67.74/34.84	   new_esEs(Pos(Zero))
67.74/34.84	   new_esEs(Pos(Succ(x0)))
67.74/34.84	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.84	   new_primModNatS02(x0, x1)
67.74/34.84	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.84	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.84	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.84	   new_primModNatS1(Zero, x0)
67.74/34.84	   new_primEqInt(x0)
67.74/34.84	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.84	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.84	   new_rem(Pos(x0), Neg(Zero))
67.74/34.84	   new_rem(Neg(x0), Pos(Zero))
67.74/34.84	   new_primMinusNatS0(x0)
67.74/34.84	   new_primEqInt2
67.74/34.84	   new_esEs(Neg(Zero))
67.74/34.84	   new_esEs(Neg(Succ(x0)))
67.74/34.84	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.84	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.84	
67.74/34.84	We have to consider all minimal (P,Q,R)-chains.
67.74/34.84	----------------------------------------
67.74/34.84	
67.74/34.84	(122) TransformationProof (EQUIVALENT)
67.74/34.84	By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(new_esEs(Neg(Succ(Zero))), Pos(Succ(Succ(x0))), Neg(Succ(Zero))) at position [0] we obtained the following new rules [LPAR04]:
67.74/34.84	
67.74/34.84	   (new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(new_primEqInt0(Zero), Pos(Succ(Succ(x0))), Neg(Succ(Zero))),new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(new_primEqInt0(Zero), Pos(Succ(Succ(x0))), Neg(Succ(Zero))))
67.74/34.84	
67.74/34.84	
67.74/34.84	----------------------------------------
67.74/34.84	
67.74/34.84	(123)
67.74/34.84	Obligation:
67.74/34.84	Q DP problem:
67.74/34.84	The TRS P consists of the following rules:
67.74/34.84	
67.74/34.84	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Succ(x1))), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, x1, x0, x1))), Neg(Succ(Succ(x1))), Neg(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Succ(x1))), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, x1, x0, x1))), Pos(Succ(Succ(x1))), Pos(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Succ(x1))), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, x1, x0, x1))), Neg(Succ(Succ(x1))), Pos(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, x1, x0, x1))), Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Zero))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS1, Zero))), Pos(Succ(Zero)), Neg(Succ(Zero)))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(new_primEqInt0(Zero), Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.84	
67.74/34.84	The TRS R consists of the following rules:
67.74/34.84	
67.74/34.84	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.84	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.84	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.84	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.84	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.84	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.84	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.84	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.84	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.84	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.84	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.84	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.84	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.84	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.84	   new_error -> error([])
67.74/34.84	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.84	   new_primEqInt2 -> True
67.74/34.84	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.84	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.84	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.84	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.84	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.84	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.84	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.84	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.84	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.84	   new_primMinusNatS1 -> Zero
67.74/34.84	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.84	   new_primEqInt1 -> True
67.74/34.84	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.84	   new_primEqInt0(vuz3260) -> False
67.74/34.84	   new_primEqInt(vuz3250) -> False
67.74/34.84	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.84	
67.74/34.84	The set Q consists of the following terms:
67.74/34.84	
67.74/34.84	   new_rem(Neg(x0), Neg(Zero))
67.74/34.84	   new_primEqInt1
67.74/34.84	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.84	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.84	   new_primMinusNatS1
67.74/34.84	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.84	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.84	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.84	   new_primMinusNatS2(Zero, Zero)
67.74/34.84	   new_error
67.74/34.84	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.84	   new_rem(Pos(x0), Pos(Zero))
67.74/34.84	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.84	   new_primEqInt0(x0)
67.74/34.84	   new_esEs(Pos(Zero))
67.74/34.84	   new_esEs(Pos(Succ(x0)))
67.74/34.84	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.84	   new_primModNatS02(x0, x1)
67.74/34.84	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.84	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.84	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.84	   new_primModNatS1(Zero, x0)
67.74/34.84	   new_primEqInt(x0)
67.74/34.84	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.84	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.84	   new_rem(Pos(x0), Neg(Zero))
67.74/34.84	   new_rem(Neg(x0), Pos(Zero))
67.74/34.84	   new_primMinusNatS0(x0)
67.74/34.84	   new_primEqInt2
67.74/34.84	   new_esEs(Neg(Zero))
67.74/34.84	   new_esEs(Neg(Succ(x0)))
67.74/34.84	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.84	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.84	
67.74/34.84	We have to consider all minimal (P,Q,R)-chains.
67.74/34.84	----------------------------------------
67.74/34.84	
67.74/34.84	(124) TransformationProof (EQUIVALENT)
67.74/34.84	By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Zero))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS1, Zero))), Pos(Succ(Zero)), Neg(Succ(Zero))) at position [0,0,0,0] we obtained the following new rules [LPAR04]:
67.74/34.84	
67.74/34.84	   (new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Zero))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Zero, Zero))), Pos(Succ(Zero)), Neg(Succ(Zero))),new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Zero))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Zero, Zero))), Pos(Succ(Zero)), Neg(Succ(Zero))))
67.74/34.84	
67.74/34.84	
67.74/34.84	----------------------------------------
67.74/34.84	
67.74/34.84	(125)
67.74/34.84	Obligation:
67.74/34.84	Q DP problem:
67.74/34.84	The TRS P consists of the following rules:
67.74/34.84	
67.74/34.84	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Succ(x1))), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, x1, x0, x1))), Neg(Succ(Succ(x1))), Neg(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Succ(x1))), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, x1, x0, x1))), Pos(Succ(Succ(x1))), Pos(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Succ(x1))), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, x1, x0, x1))), Neg(Succ(Succ(x1))), Pos(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, x1, x0, x1))), Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(new_primEqInt0(Zero), Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Zero))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Zero, Zero))), Pos(Succ(Zero)), Neg(Succ(Zero)))
67.74/34.84	
67.74/34.84	The TRS R consists of the following rules:
67.74/34.84	
67.74/34.84	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.84	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.84	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.84	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.84	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.84	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.84	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.84	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.84	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.84	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.84	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.84	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.84	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.84	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.84	   new_error -> error([])
67.74/34.84	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.84	   new_primEqInt2 -> True
67.74/34.84	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.84	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.84	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.84	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.84	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.84	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.84	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.84	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.84	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.84	   new_primMinusNatS1 -> Zero
67.74/34.84	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.84	   new_primEqInt1 -> True
67.74/34.84	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.84	   new_primEqInt0(vuz3260) -> False
67.74/34.84	   new_primEqInt(vuz3250) -> False
67.74/34.84	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.84	
67.74/34.84	The set Q consists of the following terms:
67.74/34.84	
67.74/34.84	   new_rem(Neg(x0), Neg(Zero))
67.74/34.84	   new_primEqInt1
67.74/34.84	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.84	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.84	   new_primMinusNatS1
67.74/34.84	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.84	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.84	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.84	   new_primMinusNatS2(Zero, Zero)
67.74/34.84	   new_error
67.74/34.84	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.84	   new_rem(Pos(x0), Pos(Zero))
67.74/34.84	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.84	   new_primEqInt0(x0)
67.74/34.84	   new_esEs(Pos(Zero))
67.74/34.84	   new_esEs(Pos(Succ(x0)))
67.74/34.84	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.84	   new_primModNatS02(x0, x1)
67.74/34.84	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.84	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.84	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.84	   new_primModNatS1(Zero, x0)
67.74/34.84	   new_primEqInt(x0)
67.74/34.84	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.84	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.84	   new_rem(Pos(x0), Neg(Zero))
67.74/34.84	   new_rem(Neg(x0), Pos(Zero))
67.74/34.84	   new_primMinusNatS0(x0)
67.74/34.84	   new_primEqInt2
67.74/34.84	   new_esEs(Neg(Zero))
67.74/34.84	   new_esEs(Neg(Succ(x0)))
67.74/34.84	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.84	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.84	
67.74/34.84	We have to consider all minimal (P,Q,R)-chains.
67.74/34.84	----------------------------------------
67.74/34.84	
67.74/34.84	(126) TransformationProof (EQUIVALENT)
67.74/34.84	By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(new_primEqInt0(Zero), Pos(Succ(Succ(x0))), Neg(Succ(Zero))) at position [0] we obtained the following new rules [LPAR04]:
67.74/34.84	
67.74/34.84	   (new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero))),new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero))))
67.74/34.84	
67.74/34.84	
67.74/34.84	----------------------------------------
67.74/34.84	
67.74/34.84	(127)
67.74/34.84	Obligation:
67.74/34.84	Q DP problem:
67.74/34.84	The TRS P consists of the following rules:
67.74/34.84	
67.74/34.84	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Succ(x1))), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, x1, x0, x1))), Neg(Succ(Succ(x1))), Neg(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Succ(x1))), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, x1, x0, x1))), Pos(Succ(Succ(x1))), Pos(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Succ(x1))), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, x1, x0, x1))), Neg(Succ(Succ(x1))), Pos(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, x1, x0, x1))), Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Zero))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Zero, Zero))), Pos(Succ(Zero)), Neg(Succ(Zero)))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.84	
67.74/34.84	The TRS R consists of the following rules:
67.74/34.84	
67.74/34.84	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.84	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.84	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.84	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.84	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.84	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.84	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.84	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.84	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.84	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.84	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.84	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.84	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.84	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.84	   new_error -> error([])
67.74/34.84	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.84	   new_primEqInt2 -> True
67.74/34.84	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.84	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.84	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.84	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.84	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.84	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.84	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.84	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.84	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.84	   new_primMinusNatS1 -> Zero
67.74/34.84	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.84	   new_primEqInt1 -> True
67.74/34.84	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.84	   new_primEqInt0(vuz3260) -> False
67.74/34.84	   new_primEqInt(vuz3250) -> False
67.74/34.84	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.84	
67.74/34.84	The set Q consists of the following terms:
67.74/34.84	
67.74/34.84	   new_rem(Neg(x0), Neg(Zero))
67.74/34.84	   new_primEqInt1
67.74/34.84	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.84	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.84	   new_primMinusNatS1
67.74/34.84	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.84	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.84	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.84	   new_primMinusNatS2(Zero, Zero)
67.74/34.84	   new_error
67.74/34.84	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.84	   new_rem(Pos(x0), Pos(Zero))
67.74/34.84	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.84	   new_primEqInt0(x0)
67.74/34.84	   new_esEs(Pos(Zero))
67.74/34.84	   new_esEs(Pos(Succ(x0)))
67.74/34.84	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.84	   new_primModNatS02(x0, x1)
67.74/34.84	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.84	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.84	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.84	   new_primModNatS1(Zero, x0)
67.74/34.84	   new_primEqInt(x0)
67.74/34.84	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.84	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.84	   new_rem(Pos(x0), Neg(Zero))
67.74/34.84	   new_rem(Neg(x0), Pos(Zero))
67.74/34.84	   new_primMinusNatS0(x0)
67.74/34.84	   new_primEqInt2
67.74/34.84	   new_esEs(Neg(Zero))
67.74/34.84	   new_esEs(Neg(Succ(x0)))
67.74/34.84	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.84	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.84	
67.74/34.84	We have to consider all minimal (P,Q,R)-chains.
67.74/34.84	----------------------------------------
67.74/34.84	
67.74/34.84	(128) TransformationProof (EQUIVALENT)
67.74/34.84	By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Zero))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Zero, Zero))), Pos(Succ(Zero)), Neg(Succ(Zero))) at position [0,0,0] we obtained the following new rules [LPAR04]:
67.74/34.84	
67.74/34.84	   (new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Zero))) -> new_gcd0Gcd'1(new_esEs(Neg(Zero)), Pos(Succ(Zero)), Neg(Succ(Zero))),new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Zero))) -> new_gcd0Gcd'1(new_esEs(Neg(Zero)), Pos(Succ(Zero)), Neg(Succ(Zero))))
67.74/34.84	
67.74/34.84	
67.74/34.84	----------------------------------------
67.74/34.84	
67.74/34.84	(129)
67.74/34.84	Obligation:
67.74/34.84	Q DP problem:
67.74/34.84	The TRS P consists of the following rules:
67.74/34.84	
67.74/34.84	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Succ(x1))), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, x1, x0, x1))), Neg(Succ(Succ(x1))), Neg(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Succ(x1))), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, x1, x0, x1))), Pos(Succ(Succ(x1))), Pos(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Succ(x1))), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, x1, x0, x1))), Neg(Succ(Succ(x1))), Pos(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, x1, x0, x1))), Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Zero))) -> new_gcd0Gcd'1(new_esEs(Neg(Zero)), Pos(Succ(Zero)), Neg(Succ(Zero)))
67.74/34.84	
67.74/34.84	The TRS R consists of the following rules:
67.74/34.84	
67.74/34.84	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.84	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.84	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.84	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.84	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.84	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.84	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.84	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.84	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.84	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.84	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.84	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.84	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.84	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.84	   new_error -> error([])
67.74/34.84	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.84	   new_primEqInt2 -> True
67.74/34.84	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.84	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.84	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.84	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.84	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.84	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.84	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.84	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.84	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.84	   new_primMinusNatS1 -> Zero
67.74/34.84	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.84	   new_primEqInt1 -> True
67.74/34.84	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.84	   new_primEqInt0(vuz3260) -> False
67.74/34.84	   new_primEqInt(vuz3250) -> False
67.74/34.84	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.84	
67.74/34.84	The set Q consists of the following terms:
67.74/34.84	
67.74/34.84	   new_rem(Neg(x0), Neg(Zero))
67.74/34.84	   new_primEqInt1
67.74/34.84	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.84	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.84	   new_primMinusNatS1
67.74/34.84	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.84	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.84	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.84	   new_primMinusNatS2(Zero, Zero)
67.74/34.84	   new_error
67.74/34.84	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.84	   new_rem(Pos(x0), Pos(Zero))
67.74/34.84	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.84	   new_primEqInt0(x0)
67.74/34.84	   new_esEs(Pos(Zero))
67.74/34.84	   new_esEs(Pos(Succ(x0)))
67.74/34.84	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.84	   new_primModNatS02(x0, x1)
67.74/34.84	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.84	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.84	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.84	   new_primModNatS1(Zero, x0)
67.74/34.84	   new_primEqInt(x0)
67.74/34.84	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.84	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.84	   new_rem(Pos(x0), Neg(Zero))
67.74/34.84	   new_rem(Neg(x0), Pos(Zero))
67.74/34.84	   new_primMinusNatS0(x0)
67.74/34.84	   new_primEqInt2
67.74/34.84	   new_esEs(Neg(Zero))
67.74/34.84	   new_esEs(Neg(Succ(x0)))
67.74/34.84	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.84	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.84	
67.74/34.84	We have to consider all minimal (P,Q,R)-chains.
67.74/34.84	----------------------------------------
67.74/34.84	
67.74/34.84	(130) DependencyGraphProof (EQUIVALENT)
67.74/34.84	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
67.74/34.84	----------------------------------------
67.74/34.84	
67.74/34.84	(131)
67.74/34.84	Obligation:
67.74/34.84	Q DP problem:
67.74/34.84	The TRS P consists of the following rules:
67.74/34.84	
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Succ(x1))), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, x1, x0, x1))), Neg(Succ(Succ(x1))), Neg(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.84	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Succ(x1))), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, x1, x0, x1))), Pos(Succ(Succ(x1))), Pos(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Succ(x1))), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, x1, x0, x1))), Neg(Succ(Succ(x1))), Pos(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, x1, x0, x1))), Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.84	
67.74/34.84	The TRS R consists of the following rules:
67.74/34.84	
67.74/34.84	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.84	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.84	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.84	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.84	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.84	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.84	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.84	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.84	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.84	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.84	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.84	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.84	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.84	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.84	   new_error -> error([])
67.74/34.84	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.84	   new_primEqInt2 -> True
67.74/34.84	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.84	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.84	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.84	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.84	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.84	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.84	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.84	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.84	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.84	   new_primMinusNatS1 -> Zero
67.74/34.84	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.84	   new_primEqInt1 -> True
67.74/34.84	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.84	   new_primEqInt0(vuz3260) -> False
67.74/34.84	   new_primEqInt(vuz3250) -> False
67.74/34.84	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.84	
67.74/34.84	The set Q consists of the following terms:
67.74/34.84	
67.74/34.84	   new_rem(Neg(x0), Neg(Zero))
67.74/34.84	   new_primEqInt1
67.74/34.84	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.84	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.84	   new_primMinusNatS1
67.74/34.84	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.84	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.84	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.84	   new_primMinusNatS2(Zero, Zero)
67.74/34.84	   new_error
67.74/34.84	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.84	   new_rem(Pos(x0), Pos(Zero))
67.74/34.84	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.84	   new_primEqInt0(x0)
67.74/34.84	   new_esEs(Pos(Zero))
67.74/34.84	   new_esEs(Pos(Succ(x0)))
67.74/34.84	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.84	   new_primModNatS02(x0, x1)
67.74/34.84	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.84	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.84	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.84	   new_primModNatS1(Zero, x0)
67.74/34.84	   new_primEqInt(x0)
67.74/34.84	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.84	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.84	   new_rem(Pos(x0), Neg(Zero))
67.74/34.84	   new_rem(Neg(x0), Pos(Zero))
67.74/34.84	   new_primMinusNatS0(x0)
67.74/34.84	   new_primEqInt2
67.74/34.84	   new_esEs(Neg(Zero))
67.74/34.84	   new_esEs(Neg(Succ(x0)))
67.74/34.84	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.84	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.84	
67.74/34.84	We have to consider all minimal (P,Q,R)-chains.
67.74/34.84	----------------------------------------
67.74/34.84	
67.74/34.84	(132) TransformationProof (EQUIVALENT)
67.74/34.84	By narrowing [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(x1))), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, x1, x0, x1))), Neg(Succ(Succ(x1))), Neg(Succ(Succ(x0)))) at position [0] we obtained the following new rules [LPAR04]:
67.74/34.84	
67.74/34.84	   (new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))))
67.74/34.84	   (new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Neg(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Neg(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))))
67.74/34.84	   (new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS02(Zero, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))),new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS02(Zero, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))))
67.74/34.84	   (new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS02(Succ(x2), Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))),new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS02(Succ(x2), Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))))
67.74/34.84	
67.74/34.84	
67.74/34.84	----------------------------------------
67.74/34.84	
67.74/34.84	(133)
67.74/34.84	Obligation:
67.74/34.84	Q DP problem:
67.74/34.84	The TRS P consists of the following rules:
67.74/34.84	
67.74/34.84	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.84	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Succ(x1))), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, x1, x0, x1))), Pos(Succ(Succ(x1))), Pos(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Succ(x1))), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, x1, x0, x1))), Neg(Succ(Succ(x1))), Pos(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, x1, x0, x1))), Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Neg(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS02(Zero, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Zero))))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS02(Succ(x2), Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.84	
67.74/34.84	The TRS R consists of the following rules:
67.74/34.84	
67.74/34.84	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.84	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.84	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.84	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.84	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.84	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.84	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.84	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.84	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.84	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.84	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.84	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.84	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.84	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.84	   new_error -> error([])
67.74/34.84	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.84	   new_primEqInt2 -> True
67.74/34.84	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.84	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.84	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.84	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.84	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.84	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.84	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.84	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.84	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.84	   new_primMinusNatS1 -> Zero
67.74/34.84	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.84	   new_primEqInt1 -> True
67.74/34.84	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.84	   new_primEqInt0(vuz3260) -> False
67.74/34.84	   new_primEqInt(vuz3250) -> False
67.74/34.84	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.84	
67.74/34.84	The set Q consists of the following terms:
67.74/34.84	
67.74/34.84	   new_rem(Neg(x0), Neg(Zero))
67.74/34.84	   new_primEqInt1
67.74/34.84	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.84	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.84	   new_primMinusNatS1
67.74/34.84	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.84	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.84	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.84	   new_primMinusNatS2(Zero, Zero)
67.74/34.84	   new_error
67.74/34.84	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.84	   new_rem(Pos(x0), Pos(Zero))
67.74/34.84	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.84	   new_primEqInt0(x0)
67.74/34.84	   new_esEs(Pos(Zero))
67.74/34.84	   new_esEs(Pos(Succ(x0)))
67.74/34.84	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.84	   new_primModNatS02(x0, x1)
67.74/34.84	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.84	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.84	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.84	   new_primModNatS1(Zero, x0)
67.74/34.84	   new_primEqInt(x0)
67.74/34.84	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.84	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.84	   new_rem(Pos(x0), Neg(Zero))
67.74/34.84	   new_rem(Neg(x0), Pos(Zero))
67.74/34.84	   new_primMinusNatS0(x0)
67.74/34.84	   new_primEqInt2
67.74/34.84	   new_esEs(Neg(Zero))
67.74/34.84	   new_esEs(Neg(Succ(x0)))
67.74/34.84	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.84	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.84	
67.74/34.84	We have to consider all minimal (P,Q,R)-chains.
67.74/34.84	----------------------------------------
67.74/34.84	
67.74/34.84	(134) TransformationProof (EQUIVALENT)
67.74/34.84	By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Neg(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) at position [0] we obtained the following new rules [LPAR04]:
67.74/34.84	
67.74/34.84	   (new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_primEqInt0(Succ(Zero)), Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_primEqInt0(Succ(Zero)), Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))))
67.74/34.84	
67.74/34.84	
67.74/34.84	----------------------------------------
67.74/34.84	
67.74/34.84	(135)
67.74/34.84	Obligation:
67.74/34.84	Q DP problem:
67.74/34.84	The TRS P consists of the following rules:
67.74/34.84	
67.74/34.84	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.84	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Succ(x1))), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, x1, x0, x1))), Pos(Succ(Succ(x1))), Pos(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Succ(x1))), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, x1, x0, x1))), Neg(Succ(Succ(x1))), Pos(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, x1, x0, x1))), Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS02(Zero, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Zero))))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS02(Succ(x2), Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_primEqInt0(Succ(Zero)), Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.84	
67.74/34.84	The TRS R consists of the following rules:
67.74/34.84	
67.74/34.84	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.84	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.84	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.84	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.84	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.84	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.84	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.84	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.84	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.84	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.84	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.84	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.84	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.84	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.84	   new_error -> error([])
67.74/34.84	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.84	   new_primEqInt2 -> True
67.74/34.84	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.84	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.84	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.84	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.84	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.84	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.84	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.84	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.84	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.84	   new_primMinusNatS1 -> Zero
67.74/34.84	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.84	   new_primEqInt1 -> True
67.74/34.84	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.84	   new_primEqInt0(vuz3260) -> False
67.74/34.84	   new_primEqInt(vuz3250) -> False
67.74/34.84	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.84	
67.74/34.84	The set Q consists of the following terms:
67.74/34.84	
67.74/34.84	   new_rem(Neg(x0), Neg(Zero))
67.74/34.84	   new_primEqInt1
67.74/34.84	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.84	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.84	   new_primMinusNatS1
67.74/34.84	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.84	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.84	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.84	   new_primMinusNatS2(Zero, Zero)
67.74/34.84	   new_error
67.74/34.84	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.84	   new_rem(Pos(x0), Pos(Zero))
67.74/34.84	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.84	   new_primEqInt0(x0)
67.74/34.84	   new_esEs(Pos(Zero))
67.74/34.84	   new_esEs(Pos(Succ(x0)))
67.74/34.84	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.84	   new_primModNatS02(x0, x1)
67.74/34.84	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.84	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.84	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.84	   new_primModNatS1(Zero, x0)
67.74/34.84	   new_primEqInt(x0)
67.74/34.84	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.84	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.84	   new_rem(Pos(x0), Neg(Zero))
67.74/34.84	   new_rem(Neg(x0), Pos(Zero))
67.74/34.84	   new_primMinusNatS0(x0)
67.74/34.84	   new_primEqInt2
67.74/34.84	   new_esEs(Neg(Zero))
67.74/34.84	   new_esEs(Neg(Succ(x0)))
67.74/34.84	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.84	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.84	
67.74/34.84	We have to consider all minimal (P,Q,R)-chains.
67.74/34.84	----------------------------------------
67.74/34.84	
67.74/34.84	(136) TransformationProof (EQUIVALENT)
67.74/34.84	By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS02(Zero, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) at position [0,0,0] we obtained the following new rules [LPAR04]:
67.74/34.84	
67.74/34.84	   (new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Succ(Zero), Succ(Zero)), Succ(Zero)))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))),new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Succ(Zero), Succ(Zero)), Succ(Zero)))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))))
67.74/34.84	
67.74/34.84	
67.74/34.84	----------------------------------------
67.74/34.84	
67.74/34.84	(137)
67.74/34.84	Obligation:
67.74/34.84	Q DP problem:
67.74/34.84	The TRS P consists of the following rules:
67.74/34.84	
67.74/34.84	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.84	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Succ(x1))), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, x1, x0, x1))), Pos(Succ(Succ(x1))), Pos(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Succ(x1))), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, x1, x0, x1))), Neg(Succ(Succ(x1))), Pos(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, x1, x0, x1))), Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS02(Succ(x2), Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_primEqInt0(Succ(Zero)), Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Succ(Zero), Succ(Zero)), Succ(Zero)))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Zero))))
67.74/34.84	
67.74/34.84	The TRS R consists of the following rules:
67.74/34.84	
67.74/34.84	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.84	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.84	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.84	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.84	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.84	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.84	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.84	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.84	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.84	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.84	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.84	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.84	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.84	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.84	   new_error -> error([])
67.74/34.84	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.84	   new_primEqInt2 -> True
67.74/34.84	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.84	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.84	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.84	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.84	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.84	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.84	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.84	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.84	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.84	   new_primMinusNatS1 -> Zero
67.74/34.84	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.84	   new_primEqInt1 -> True
67.74/34.84	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.84	   new_primEqInt0(vuz3260) -> False
67.74/34.84	   new_primEqInt(vuz3250) -> False
67.74/34.84	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.84	
67.74/34.84	The set Q consists of the following terms:
67.74/34.84	
67.74/34.84	   new_rem(Neg(x0), Neg(Zero))
67.74/34.84	   new_primEqInt1
67.74/34.84	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.84	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.84	   new_primMinusNatS1
67.74/34.84	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.84	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.84	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.84	   new_primMinusNatS2(Zero, Zero)
67.74/34.84	   new_error
67.74/34.84	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.84	   new_rem(Pos(x0), Pos(Zero))
67.74/34.84	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.84	   new_primEqInt0(x0)
67.74/34.84	   new_esEs(Pos(Zero))
67.74/34.84	   new_esEs(Pos(Succ(x0)))
67.74/34.84	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.84	   new_primModNatS02(x0, x1)
67.74/34.84	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.84	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.84	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.84	   new_primModNatS1(Zero, x0)
67.74/34.84	   new_primEqInt(x0)
67.74/34.84	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.84	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.84	   new_rem(Pos(x0), Neg(Zero))
67.74/34.84	   new_rem(Neg(x0), Pos(Zero))
67.74/34.84	   new_primMinusNatS0(x0)
67.74/34.84	   new_primEqInt2
67.74/34.84	   new_esEs(Neg(Zero))
67.74/34.84	   new_esEs(Neg(Succ(x0)))
67.74/34.84	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.84	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.84	
67.74/34.84	We have to consider all minimal (P,Q,R)-chains.
67.74/34.84	----------------------------------------
67.74/34.84	
67.74/34.84	(138) TransformationProof (EQUIVALENT)
67.74/34.84	By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS02(Succ(x2), Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) at position [0,0,0] we obtained the following new rules [LPAR04]:
67.74/34.84	
67.74/34.84	   (new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Succ(Succ(x2)), Succ(Zero)), Succ(Zero)))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))),new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Succ(Succ(x2)), Succ(Zero)), Succ(Zero)))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))))
67.74/34.84	
67.74/34.84	
67.74/34.84	----------------------------------------
67.74/34.84	
67.74/34.84	(139)
67.74/34.84	Obligation:
67.74/34.84	Q DP problem:
67.74/34.84	The TRS P consists of the following rules:
67.74/34.84	
67.74/34.84	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.84	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Succ(x1))), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, x1, x0, x1))), Pos(Succ(Succ(x1))), Pos(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Succ(x1))), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, x1, x0, x1))), Neg(Succ(Succ(x1))), Pos(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, x1, x0, x1))), Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_primEqInt0(Succ(Zero)), Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Succ(Zero), Succ(Zero)), Succ(Zero)))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Zero))))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Succ(Succ(x2)), Succ(Zero)), Succ(Zero)))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.84	
67.74/34.84	The TRS R consists of the following rules:
67.74/34.84	
67.74/34.84	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.84	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.84	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.84	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.84	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.84	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.84	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.84	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.84	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.84	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.84	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.84	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.84	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.84	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.84	   new_error -> error([])
67.74/34.84	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.84	   new_primEqInt2 -> True
67.74/34.84	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.84	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.84	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.84	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.84	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.84	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.84	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.84	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.84	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.84	   new_primMinusNatS1 -> Zero
67.74/34.84	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.84	   new_primEqInt1 -> True
67.74/34.84	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.84	   new_primEqInt0(vuz3260) -> False
67.74/34.84	   new_primEqInt(vuz3250) -> False
67.74/34.84	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.84	
67.74/34.84	The set Q consists of the following terms:
67.74/34.84	
67.74/34.84	   new_rem(Neg(x0), Neg(Zero))
67.74/34.84	   new_primEqInt1
67.74/34.84	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.84	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.84	   new_primMinusNatS1
67.74/34.84	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.84	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.84	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.84	   new_primMinusNatS2(Zero, Zero)
67.74/34.84	   new_error
67.74/34.84	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.84	   new_rem(Pos(x0), Pos(Zero))
67.74/34.84	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.84	   new_primEqInt0(x0)
67.74/34.84	   new_esEs(Pos(Zero))
67.74/34.84	   new_esEs(Pos(Succ(x0)))
67.74/34.84	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.84	   new_primModNatS02(x0, x1)
67.74/34.84	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.84	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.84	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.84	   new_primModNatS1(Zero, x0)
67.74/34.84	   new_primEqInt(x0)
67.74/34.84	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.84	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.84	   new_rem(Pos(x0), Neg(Zero))
67.74/34.84	   new_rem(Neg(x0), Pos(Zero))
67.74/34.84	   new_primMinusNatS0(x0)
67.74/34.84	   new_primEqInt2
67.74/34.84	   new_esEs(Neg(Zero))
67.74/34.84	   new_esEs(Neg(Succ(x0)))
67.74/34.84	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.84	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.84	
67.74/34.84	We have to consider all minimal (P,Q,R)-chains.
67.74/34.84	----------------------------------------
67.74/34.84	
67.74/34.84	(140) TransformationProof (EQUIVALENT)
67.74/34.84	By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_primEqInt0(Succ(Zero)), Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) at position [0] we obtained the following new rules [LPAR04]:
67.74/34.84	
67.74/34.84	   (new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))))
67.74/34.84	
67.74/34.84	
67.74/34.84	----------------------------------------
67.74/34.84	
67.74/34.84	(141)
67.74/34.84	Obligation:
67.74/34.84	Q DP problem:
67.74/34.84	The TRS P consists of the following rules:
67.74/34.84	
67.74/34.84	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.84	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Succ(x1))), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, x1, x0, x1))), Pos(Succ(Succ(x1))), Pos(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Succ(x1))), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, x1, x0, x1))), Neg(Succ(Succ(x1))), Pos(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, x1, x0, x1))), Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Succ(Zero), Succ(Zero)), Succ(Zero)))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Zero))))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Succ(Succ(x2)), Succ(Zero)), Succ(Zero)))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.84	
67.74/34.84	The TRS R consists of the following rules:
67.74/34.84	
67.74/34.84	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.84	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.84	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.84	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.84	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.84	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.84	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.84	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.84	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.84	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.84	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.84	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.84	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.84	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.84	   new_error -> error([])
67.74/34.84	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.84	   new_primEqInt2 -> True
67.74/34.84	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.84	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.84	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.84	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.84	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.84	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.84	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.84	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.84	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.84	   new_primMinusNatS1 -> Zero
67.74/34.84	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.84	   new_primEqInt1 -> True
67.74/34.84	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.84	   new_primEqInt0(vuz3260) -> False
67.74/34.84	   new_primEqInt(vuz3250) -> False
67.74/34.84	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.84	
67.74/34.84	The set Q consists of the following terms:
67.74/34.84	
67.74/34.84	   new_rem(Neg(x0), Neg(Zero))
67.74/34.84	   new_primEqInt1
67.74/34.84	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.84	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.84	   new_primMinusNatS1
67.74/34.84	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.84	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.84	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.84	   new_primMinusNatS2(Zero, Zero)
67.74/34.84	   new_error
67.74/34.84	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.84	   new_rem(Pos(x0), Pos(Zero))
67.74/34.84	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.84	   new_primEqInt0(x0)
67.74/34.84	   new_esEs(Pos(Zero))
67.74/34.84	   new_esEs(Pos(Succ(x0)))
67.74/34.84	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.84	   new_primModNatS02(x0, x1)
67.74/34.84	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.84	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.84	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.84	   new_primModNatS1(Zero, x0)
67.74/34.84	   new_primEqInt(x0)
67.74/34.84	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.84	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.84	   new_rem(Pos(x0), Neg(Zero))
67.74/34.84	   new_rem(Neg(x0), Pos(Zero))
67.74/34.84	   new_primMinusNatS0(x0)
67.74/34.84	   new_primEqInt2
67.74/34.84	   new_esEs(Neg(Zero))
67.74/34.84	   new_esEs(Neg(Succ(x0)))
67.74/34.84	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.84	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.84	
67.74/34.84	We have to consider all minimal (P,Q,R)-chains.
67.74/34.84	----------------------------------------
67.74/34.84	
67.74/34.84	(142) TransformationProof (EQUIVALENT)
67.74/34.84	By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Succ(Zero), Succ(Zero)), Succ(Zero)))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) at position [0,0,0,0] we obtained the following new rules [LPAR04]:
67.74/34.84	
67.74/34.84	   (new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Zero, Zero), Succ(Zero)))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))),new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Zero, Zero), Succ(Zero)))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))))
67.74/34.84	
67.74/34.84	
67.74/34.84	----------------------------------------
67.74/34.84	
67.74/34.84	(143)
67.74/34.84	Obligation:
67.74/34.84	Q DP problem:
67.74/34.84	The TRS P consists of the following rules:
67.74/34.84	
67.74/34.84	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.84	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Succ(x1))), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, x1, x0, x1))), Pos(Succ(Succ(x1))), Pos(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Succ(x1))), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, x1, x0, x1))), Neg(Succ(Succ(x1))), Pos(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, x1, x0, x1))), Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Succ(Succ(x2)), Succ(Zero)), Succ(Zero)))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Zero, Zero), Succ(Zero)))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Zero))))
67.74/34.84	
67.74/34.84	The TRS R consists of the following rules:
67.74/34.84	
67.74/34.84	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.84	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.84	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.84	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.84	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.84	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.84	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.84	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.84	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.84	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.84	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.84	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.84	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.84	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.84	   new_error -> error([])
67.74/34.84	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.84	   new_primEqInt2 -> True
67.74/34.84	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.84	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.84	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.84	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.84	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.84	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.84	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.84	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.84	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.84	   new_primMinusNatS1 -> Zero
67.74/34.84	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.84	   new_primEqInt1 -> True
67.74/34.84	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.84	   new_primEqInt0(vuz3260) -> False
67.74/34.84	   new_primEqInt(vuz3250) -> False
67.74/34.84	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.84	
67.74/34.84	The set Q consists of the following terms:
67.74/34.84	
67.74/34.84	   new_rem(Neg(x0), Neg(Zero))
67.74/34.84	   new_primEqInt1
67.74/34.84	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.84	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.84	   new_primMinusNatS1
67.74/34.84	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.84	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.84	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.84	   new_primMinusNatS2(Zero, Zero)
67.74/34.84	   new_error
67.74/34.84	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.84	   new_rem(Pos(x0), Pos(Zero))
67.74/34.84	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.84	   new_primEqInt0(x0)
67.74/34.84	   new_esEs(Pos(Zero))
67.74/34.84	   new_esEs(Pos(Succ(x0)))
67.74/34.84	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.84	   new_primModNatS02(x0, x1)
67.74/34.84	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.84	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.84	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.84	   new_primModNatS1(Zero, x0)
67.74/34.84	   new_primEqInt(x0)
67.74/34.84	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.84	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.84	   new_rem(Pos(x0), Neg(Zero))
67.74/34.84	   new_rem(Neg(x0), Pos(Zero))
67.74/34.84	   new_primMinusNatS0(x0)
67.74/34.84	   new_primEqInt2
67.74/34.84	   new_esEs(Neg(Zero))
67.74/34.84	   new_esEs(Neg(Succ(x0)))
67.74/34.84	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.84	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.84	
67.74/34.84	We have to consider all minimal (P,Q,R)-chains.
67.74/34.84	----------------------------------------
67.74/34.84	
67.74/34.84	(144) TransformationProof (EQUIVALENT)
67.74/34.84	By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Succ(Succ(x2)), Succ(Zero)), Succ(Zero)))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]:
67.74/34.84	
67.74/34.84	   (new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Succ(x2), Zero), Succ(Zero)))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))),new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Succ(x2), Zero), Succ(Zero)))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))))
67.74/34.84	
67.74/34.84	
67.74/34.84	----------------------------------------
67.74/34.84	
67.74/34.84	(145)
67.74/34.84	Obligation:
67.74/34.84	Q DP problem:
67.74/34.84	The TRS P consists of the following rules:
67.74/34.84	
67.74/34.84	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.84	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Succ(x1))), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, x1, x0, x1))), Pos(Succ(Succ(x1))), Pos(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Succ(x1))), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, x1, x0, x1))), Neg(Succ(Succ(x1))), Pos(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, x1, x0, x1))), Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Zero, Zero), Succ(Zero)))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Zero))))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Succ(x2), Zero), Succ(Zero)))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.84	
67.74/34.84	The TRS R consists of the following rules:
67.74/34.84	
67.74/34.84	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.84	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.84	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.84	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.84	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.84	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.84	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.84	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.84	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.84	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.84	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.84	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.84	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.84	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.84	   new_error -> error([])
67.74/34.84	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.84	   new_primEqInt2 -> True
67.74/34.84	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.84	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.84	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.84	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.84	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.84	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.84	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.84	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.84	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.84	   new_primMinusNatS1 -> Zero
67.74/34.84	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.84	   new_primEqInt1 -> True
67.74/34.84	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.84	   new_primEqInt0(vuz3260) -> False
67.74/34.84	   new_primEqInt(vuz3250) -> False
67.74/34.84	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.84	
67.74/34.84	The set Q consists of the following terms:
67.74/34.84	
67.74/34.84	   new_rem(Neg(x0), Neg(Zero))
67.74/34.84	   new_primEqInt1
67.74/34.84	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.84	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.84	   new_primMinusNatS1
67.74/34.84	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.84	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.84	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.84	   new_primMinusNatS2(Zero, Zero)
67.74/34.84	   new_error
67.74/34.84	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.84	   new_rem(Pos(x0), Pos(Zero))
67.74/34.84	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.84	   new_primEqInt0(x0)
67.74/34.84	   new_esEs(Pos(Zero))
67.74/34.84	   new_esEs(Pos(Succ(x0)))
67.74/34.84	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.84	   new_primModNatS02(x0, x1)
67.74/34.84	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.84	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.84	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.84	   new_primModNatS1(Zero, x0)
67.74/34.84	   new_primEqInt(x0)
67.74/34.84	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.84	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.84	   new_rem(Pos(x0), Neg(Zero))
67.74/34.84	   new_rem(Neg(x0), Pos(Zero))
67.74/34.84	   new_primMinusNatS0(x0)
67.74/34.84	   new_primEqInt2
67.74/34.84	   new_esEs(Neg(Zero))
67.74/34.84	   new_esEs(Neg(Succ(x0)))
67.74/34.84	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.84	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.84	
67.74/34.84	We have to consider all minimal (P,Q,R)-chains.
67.74/34.84	----------------------------------------
67.74/34.84	
67.74/34.84	(146) TransformationProof (EQUIVALENT)
67.74/34.84	By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Zero, Zero), Succ(Zero)))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) at position [0,0,0,0] we obtained the following new rules [LPAR04]:
67.74/34.84	
67.74/34.84	   (new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Zero, Succ(Zero)))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))),new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Zero, Succ(Zero)))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))))
67.74/34.84	
67.74/34.84	
67.74/34.84	----------------------------------------
67.74/34.84	
67.74/34.84	(147)
67.74/34.84	Obligation:
67.74/34.84	Q DP problem:
67.74/34.84	The TRS P consists of the following rules:
67.74/34.84	
67.74/34.84	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.84	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Succ(x1))), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, x1, x0, x1))), Pos(Succ(Succ(x1))), Pos(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Succ(x1))), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, x1, x0, x1))), Neg(Succ(Succ(x1))), Pos(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, x1, x0, x1))), Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Succ(x2), Zero), Succ(Zero)))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Zero, Succ(Zero)))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Zero))))
67.74/34.84	
67.74/34.84	The TRS R consists of the following rules:
67.74/34.84	
67.74/34.84	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.84	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.84	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.84	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.84	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.84	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.84	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.84	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.84	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.84	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.84	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.84	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.84	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.84	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.84	   new_error -> error([])
67.74/34.84	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.84	   new_primEqInt2 -> True
67.74/34.84	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.84	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.84	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.84	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.84	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.84	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.84	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.84	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.84	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.84	   new_primMinusNatS1 -> Zero
67.74/34.84	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.84	   new_primEqInt1 -> True
67.74/34.84	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.84	   new_primEqInt0(vuz3260) -> False
67.74/34.84	   new_primEqInt(vuz3250) -> False
67.74/34.84	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.84	
67.74/34.84	The set Q consists of the following terms:
67.74/34.84	
67.74/34.84	   new_rem(Neg(x0), Neg(Zero))
67.74/34.84	   new_primEqInt1
67.74/34.84	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.84	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.84	   new_primMinusNatS1
67.74/34.84	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.84	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.84	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.84	   new_primMinusNatS2(Zero, Zero)
67.74/34.84	   new_error
67.74/34.84	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.84	   new_rem(Pos(x0), Pos(Zero))
67.74/34.84	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.84	   new_primEqInt0(x0)
67.74/34.84	   new_esEs(Pos(Zero))
67.74/34.84	   new_esEs(Pos(Succ(x0)))
67.74/34.84	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.84	   new_primModNatS02(x0, x1)
67.74/34.84	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.84	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.84	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.84	   new_primModNatS1(Zero, x0)
67.74/34.84	   new_primEqInt(x0)
67.74/34.84	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.84	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.84	   new_rem(Pos(x0), Neg(Zero))
67.74/34.84	   new_rem(Neg(x0), Pos(Zero))
67.74/34.84	   new_primMinusNatS0(x0)
67.74/34.84	   new_primEqInt2
67.74/34.84	   new_esEs(Neg(Zero))
67.74/34.84	   new_esEs(Neg(Succ(x0)))
67.74/34.84	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.84	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.84	
67.74/34.84	We have to consider all minimal (P,Q,R)-chains.
67.74/34.84	----------------------------------------
67.74/34.84	
67.74/34.84	(148) TransformationProof (EQUIVALENT)
67.74/34.84	By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Succ(x2), Zero), Succ(Zero)))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]:
67.74/34.84	
67.74/34.84	   (new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))),new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))))
67.74/34.84	
67.74/34.84	
67.74/34.84	----------------------------------------
67.74/34.84	
67.74/34.84	(149)
67.74/34.84	Obligation:
67.74/34.84	Q DP problem:
67.74/34.84	The TRS P consists of the following rules:
67.74/34.84	
67.74/34.84	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.84	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Succ(x1))), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, x1, x0, x1))), Pos(Succ(Succ(x1))), Pos(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Succ(x1))), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, x1, x0, x1))), Neg(Succ(Succ(x1))), Pos(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, x1, x0, x1))), Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Zero, Succ(Zero)))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Zero))))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.84	
67.74/34.84	The TRS R consists of the following rules:
67.74/34.84	
67.74/34.84	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.84	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.84	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.84	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.84	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.84	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.84	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.84	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.84	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.84	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.84	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.84	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.84	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.84	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.84	   new_error -> error([])
67.74/34.84	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.84	   new_primEqInt2 -> True
67.74/34.84	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.84	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.84	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.84	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.84	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.84	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.84	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.84	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.84	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.84	   new_primMinusNatS1 -> Zero
67.74/34.84	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.84	   new_primEqInt1 -> True
67.74/34.84	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.84	   new_primEqInt0(vuz3260) -> False
67.74/34.84	   new_primEqInt(vuz3250) -> False
67.74/34.84	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.84	
67.74/34.84	The set Q consists of the following terms:
67.74/34.84	
67.74/34.84	   new_rem(Neg(x0), Neg(Zero))
67.74/34.84	   new_primEqInt1
67.74/34.84	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.84	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.84	   new_primMinusNatS1
67.74/34.84	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.84	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.84	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.84	   new_primMinusNatS2(Zero, Zero)
67.74/34.84	   new_error
67.74/34.84	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.84	   new_rem(Pos(x0), Pos(Zero))
67.74/34.84	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.84	   new_primEqInt0(x0)
67.74/34.84	   new_esEs(Pos(Zero))
67.74/34.84	   new_esEs(Pos(Succ(x0)))
67.74/34.84	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.84	   new_primModNatS02(x0, x1)
67.74/34.84	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.84	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.84	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.84	   new_primModNatS1(Zero, x0)
67.74/34.84	   new_primEqInt(x0)
67.74/34.84	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.84	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.84	   new_rem(Pos(x0), Neg(Zero))
67.74/34.84	   new_rem(Neg(x0), Pos(Zero))
67.74/34.84	   new_primMinusNatS0(x0)
67.74/34.84	   new_primEqInt2
67.74/34.84	   new_esEs(Neg(Zero))
67.74/34.84	   new_esEs(Neg(Succ(x0)))
67.74/34.84	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.84	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.84	
67.74/34.84	We have to consider all minimal (P,Q,R)-chains.
67.74/34.84	----------------------------------------
67.74/34.84	
67.74/34.84	(150) TransformationProof (EQUIVALENT)
67.74/34.84	By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Zero, Succ(Zero)))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) at position [0,0,0] we obtained the following new rules [LPAR04]:
67.74/34.84	
67.74/34.84	   (new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Neg(Zero)), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))),new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Neg(Zero)), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))))
67.74/34.84	
67.74/34.84	
67.74/34.84	----------------------------------------
67.74/34.84	
67.74/34.84	(151)
67.74/34.84	Obligation:
67.74/34.84	Q DP problem:
67.74/34.84	The TRS P consists of the following rules:
67.74/34.84	
67.74/34.84	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.84	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Succ(x1))), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, x1, x0, x1))), Pos(Succ(Succ(x1))), Pos(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Succ(x1))), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, x1, x0, x1))), Neg(Succ(Succ(x1))), Pos(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, x1, x0, x1))), Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.84	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.84	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Neg(Zero)), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Zero))))
67.74/34.84	
67.74/34.84	The TRS R consists of the following rules:
67.74/34.84	
67.74/34.84	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.84	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.84	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.84	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.84	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.84	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.84	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.84	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.84	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.84	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.84	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.84	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.84	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.84	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.84	   new_error -> error([])
67.74/34.84	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.84	   new_primEqInt2 -> True
67.74/34.84	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.84	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.84	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.84	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.84	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.84	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.84	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.84	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.84	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.84	   new_primMinusNatS1 -> Zero
67.74/34.84	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.84	   new_primEqInt1 -> True
67.74/34.85	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.85	   new_primEqInt0(vuz3260) -> False
67.74/34.85	   new_primEqInt(vuz3250) -> False
67.74/34.85	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.85	
67.74/34.85	The set Q consists of the following terms:
67.74/34.85	
67.74/34.85	   new_rem(Neg(x0), Neg(Zero))
67.74/34.85	   new_primEqInt1
67.74/34.85	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.85	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.85	   new_primMinusNatS1
67.74/34.85	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.85	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.85	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.85	   new_primMinusNatS2(Zero, Zero)
67.74/34.85	   new_error
67.74/34.85	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.85	   new_rem(Pos(x0), Pos(Zero))
67.74/34.85	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.85	   new_primEqInt0(x0)
67.74/34.85	   new_esEs(Pos(Zero))
67.74/34.85	   new_esEs(Pos(Succ(x0)))
67.74/34.85	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.85	   new_primModNatS02(x0, x1)
67.74/34.85	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.85	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.85	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.85	   new_primModNatS1(Zero, x0)
67.74/34.85	   new_primEqInt(x0)
67.74/34.85	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.85	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.85	   new_rem(Pos(x0), Neg(Zero))
67.74/34.85	   new_rem(Neg(x0), Pos(Zero))
67.74/34.85	   new_primMinusNatS0(x0)
67.74/34.85	   new_primEqInt2
67.74/34.85	   new_esEs(Neg(Zero))
67.74/34.85	   new_esEs(Neg(Succ(x0)))
67.74/34.85	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.85	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.85	
67.74/34.85	We have to consider all minimal (P,Q,R)-chains.
67.74/34.85	----------------------------------------
67.74/34.85	
67.74/34.85	(152) DependencyGraphProof (EQUIVALENT)
67.74/34.85	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
67.74/34.85	----------------------------------------
67.74/34.85	
67.74/34.85	(153)
67.74/34.85	Obligation:
67.74/34.85	Q DP problem:
67.74/34.85	The TRS P consists of the following rules:
67.74/34.85	
67.74/34.85	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.85	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Succ(x1))), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, x1, x0, x1))), Pos(Succ(Succ(x1))), Pos(Succ(Succ(x0))))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(x1))), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, x1, x0, x1))), Neg(Succ(Succ(x1))), Pos(Succ(Succ(x0))))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, x1, x0, x1))), Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0))))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.85	
67.74/34.85	The TRS R consists of the following rules:
67.74/34.85	
67.74/34.85	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.85	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.85	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.85	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.85	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.85	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.85	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.85	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.85	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.85	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.85	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.85	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.85	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.85	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.85	   new_error -> error([])
67.74/34.85	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.85	   new_primEqInt2 -> True
67.74/34.85	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.85	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.85	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.85	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.85	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.85	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.85	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.85	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.85	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.85	   new_primMinusNatS1 -> Zero
67.74/34.85	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.85	   new_primEqInt1 -> True
67.74/34.85	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.85	   new_primEqInt0(vuz3260) -> False
67.74/34.85	   new_primEqInt(vuz3250) -> False
67.74/34.85	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.85	
67.74/34.85	The set Q consists of the following terms:
67.74/34.85	
67.74/34.85	   new_rem(Neg(x0), Neg(Zero))
67.74/34.85	   new_primEqInt1
67.74/34.85	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.85	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.85	   new_primMinusNatS1
67.74/34.85	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.85	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.85	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.85	   new_primMinusNatS2(Zero, Zero)
67.74/34.85	   new_error
67.74/34.85	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.85	   new_rem(Pos(x0), Pos(Zero))
67.74/34.85	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.85	   new_primEqInt0(x0)
67.74/34.85	   new_esEs(Pos(Zero))
67.74/34.85	   new_esEs(Pos(Succ(x0)))
67.74/34.85	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.85	   new_primModNatS02(x0, x1)
67.74/34.85	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.85	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.85	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.85	   new_primModNatS1(Zero, x0)
67.74/34.85	   new_primEqInt(x0)
67.74/34.85	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.85	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.85	   new_rem(Pos(x0), Neg(Zero))
67.74/34.85	   new_rem(Neg(x0), Pos(Zero))
67.74/34.85	   new_primMinusNatS0(x0)
67.74/34.85	   new_primEqInt2
67.74/34.85	   new_esEs(Neg(Zero))
67.74/34.85	   new_esEs(Neg(Succ(x0)))
67.74/34.85	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.85	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.85	
67.74/34.85	We have to consider all minimal (P,Q,R)-chains.
67.74/34.85	----------------------------------------
67.74/34.85	
67.74/34.85	(154) TransformationProof (EQUIVALENT)
67.74/34.85	By narrowing [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(x0)))) at position [0] we obtained the following new rules [LPAR04]:
67.74/34.85	
67.74/34.85	   (new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS0(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))),new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS0(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))))
67.74/34.85	   (new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS1, Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Zero)))),new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS1, Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Zero)))))
67.74/34.85	
67.74/34.85	
67.74/34.85	----------------------------------------
67.74/34.85	
67.74/34.85	(155)
67.74/34.85	Obligation:
67.74/34.85	Q DP problem:
67.74/34.85	The TRS P consists of the following rules:
67.74/34.85	
67.74/34.85	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.85	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Succ(x1))), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, x1, x0, x1))), Pos(Succ(Succ(x1))), Pos(Succ(Succ(x0))))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(x1))), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, x1, x0, x1))), Neg(Succ(Succ(x1))), Pos(Succ(Succ(x0))))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, x1, x0, x1))), Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0))))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS0(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS1, Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Zero))))
67.74/34.85	
67.74/34.85	The TRS R consists of the following rules:
67.74/34.85	
67.74/34.85	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.85	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.85	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.85	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.85	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.85	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.85	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.85	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.85	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.85	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.85	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.85	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.85	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.85	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.85	   new_error -> error([])
67.74/34.85	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.85	   new_primEqInt2 -> True
67.74/34.85	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.85	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.85	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.85	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.85	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.85	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.85	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.85	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.85	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.85	   new_primMinusNatS1 -> Zero
67.74/34.85	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.85	   new_primEqInt1 -> True
67.74/34.85	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.85	   new_primEqInt0(vuz3260) -> False
67.74/34.85	   new_primEqInt(vuz3250) -> False
67.74/34.85	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.85	
67.74/34.85	The set Q consists of the following terms:
67.74/34.85	
67.74/34.85	   new_rem(Neg(x0), Neg(Zero))
67.74/34.85	   new_primEqInt1
67.74/34.85	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.85	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.85	   new_primMinusNatS1
67.74/34.85	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.85	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.85	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.85	   new_primMinusNatS2(Zero, Zero)
67.74/34.85	   new_error
67.74/34.85	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.85	   new_rem(Pos(x0), Pos(Zero))
67.74/34.85	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.85	   new_primEqInt0(x0)
67.74/34.85	   new_esEs(Pos(Zero))
67.74/34.85	   new_esEs(Pos(Succ(x0)))
67.74/34.85	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.85	   new_primModNatS02(x0, x1)
67.74/34.85	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.85	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.85	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.85	   new_primModNatS1(Zero, x0)
67.74/34.85	   new_primEqInt(x0)
67.74/34.85	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.85	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.85	   new_rem(Pos(x0), Neg(Zero))
67.74/34.85	   new_rem(Neg(x0), Pos(Zero))
67.74/34.85	   new_primMinusNatS0(x0)
67.74/34.85	   new_primEqInt2
67.74/34.85	   new_esEs(Neg(Zero))
67.74/34.85	   new_esEs(Neg(Succ(x0)))
67.74/34.85	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.85	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.85	
67.74/34.85	We have to consider all minimal (P,Q,R)-chains.
67.74/34.85	----------------------------------------
67.74/34.85	
67.74/34.85	(156) TransformationProof (EQUIVALENT)
67.74/34.85	By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS0(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]:
67.74/34.85	
67.74/34.85	   (new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))),new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))))
67.74/34.85	
67.74/34.85	
67.74/34.85	----------------------------------------
67.74/34.85	
67.74/34.85	(157)
67.74/34.85	Obligation:
67.74/34.85	Q DP problem:
67.74/34.85	The TRS P consists of the following rules:
67.74/34.85	
67.74/34.85	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.85	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Succ(x1))), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, x1, x0, x1))), Pos(Succ(Succ(x1))), Pos(Succ(Succ(x0))))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(x1))), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, x1, x0, x1))), Neg(Succ(Succ(x1))), Pos(Succ(Succ(x0))))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, x1, x0, x1))), Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0))))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS1, Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Zero))))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.85	
67.74/34.85	The TRS R consists of the following rules:
67.74/34.85	
67.74/34.85	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.85	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.85	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.85	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.85	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.85	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.85	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.85	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.85	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.85	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.85	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.85	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.85	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.85	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.85	   new_error -> error([])
67.74/34.85	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.85	   new_primEqInt2 -> True
67.74/34.85	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.85	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.85	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.85	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.85	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.85	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.85	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.85	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.85	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.85	   new_primMinusNatS1 -> Zero
67.74/34.85	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.85	   new_primEqInt1 -> True
67.74/34.85	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.85	   new_primEqInt0(vuz3260) -> False
67.74/34.85	   new_primEqInt(vuz3250) -> False
67.74/34.85	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.85	
67.74/34.85	The set Q consists of the following terms:
67.74/34.85	
67.74/34.85	   new_rem(Neg(x0), Neg(Zero))
67.74/34.85	   new_primEqInt1
67.74/34.85	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.85	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.85	   new_primMinusNatS1
67.74/34.85	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.85	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.85	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.85	   new_primMinusNatS2(Zero, Zero)
67.74/34.85	   new_error
67.74/34.85	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.85	   new_rem(Pos(x0), Pos(Zero))
67.74/34.85	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.85	   new_primEqInt0(x0)
67.74/34.85	   new_esEs(Pos(Zero))
67.74/34.85	   new_esEs(Pos(Succ(x0)))
67.74/34.85	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.85	   new_primModNatS02(x0, x1)
67.74/34.85	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.85	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.85	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.85	   new_primModNatS1(Zero, x0)
67.74/34.85	   new_primEqInt(x0)
67.74/34.85	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.85	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.85	   new_rem(Pos(x0), Neg(Zero))
67.74/34.85	   new_rem(Neg(x0), Pos(Zero))
67.74/34.85	   new_primMinusNatS0(x0)
67.74/34.85	   new_primEqInt2
67.74/34.85	   new_esEs(Neg(Zero))
67.74/34.85	   new_esEs(Neg(Succ(x0)))
67.74/34.85	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.85	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.85	
67.74/34.85	We have to consider all minimal (P,Q,R)-chains.
67.74/34.85	----------------------------------------
67.74/34.85	
67.74/34.85	(158) TransformationProof (EQUIVALENT)
67.74/34.85	By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS1, Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Zero)))) at position [0,0,0,0] we obtained the following new rules [LPAR04]:
67.74/34.85	
67.74/34.85	   (new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Zero, Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Zero)))),new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Zero, Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Zero)))))
67.74/34.85	
67.74/34.85	
67.74/34.85	----------------------------------------
67.74/34.85	
67.74/34.85	(159)
67.74/34.85	Obligation:
67.74/34.85	Q DP problem:
67.74/34.85	The TRS P consists of the following rules:
67.74/34.85	
67.74/34.85	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.85	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Succ(x1))), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, x1, x0, x1))), Pos(Succ(Succ(x1))), Pos(Succ(Succ(x0))))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(x1))), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, x1, x0, x1))), Neg(Succ(Succ(x1))), Pos(Succ(Succ(x0))))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, x1, x0, x1))), Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0))))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Zero, Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Zero))))
67.74/34.85	
67.74/34.85	The TRS R consists of the following rules:
67.74/34.85	
67.74/34.85	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.85	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.85	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.85	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.85	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.85	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.85	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.85	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.85	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.85	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.85	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.85	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.85	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.85	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.85	   new_error -> error([])
67.74/34.85	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.85	   new_primEqInt2 -> True
67.74/34.85	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.85	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.85	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.85	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.85	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.85	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.85	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.85	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.85	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.85	   new_primMinusNatS1 -> Zero
67.74/34.85	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.85	   new_primEqInt1 -> True
67.74/34.85	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.85	   new_primEqInt0(vuz3260) -> False
67.74/34.85	   new_primEqInt(vuz3250) -> False
67.74/34.85	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.85	
67.74/34.85	The set Q consists of the following terms:
67.74/34.85	
67.74/34.85	   new_rem(Neg(x0), Neg(Zero))
67.74/34.85	   new_primEqInt1
67.74/34.85	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.85	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.85	   new_primMinusNatS1
67.74/34.85	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.85	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.85	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.85	   new_primMinusNatS2(Zero, Zero)
67.74/34.85	   new_error
67.74/34.85	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.85	   new_rem(Pos(x0), Pos(Zero))
67.74/34.85	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.85	   new_primEqInt0(x0)
67.74/34.85	   new_esEs(Pos(Zero))
67.74/34.85	   new_esEs(Pos(Succ(x0)))
67.74/34.85	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.85	   new_primModNatS02(x0, x1)
67.74/34.85	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.85	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.85	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.85	   new_primModNatS1(Zero, x0)
67.74/34.85	   new_primEqInt(x0)
67.74/34.85	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.85	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.85	   new_rem(Pos(x0), Neg(Zero))
67.74/34.85	   new_rem(Neg(x0), Pos(Zero))
67.74/34.85	   new_primMinusNatS0(x0)
67.74/34.85	   new_primEqInt2
67.74/34.85	   new_esEs(Neg(Zero))
67.74/34.85	   new_esEs(Neg(Succ(x0)))
67.74/34.85	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.85	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.85	
67.74/34.85	We have to consider all minimal (P,Q,R)-chains.
67.74/34.85	----------------------------------------
67.74/34.85	
67.74/34.85	(160) TransformationProof (EQUIVALENT)
67.74/34.85	By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Zero, Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Zero)))) at position [0,0,0] we obtained the following new rules [LPAR04]:
67.74/34.85	
67.74/34.85	   (new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Neg(Zero)), Neg(Succ(Zero)), Neg(Succ(Succ(Zero)))),new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Neg(Zero)), Neg(Succ(Zero)), Neg(Succ(Succ(Zero)))))
67.74/34.85	
67.74/34.85	
67.74/34.85	----------------------------------------
67.74/34.85	
67.74/34.85	(161)
67.74/34.85	Obligation:
67.74/34.85	Q DP problem:
67.74/34.85	The TRS P consists of the following rules:
67.74/34.85	
67.74/34.85	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.85	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Succ(x1))), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, x1, x0, x1))), Pos(Succ(Succ(x1))), Pos(Succ(Succ(x0))))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(x1))), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, x1, x0, x1))), Neg(Succ(Succ(x1))), Pos(Succ(Succ(x0))))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, x1, x0, x1))), Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0))))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Neg(Zero)), Neg(Succ(Zero)), Neg(Succ(Succ(Zero))))
67.74/34.85	
67.74/34.85	The TRS R consists of the following rules:
67.74/34.85	
67.74/34.85	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.85	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.85	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.85	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.85	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.85	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.85	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.85	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.85	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.85	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.85	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.85	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.85	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.85	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.85	   new_error -> error([])
67.74/34.85	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.85	   new_primEqInt2 -> True
67.74/34.85	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.85	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.85	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.85	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.85	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.85	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.85	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.85	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.85	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.85	   new_primMinusNatS1 -> Zero
67.74/34.85	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.85	   new_primEqInt1 -> True
67.74/34.85	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.85	   new_primEqInt0(vuz3260) -> False
67.74/34.85	   new_primEqInt(vuz3250) -> False
67.74/34.85	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.85	
67.74/34.85	The set Q consists of the following terms:
67.74/34.85	
67.74/34.85	   new_rem(Neg(x0), Neg(Zero))
67.74/34.85	   new_primEqInt1
67.74/34.85	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.85	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.85	   new_primMinusNatS1
67.74/34.85	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.85	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.85	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.85	   new_primMinusNatS2(Zero, Zero)
67.74/34.85	   new_error
67.74/34.85	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.85	   new_rem(Pos(x0), Pos(Zero))
67.74/34.85	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.85	   new_primEqInt0(x0)
67.74/34.85	   new_esEs(Pos(Zero))
67.74/34.85	   new_esEs(Pos(Succ(x0)))
67.74/34.85	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.85	   new_primModNatS02(x0, x1)
67.74/34.85	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.85	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.85	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.85	   new_primModNatS1(Zero, x0)
67.74/34.85	   new_primEqInt(x0)
67.74/34.85	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.85	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.85	   new_rem(Pos(x0), Neg(Zero))
67.74/34.85	   new_rem(Neg(x0), Pos(Zero))
67.74/34.85	   new_primMinusNatS0(x0)
67.74/34.85	   new_primEqInt2
67.74/34.85	   new_esEs(Neg(Zero))
67.74/34.85	   new_esEs(Neg(Succ(x0)))
67.74/34.85	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.85	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.85	
67.74/34.85	We have to consider all minimal (P,Q,R)-chains.
67.74/34.85	----------------------------------------
67.74/34.85	
67.74/34.85	(162) DependencyGraphProof (EQUIVALENT)
67.74/34.85	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
67.74/34.85	----------------------------------------
67.74/34.85	
67.74/34.85	(163)
67.74/34.85	Obligation:
67.74/34.85	Q DP problem:
67.74/34.85	The TRS P consists of the following rules:
67.74/34.85	
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.85	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.85	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Succ(x1))), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, x1, x0, x1))), Pos(Succ(Succ(x1))), Pos(Succ(Succ(x0))))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(x1))), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, x1, x0, x1))), Neg(Succ(Succ(x1))), Pos(Succ(Succ(x0))))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, x1, x0, x1))), Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0))))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.85	
67.74/34.85	The TRS R consists of the following rules:
67.74/34.85	
67.74/34.85	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.85	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.85	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.85	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.85	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.85	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.85	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.85	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.85	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.85	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.85	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.85	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.85	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.85	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.85	   new_error -> error([])
67.74/34.85	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.85	   new_primEqInt2 -> True
67.74/34.85	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.85	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.85	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.85	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.85	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.85	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.85	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.85	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.85	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.85	   new_primMinusNatS1 -> Zero
67.74/34.85	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.85	   new_primEqInt1 -> True
67.74/34.85	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.85	   new_primEqInt0(vuz3260) -> False
67.74/34.85	   new_primEqInt(vuz3250) -> False
67.74/34.85	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.85	
67.74/34.85	The set Q consists of the following terms:
67.74/34.85	
67.74/34.85	   new_rem(Neg(x0), Neg(Zero))
67.74/34.85	   new_primEqInt1
67.74/34.85	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.85	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.85	   new_primMinusNatS1
67.74/34.85	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.85	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.85	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.85	   new_primMinusNatS2(Zero, Zero)
67.74/34.85	   new_error
67.74/34.85	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.85	   new_rem(Pos(x0), Pos(Zero))
67.74/34.85	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.85	   new_primEqInt0(x0)
67.74/34.85	   new_esEs(Pos(Zero))
67.74/34.85	   new_esEs(Pos(Succ(x0)))
67.74/34.85	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.85	   new_primModNatS02(x0, x1)
67.74/34.85	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.85	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.85	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.85	   new_primModNatS1(Zero, x0)
67.74/34.85	   new_primEqInt(x0)
67.74/34.85	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.85	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.85	   new_rem(Pos(x0), Neg(Zero))
67.74/34.85	   new_rem(Neg(x0), Pos(Zero))
67.74/34.85	   new_primMinusNatS0(x0)
67.74/34.85	   new_primEqInt2
67.74/34.85	   new_esEs(Neg(Zero))
67.74/34.85	   new_esEs(Neg(Succ(x0)))
67.74/34.85	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.85	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.85	
67.74/34.85	We have to consider all minimal (P,Q,R)-chains.
67.74/34.85	----------------------------------------
67.74/34.85	
67.74/34.85	(164) TransformationProof (EQUIVALENT)
67.74/34.85	By narrowing [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(x1))), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, x1, x0, x1))), Pos(Succ(Succ(x1))), Pos(Succ(Succ(x0)))) at position [0] we obtained the following new rules [LPAR04]:
67.74/34.85	
67.74/34.85	   (new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))))
67.74/34.85	   (new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Pos(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Pos(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))))
67.74/34.85	   (new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS02(Zero, Zero))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))),new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS02(Zero, Zero))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))))
67.74/34.85	   (new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS02(Succ(x2), Zero))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))),new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS02(Succ(x2), Zero))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))))
67.74/34.85	
67.74/34.85	
67.74/34.85	----------------------------------------
67.74/34.85	
67.74/34.85	(165)
67.74/34.85	Obligation:
67.74/34.85	Q DP problem:
67.74/34.85	The TRS P consists of the following rules:
67.74/34.85	
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.85	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.85	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(x1))), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, x1, x0, x1))), Neg(Succ(Succ(x1))), Pos(Succ(Succ(x0))))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, x1, x0, x1))), Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0))))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Pos(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS02(Zero, Zero))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Zero))))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS02(Succ(x2), Zero))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.85	
67.74/34.85	The TRS R consists of the following rules:
67.74/34.85	
67.74/34.85	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.85	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.85	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.85	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.85	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.85	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.85	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.85	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.85	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.85	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.85	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.85	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.85	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.85	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.85	   new_error -> error([])
67.74/34.85	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.85	   new_primEqInt2 -> True
67.74/34.85	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.85	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.85	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.85	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.85	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.85	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.85	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.85	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.85	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.85	   new_primMinusNatS1 -> Zero
67.74/34.85	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.85	   new_primEqInt1 -> True
67.74/34.85	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.85	   new_primEqInt0(vuz3260) -> False
67.74/34.85	   new_primEqInt(vuz3250) -> False
67.74/34.85	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.85	
67.74/34.85	The set Q consists of the following terms:
67.74/34.85	
67.74/34.85	   new_rem(Neg(x0), Neg(Zero))
67.74/34.85	   new_primEqInt1
67.74/34.85	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.85	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.85	   new_primMinusNatS1
67.74/34.85	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.85	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.85	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.85	   new_primMinusNatS2(Zero, Zero)
67.74/34.85	   new_error
67.74/34.85	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.85	   new_rem(Pos(x0), Pos(Zero))
67.74/34.85	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.85	   new_primEqInt0(x0)
67.74/34.85	   new_esEs(Pos(Zero))
67.74/34.85	   new_esEs(Pos(Succ(x0)))
67.74/34.85	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.85	   new_primModNatS02(x0, x1)
67.74/34.85	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.85	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.85	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.85	   new_primModNatS1(Zero, x0)
67.74/34.85	   new_primEqInt(x0)
67.74/34.85	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.85	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.85	   new_rem(Pos(x0), Neg(Zero))
67.74/34.85	   new_rem(Neg(x0), Pos(Zero))
67.74/34.85	   new_primMinusNatS0(x0)
67.74/34.85	   new_primEqInt2
67.74/34.85	   new_esEs(Neg(Zero))
67.74/34.85	   new_esEs(Neg(Succ(x0)))
67.74/34.85	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.85	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.85	
67.74/34.85	We have to consider all minimal (P,Q,R)-chains.
67.74/34.85	----------------------------------------
67.74/34.85	
67.74/34.85	(166) TransformationProof (EQUIVALENT)
67.74/34.85	By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Pos(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) at position [0] we obtained the following new rules [LPAR04]:
67.74/34.85	
67.74/34.85	   (new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_primEqInt(Succ(Zero)), Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_primEqInt(Succ(Zero)), Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))))
67.74/34.85	
67.74/34.85	
67.74/34.85	----------------------------------------
67.74/34.85	
67.74/34.85	(167)
67.74/34.85	Obligation:
67.74/34.85	Q DP problem:
67.74/34.85	The TRS P consists of the following rules:
67.74/34.85	
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.85	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.85	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(x1))), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, x1, x0, x1))), Neg(Succ(Succ(x1))), Pos(Succ(Succ(x0))))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, x1, x0, x1))), Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0))))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS02(Zero, Zero))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Zero))))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS02(Succ(x2), Zero))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_primEqInt(Succ(Zero)), Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.85	
67.74/34.85	The TRS R consists of the following rules:
67.74/34.85	
67.74/34.85	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.85	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.85	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.85	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.85	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.85	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.85	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.85	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.85	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.85	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.85	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.85	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.85	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.85	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.85	   new_error -> error([])
67.74/34.85	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.85	   new_primEqInt2 -> True
67.74/34.85	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.85	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.85	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.85	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.85	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.85	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.85	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.85	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.85	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.85	   new_primMinusNatS1 -> Zero
67.74/34.85	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.85	   new_primEqInt1 -> True
67.74/34.85	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.85	   new_primEqInt0(vuz3260) -> False
67.74/34.85	   new_primEqInt(vuz3250) -> False
67.74/34.85	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.85	
67.74/34.85	The set Q consists of the following terms:
67.74/34.85	
67.74/34.85	   new_rem(Neg(x0), Neg(Zero))
67.74/34.85	   new_primEqInt1
67.74/34.85	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.85	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.85	   new_primMinusNatS1
67.74/34.85	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.85	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.85	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.85	   new_primMinusNatS2(Zero, Zero)
67.74/34.85	   new_error
67.74/34.85	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.85	   new_rem(Pos(x0), Pos(Zero))
67.74/34.85	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.85	   new_primEqInt0(x0)
67.74/34.85	   new_esEs(Pos(Zero))
67.74/34.85	   new_esEs(Pos(Succ(x0)))
67.74/34.85	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.85	   new_primModNatS02(x0, x1)
67.74/34.85	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.85	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.85	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.85	   new_primModNatS1(Zero, x0)
67.74/34.85	   new_primEqInt(x0)
67.74/34.85	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.85	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.85	   new_rem(Pos(x0), Neg(Zero))
67.74/34.85	   new_rem(Neg(x0), Pos(Zero))
67.74/34.85	   new_primMinusNatS0(x0)
67.74/34.85	   new_primEqInt2
67.74/34.85	   new_esEs(Neg(Zero))
67.74/34.85	   new_esEs(Neg(Succ(x0)))
67.74/34.85	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.85	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.85	
67.74/34.85	We have to consider all minimal (P,Q,R)-chains.
67.74/34.85	----------------------------------------
67.74/34.85	
67.74/34.85	(168) TransformationProof (EQUIVALENT)
67.74/34.85	By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS02(Zero, Zero))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))) at position [0,0,0] we obtained the following new rules [LPAR04]:
67.74/34.85	
67.74/34.85	   (new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Succ(Zero), Succ(Zero)), Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))),new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Succ(Zero), Succ(Zero)), Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))))
67.74/34.85	
67.74/34.85	
67.74/34.85	----------------------------------------
67.74/34.85	
67.74/34.85	(169)
67.74/34.85	Obligation:
67.74/34.85	Q DP problem:
67.74/34.85	The TRS P consists of the following rules:
67.74/34.85	
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.85	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.85	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(x1))), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, x1, x0, x1))), Neg(Succ(Succ(x1))), Pos(Succ(Succ(x0))))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, x1, x0, x1))), Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0))))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS02(Succ(x2), Zero))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_primEqInt(Succ(Zero)), Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Succ(Zero), Succ(Zero)), Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Zero))))
67.74/34.85	
67.74/34.85	The TRS R consists of the following rules:
67.74/34.85	
67.74/34.85	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.85	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.85	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.85	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.85	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.85	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.85	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.85	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.85	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.85	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.85	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.85	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.85	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.85	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.85	   new_error -> error([])
67.74/34.85	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.85	   new_primEqInt2 -> True
67.74/34.85	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.85	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.85	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.85	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.85	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.85	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.85	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.85	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.85	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.85	   new_primMinusNatS1 -> Zero
67.74/34.85	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.85	   new_primEqInt1 -> True
67.74/34.85	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.85	   new_primEqInt0(vuz3260) -> False
67.74/34.85	   new_primEqInt(vuz3250) -> False
67.74/34.85	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.85	
67.74/34.85	The set Q consists of the following terms:
67.74/34.85	
67.74/34.85	   new_rem(Neg(x0), Neg(Zero))
67.74/34.85	   new_primEqInt1
67.74/34.85	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.85	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.85	   new_primMinusNatS1
67.74/34.85	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.85	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.85	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.85	   new_primMinusNatS2(Zero, Zero)
67.74/34.85	   new_error
67.74/34.85	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.85	   new_rem(Pos(x0), Pos(Zero))
67.74/34.85	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.85	   new_primEqInt0(x0)
67.74/34.85	   new_esEs(Pos(Zero))
67.74/34.85	   new_esEs(Pos(Succ(x0)))
67.74/34.85	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.85	   new_primModNatS02(x0, x1)
67.74/34.85	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.85	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.85	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.85	   new_primModNatS1(Zero, x0)
67.74/34.85	   new_primEqInt(x0)
67.74/34.85	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.85	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.85	   new_rem(Pos(x0), Neg(Zero))
67.74/34.85	   new_rem(Neg(x0), Pos(Zero))
67.74/34.85	   new_primMinusNatS0(x0)
67.74/34.85	   new_primEqInt2
67.74/34.85	   new_esEs(Neg(Zero))
67.74/34.85	   new_esEs(Neg(Succ(x0)))
67.74/34.85	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.85	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.85	
67.74/34.85	We have to consider all minimal (P,Q,R)-chains.
67.74/34.85	----------------------------------------
67.74/34.85	
67.74/34.85	(170) TransformationProof (EQUIVALENT)
67.74/34.85	By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS02(Succ(x2), Zero))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) at position [0,0,0] we obtained the following new rules [LPAR04]:
67.74/34.85	
67.74/34.85	   (new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Succ(Succ(x2)), Succ(Zero)), Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))),new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Succ(Succ(x2)), Succ(Zero)), Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))))
67.74/34.85	
67.74/34.85	
67.74/34.85	----------------------------------------
67.74/34.85	
67.74/34.85	(171)
67.74/34.85	Obligation:
67.74/34.85	Q DP problem:
67.74/34.85	The TRS P consists of the following rules:
67.74/34.85	
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.85	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.85	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(x1))), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, x1, x0, x1))), Neg(Succ(Succ(x1))), Pos(Succ(Succ(x0))))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, x1, x0, x1))), Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0))))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_primEqInt(Succ(Zero)), Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Succ(Zero), Succ(Zero)), Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Zero))))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Succ(Succ(x2)), Succ(Zero)), Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.85	
67.74/34.85	The TRS R consists of the following rules:
67.74/34.85	
67.74/34.85	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.85	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.85	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.85	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.85	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.85	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.85	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.85	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.85	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.85	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.85	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.85	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.85	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.85	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.85	   new_error -> error([])
67.74/34.85	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.85	   new_primEqInt2 -> True
67.74/34.85	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.85	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.85	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.85	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.85	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.85	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.85	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.85	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.85	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.85	   new_primMinusNatS1 -> Zero
67.74/34.85	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.85	   new_primEqInt1 -> True
67.74/34.85	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.85	   new_primEqInt0(vuz3260) -> False
67.74/34.85	   new_primEqInt(vuz3250) -> False
67.74/34.85	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.85	
67.74/34.85	The set Q consists of the following terms:
67.74/34.85	
67.74/34.85	   new_rem(Neg(x0), Neg(Zero))
67.74/34.85	   new_primEqInt1
67.74/34.85	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.85	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.85	   new_primMinusNatS1
67.74/34.85	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.85	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.85	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.85	   new_primMinusNatS2(Zero, Zero)
67.74/34.85	   new_error
67.74/34.85	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.85	   new_rem(Pos(x0), Pos(Zero))
67.74/34.85	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.85	   new_primEqInt0(x0)
67.74/34.85	   new_esEs(Pos(Zero))
67.74/34.85	   new_esEs(Pos(Succ(x0)))
67.74/34.85	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.85	   new_primModNatS02(x0, x1)
67.74/34.85	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.85	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.85	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.85	   new_primModNatS1(Zero, x0)
67.74/34.85	   new_primEqInt(x0)
67.74/34.85	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.85	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.85	   new_rem(Pos(x0), Neg(Zero))
67.74/34.85	   new_rem(Neg(x0), Pos(Zero))
67.74/34.85	   new_primMinusNatS0(x0)
67.74/34.85	   new_primEqInt2
67.74/34.85	   new_esEs(Neg(Zero))
67.74/34.85	   new_esEs(Neg(Succ(x0)))
67.74/34.85	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.85	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.85	
67.74/34.85	We have to consider all minimal (P,Q,R)-chains.
67.74/34.85	----------------------------------------
67.74/34.85	
67.74/34.85	(172) TransformationProof (EQUIVALENT)
67.74/34.85	By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_primEqInt(Succ(Zero)), Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) at position [0] we obtained the following new rules [LPAR04]:
67.74/34.85	
67.74/34.85	   (new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))))
67.74/34.85	
67.74/34.85	
67.74/34.85	----------------------------------------
67.74/34.85	
67.74/34.85	(173)
67.74/34.85	Obligation:
67.74/34.85	Q DP problem:
67.74/34.85	The TRS P consists of the following rules:
67.74/34.85	
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.85	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.85	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(x1))), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, x1, x0, x1))), Neg(Succ(Succ(x1))), Pos(Succ(Succ(x0))))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, x1, x0, x1))), Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0))))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Succ(Zero), Succ(Zero)), Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Zero))))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Succ(Succ(x2)), Succ(Zero)), Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.85	
67.74/34.85	The TRS R consists of the following rules:
67.74/34.85	
67.74/34.85	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.85	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.85	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.85	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.85	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.85	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.85	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.85	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.85	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.85	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.85	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.85	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.85	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.85	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.85	   new_error -> error([])
67.74/34.85	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.85	   new_primEqInt2 -> True
67.74/34.85	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.85	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.85	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.85	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.85	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.85	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.85	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.85	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.85	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.85	   new_primMinusNatS1 -> Zero
67.74/34.85	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.85	   new_primEqInt1 -> True
67.74/34.85	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.85	   new_primEqInt0(vuz3260) -> False
67.74/34.85	   new_primEqInt(vuz3250) -> False
67.74/34.85	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.85	
67.74/34.85	The set Q consists of the following terms:
67.74/34.85	
67.74/34.85	   new_rem(Neg(x0), Neg(Zero))
67.74/34.85	   new_primEqInt1
67.74/34.85	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.85	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.85	   new_primMinusNatS1
67.74/34.85	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.85	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.85	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.85	   new_primMinusNatS2(Zero, Zero)
67.74/34.85	   new_error
67.74/34.85	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.85	   new_rem(Pos(x0), Pos(Zero))
67.74/34.85	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.85	   new_primEqInt0(x0)
67.74/34.85	   new_esEs(Pos(Zero))
67.74/34.85	   new_esEs(Pos(Succ(x0)))
67.74/34.85	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.85	   new_primModNatS02(x0, x1)
67.74/34.85	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.85	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.85	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.85	   new_primModNatS1(Zero, x0)
67.74/34.85	   new_primEqInt(x0)
67.74/34.85	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.85	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.85	   new_rem(Pos(x0), Neg(Zero))
67.74/34.85	   new_rem(Neg(x0), Pos(Zero))
67.74/34.85	   new_primMinusNatS0(x0)
67.74/34.85	   new_primEqInt2
67.74/34.85	   new_esEs(Neg(Zero))
67.74/34.85	   new_esEs(Neg(Succ(x0)))
67.74/34.85	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.85	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.85	
67.74/34.85	We have to consider all minimal (P,Q,R)-chains.
67.74/34.85	----------------------------------------
67.74/34.85	
67.74/34.85	(174) TransformationProof (EQUIVALENT)
67.74/34.85	By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Succ(Zero), Succ(Zero)), Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))) at position [0,0,0,0] we obtained the following new rules [LPAR04]:
67.74/34.85	
67.74/34.85	   (new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Zero, Zero), Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))),new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Zero, Zero), Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))))
67.74/34.85	
67.74/34.85	
67.74/34.85	----------------------------------------
67.74/34.85	
67.74/34.85	(175)
67.74/34.85	Obligation:
67.74/34.85	Q DP problem:
67.74/34.85	The TRS P consists of the following rules:
67.74/34.85	
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.85	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.85	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(x1))), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, x1, x0, x1))), Neg(Succ(Succ(x1))), Pos(Succ(Succ(x0))))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, x1, x0, x1))), Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0))))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Succ(Succ(x2)), Succ(Zero)), Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Zero, Zero), Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Zero))))
67.74/34.85	
67.74/34.85	The TRS R consists of the following rules:
67.74/34.85	
67.74/34.85	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.85	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.85	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.85	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.85	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.85	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.85	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.85	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.85	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.85	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.85	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.85	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.85	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.85	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.85	   new_error -> error([])
67.74/34.85	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.85	   new_primEqInt2 -> True
67.74/34.85	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.85	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.85	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.85	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.85	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.85	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.85	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.85	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.85	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.85	   new_primMinusNatS1 -> Zero
67.74/34.85	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.85	   new_primEqInt1 -> True
67.74/34.85	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.85	   new_primEqInt0(vuz3260) -> False
67.74/34.85	   new_primEqInt(vuz3250) -> False
67.74/34.85	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.85	
67.74/34.85	The set Q consists of the following terms:
67.74/34.85	
67.74/34.85	   new_rem(Neg(x0), Neg(Zero))
67.74/34.85	   new_primEqInt1
67.74/34.85	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.85	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.85	   new_primMinusNatS1
67.74/34.85	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.85	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.85	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.85	   new_primMinusNatS2(Zero, Zero)
67.74/34.85	   new_error
67.74/34.85	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.85	   new_rem(Pos(x0), Pos(Zero))
67.74/34.85	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.85	   new_primEqInt0(x0)
67.74/34.85	   new_esEs(Pos(Zero))
67.74/34.85	   new_esEs(Pos(Succ(x0)))
67.74/34.85	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.85	   new_primModNatS02(x0, x1)
67.74/34.85	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.85	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.85	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.85	   new_primModNatS1(Zero, x0)
67.74/34.85	   new_primEqInt(x0)
67.74/34.85	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.85	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.85	   new_rem(Pos(x0), Neg(Zero))
67.74/34.85	   new_rem(Neg(x0), Pos(Zero))
67.74/34.85	   new_primMinusNatS0(x0)
67.74/34.85	   new_primEqInt2
67.74/34.85	   new_esEs(Neg(Zero))
67.74/34.85	   new_esEs(Neg(Succ(x0)))
67.74/34.85	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.85	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.85	
67.74/34.85	We have to consider all minimal (P,Q,R)-chains.
67.74/34.85	----------------------------------------
67.74/34.85	
67.74/34.85	(176) TransformationProof (EQUIVALENT)
67.74/34.85	By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Succ(Succ(x2)), Succ(Zero)), Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]:
67.74/34.85	
67.74/34.85	   (new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Succ(x2), Zero), Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))),new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Succ(x2), Zero), Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))))
67.74/34.85	
67.74/34.85	
67.74/34.85	----------------------------------------
67.74/34.85	
67.74/34.85	(177)
67.74/34.85	Obligation:
67.74/34.85	Q DP problem:
67.74/34.85	The TRS P consists of the following rules:
67.74/34.85	
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.85	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.85	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(x1))), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, x1, x0, x1))), Neg(Succ(Succ(x1))), Pos(Succ(Succ(x0))))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, x1, x0, x1))), Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0))))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Zero, Zero), Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Zero))))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Succ(x2), Zero), Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.85	
67.74/34.85	The TRS R consists of the following rules:
67.74/34.85	
67.74/34.85	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.85	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.85	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.85	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.85	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.85	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.85	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.85	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.85	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.85	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.85	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.85	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.85	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.85	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.85	   new_error -> error([])
67.74/34.85	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.85	   new_primEqInt2 -> True
67.74/34.85	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.85	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.85	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.85	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.85	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.85	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.85	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.85	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.85	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.85	   new_primMinusNatS1 -> Zero
67.74/34.85	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.85	   new_primEqInt1 -> True
67.74/34.85	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.85	   new_primEqInt0(vuz3260) -> False
67.74/34.85	   new_primEqInt(vuz3250) -> False
67.74/34.85	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.85	
67.74/34.85	The set Q consists of the following terms:
67.74/34.85	
67.74/34.85	   new_rem(Neg(x0), Neg(Zero))
67.74/34.85	   new_primEqInt1
67.74/34.85	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.85	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.85	   new_primMinusNatS1
67.74/34.85	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.85	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.85	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.85	   new_primMinusNatS2(Zero, Zero)
67.74/34.85	   new_error
67.74/34.85	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.85	   new_rem(Pos(x0), Pos(Zero))
67.74/34.85	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.85	   new_primEqInt0(x0)
67.74/34.85	   new_esEs(Pos(Zero))
67.74/34.85	   new_esEs(Pos(Succ(x0)))
67.74/34.85	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.85	   new_primModNatS02(x0, x1)
67.74/34.85	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.85	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.85	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.85	   new_primModNatS1(Zero, x0)
67.74/34.85	   new_primEqInt(x0)
67.74/34.85	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.85	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.85	   new_rem(Pos(x0), Neg(Zero))
67.74/34.85	   new_rem(Neg(x0), Pos(Zero))
67.74/34.85	   new_primMinusNatS0(x0)
67.74/34.85	   new_primEqInt2
67.74/34.85	   new_esEs(Neg(Zero))
67.74/34.85	   new_esEs(Neg(Succ(x0)))
67.74/34.85	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.85	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.85	
67.74/34.85	We have to consider all minimal (P,Q,R)-chains.
67.74/34.85	----------------------------------------
67.74/34.85	
67.74/34.85	(178) TransformationProof (EQUIVALENT)
67.74/34.85	By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Zero, Zero), Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))) at position [0,0,0,0] we obtained the following new rules [LPAR04]:
67.74/34.85	
67.74/34.85	   (new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Zero, Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))),new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Zero, Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))))
67.74/34.85	
67.74/34.85	
67.74/34.85	----------------------------------------
67.74/34.85	
67.74/34.85	(179)
67.74/34.85	Obligation:
67.74/34.85	Q DP problem:
67.74/34.85	The TRS P consists of the following rules:
67.74/34.85	
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.85	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.85	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(x1))), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, x1, x0, x1))), Neg(Succ(Succ(x1))), Pos(Succ(Succ(x0))))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, x1, x0, x1))), Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0))))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Succ(x2), Zero), Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Zero, Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Zero))))
67.74/34.85	
67.74/34.85	The TRS R consists of the following rules:
67.74/34.85	
67.74/34.85	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.85	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.85	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.85	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.85	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.85	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.85	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.85	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.85	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.85	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.85	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.85	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.85	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.85	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.85	   new_error -> error([])
67.74/34.85	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.85	   new_primEqInt2 -> True
67.74/34.85	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.85	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.85	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.85	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.85	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.85	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.85	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.85	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.85	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.85	   new_primMinusNatS1 -> Zero
67.74/34.85	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.85	   new_primEqInt1 -> True
67.74/34.85	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.85	   new_primEqInt0(vuz3260) -> False
67.74/34.85	   new_primEqInt(vuz3250) -> False
67.74/34.85	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.85	
67.74/34.85	The set Q consists of the following terms:
67.74/34.85	
67.74/34.85	   new_rem(Neg(x0), Neg(Zero))
67.74/34.85	   new_primEqInt1
67.74/34.85	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.85	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.85	   new_primMinusNatS1
67.74/34.85	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.85	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.85	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.85	   new_primMinusNatS2(Zero, Zero)
67.74/34.85	   new_error
67.74/34.85	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.85	   new_rem(Pos(x0), Pos(Zero))
67.74/34.85	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.85	   new_primEqInt0(x0)
67.74/34.85	   new_esEs(Pos(Zero))
67.74/34.85	   new_esEs(Pos(Succ(x0)))
67.74/34.85	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.85	   new_primModNatS02(x0, x1)
67.74/34.85	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.85	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.85	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.85	   new_primModNatS1(Zero, x0)
67.74/34.85	   new_primEqInt(x0)
67.74/34.85	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.85	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.85	   new_rem(Pos(x0), Neg(Zero))
67.74/34.85	   new_rem(Neg(x0), Pos(Zero))
67.74/34.85	   new_primMinusNatS0(x0)
67.74/34.85	   new_primEqInt2
67.74/34.85	   new_esEs(Neg(Zero))
67.74/34.85	   new_esEs(Neg(Succ(x0)))
67.74/34.85	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.85	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.85	
67.74/34.85	We have to consider all minimal (P,Q,R)-chains.
67.74/34.85	----------------------------------------
67.74/34.85	
67.74/34.85	(180) TransformationProof (EQUIVALENT)
67.74/34.85	By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Succ(x2), Zero), Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]:
67.74/34.85	
67.74/34.85	   (new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))),new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))))
67.74/34.85	
67.74/34.85	
67.74/34.85	----------------------------------------
67.74/34.85	
67.74/34.85	(181)
67.74/34.85	Obligation:
67.74/34.85	Q DP problem:
67.74/34.85	The TRS P consists of the following rules:
67.74/34.85	
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.85	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.85	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(x1))), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, x1, x0, x1))), Neg(Succ(Succ(x1))), Pos(Succ(Succ(x0))))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, x1, x0, x1))), Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0))))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Zero, Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Zero))))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.85	
67.74/34.85	The TRS R consists of the following rules:
67.74/34.85	
67.74/34.85	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.85	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.85	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.85	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.85	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.85	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.85	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.85	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.85	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.85	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.85	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.85	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.85	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.85	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.85	   new_error -> error([])
67.74/34.85	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.85	   new_primEqInt2 -> True
67.74/34.85	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.85	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.85	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.85	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.85	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.85	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.85	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.85	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.85	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.85	   new_primMinusNatS1 -> Zero
67.74/34.85	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.85	   new_primEqInt1 -> True
67.74/34.85	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.85	   new_primEqInt0(vuz3260) -> False
67.74/34.85	   new_primEqInt(vuz3250) -> False
67.74/34.85	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.85	
67.74/34.85	The set Q consists of the following terms:
67.74/34.85	
67.74/34.85	   new_rem(Neg(x0), Neg(Zero))
67.74/34.85	   new_primEqInt1
67.74/34.85	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.85	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.85	   new_primMinusNatS1
67.74/34.85	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.85	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.85	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.85	   new_primMinusNatS2(Zero, Zero)
67.74/34.85	   new_error
67.74/34.85	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.85	   new_rem(Pos(x0), Pos(Zero))
67.74/34.85	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.85	   new_primEqInt0(x0)
67.74/34.85	   new_esEs(Pos(Zero))
67.74/34.85	   new_esEs(Pos(Succ(x0)))
67.74/34.85	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.85	   new_primModNatS02(x0, x1)
67.74/34.85	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.85	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.85	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.85	   new_primModNatS1(Zero, x0)
67.74/34.85	   new_primEqInt(x0)
67.74/34.85	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.85	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.85	   new_rem(Pos(x0), Neg(Zero))
67.74/34.85	   new_rem(Neg(x0), Pos(Zero))
67.74/34.85	   new_primMinusNatS0(x0)
67.74/34.85	   new_primEqInt2
67.74/34.85	   new_esEs(Neg(Zero))
67.74/34.85	   new_esEs(Neg(Succ(x0)))
67.74/34.85	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.85	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.85	
67.74/34.85	We have to consider all minimal (P,Q,R)-chains.
67.74/34.85	----------------------------------------
67.74/34.85	
67.74/34.85	(182) TransformationProof (EQUIVALENT)
67.74/34.85	By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Zero, Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))) at position [0,0,0] we obtained the following new rules [LPAR04]:
67.74/34.85	
67.74/34.85	   (new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Pos(Zero)), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))),new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Pos(Zero)), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))))
67.74/34.85	
67.74/34.85	
67.74/34.85	----------------------------------------
67.74/34.85	
67.74/34.85	(183)
67.74/34.85	Obligation:
67.74/34.85	Q DP problem:
67.74/34.85	The TRS P consists of the following rules:
67.74/34.85	
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.85	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.85	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(x1))), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, x1, x0, x1))), Neg(Succ(Succ(x1))), Pos(Succ(Succ(x0))))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, x1, x0, x1))), Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0))))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Pos(Zero)), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Zero))))
67.74/34.85	
67.74/34.85	The TRS R consists of the following rules:
67.74/34.85	
67.74/34.85	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.85	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.85	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.85	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.85	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.85	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.85	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.85	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.85	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.85	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.85	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.85	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.85	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.85	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.85	   new_error -> error([])
67.74/34.85	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.85	   new_primEqInt2 -> True
67.74/34.85	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.85	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.85	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.85	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.85	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.85	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.85	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.85	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.85	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.85	   new_primMinusNatS1 -> Zero
67.74/34.85	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.85	   new_primEqInt1 -> True
67.74/34.85	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.85	   new_primEqInt0(vuz3260) -> False
67.74/34.85	   new_primEqInt(vuz3250) -> False
67.74/34.85	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.85	
67.74/34.85	The set Q consists of the following terms:
67.74/34.85	
67.74/34.85	   new_rem(Neg(x0), Neg(Zero))
67.74/34.85	   new_primEqInt1
67.74/34.85	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.85	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.85	   new_primMinusNatS1
67.74/34.85	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.85	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.85	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.85	   new_primMinusNatS2(Zero, Zero)
67.74/34.85	   new_error
67.74/34.85	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.85	   new_rem(Pos(x0), Pos(Zero))
67.74/34.85	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.85	   new_primEqInt0(x0)
67.74/34.85	   new_esEs(Pos(Zero))
67.74/34.85	   new_esEs(Pos(Succ(x0)))
67.74/34.85	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.85	   new_primModNatS02(x0, x1)
67.74/34.85	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.85	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.85	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.85	   new_primModNatS1(Zero, x0)
67.74/34.85	   new_primEqInt(x0)
67.74/34.85	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.85	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.85	   new_rem(Pos(x0), Neg(Zero))
67.74/34.85	   new_rem(Neg(x0), Pos(Zero))
67.74/34.85	   new_primMinusNatS0(x0)
67.74/34.85	   new_primEqInt2
67.74/34.85	   new_esEs(Neg(Zero))
67.74/34.85	   new_esEs(Neg(Succ(x0)))
67.74/34.85	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.85	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.85	
67.74/34.85	We have to consider all minimal (P,Q,R)-chains.
67.74/34.85	----------------------------------------
67.74/34.85	
67.74/34.85	(184) DependencyGraphProof (EQUIVALENT)
67.74/34.85	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
67.74/34.85	----------------------------------------
67.74/34.85	
67.74/34.85	(185)
67.74/34.85	Obligation:
67.74/34.85	Q DP problem:
67.74/34.85	The TRS P consists of the following rules:
67.74/34.85	
67.74/34.85	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.85	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(x1))), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, x1, x0, x1))), Neg(Succ(Succ(x1))), Pos(Succ(Succ(x0))))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, x1, x0, x1))), Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0))))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.85	
67.74/34.85	The TRS R consists of the following rules:
67.74/34.85	
67.74/34.85	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.85	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.85	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.85	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.85	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.85	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.85	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.85	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.85	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.85	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.85	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.85	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.85	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.85	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.85	   new_error -> error([])
67.74/34.85	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.85	   new_primEqInt2 -> True
67.74/34.85	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.85	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.85	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.85	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.85	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.85	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.85	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.85	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.85	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.85	   new_primMinusNatS1 -> Zero
67.74/34.85	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.85	   new_primEqInt1 -> True
67.74/34.85	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.85	   new_primEqInt0(vuz3260) -> False
67.74/34.85	   new_primEqInt(vuz3250) -> False
67.74/34.85	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.85	
67.74/34.85	The set Q consists of the following terms:
67.74/34.85	
67.74/34.85	   new_rem(Neg(x0), Neg(Zero))
67.74/34.85	   new_primEqInt1
67.74/34.85	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.85	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.85	   new_primMinusNatS1
67.74/34.85	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.85	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.85	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.85	   new_primMinusNatS2(Zero, Zero)
67.74/34.85	   new_error
67.74/34.85	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.85	   new_rem(Pos(x0), Pos(Zero))
67.74/34.85	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.85	   new_primEqInt0(x0)
67.74/34.85	   new_esEs(Pos(Zero))
67.74/34.85	   new_esEs(Pos(Succ(x0)))
67.74/34.85	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.85	   new_primModNatS02(x0, x1)
67.74/34.85	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.85	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.85	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.85	   new_primModNatS1(Zero, x0)
67.74/34.85	   new_primEqInt(x0)
67.74/34.85	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.85	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.85	   new_rem(Pos(x0), Neg(Zero))
67.74/34.85	   new_rem(Neg(x0), Pos(Zero))
67.74/34.85	   new_primMinusNatS0(x0)
67.74/34.85	   new_primEqInt2
67.74/34.85	   new_esEs(Neg(Zero))
67.74/34.85	   new_esEs(Neg(Succ(x0)))
67.74/34.85	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.85	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.85	
67.74/34.85	We have to consider all minimal (P,Q,R)-chains.
67.74/34.85	----------------------------------------
67.74/34.85	
67.74/34.85	(186) TransformationProof (EQUIVALENT)
67.74/34.85	By narrowing [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(x0)))) at position [0] we obtained the following new rules [LPAR04]:
67.74/34.85	
67.74/34.85	   (new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS0(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))),new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS0(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))))
67.74/34.85	   (new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS1, Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Zero)))),new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS1, Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Zero)))))
67.74/34.85	
67.74/34.85	
67.74/34.85	----------------------------------------
67.74/34.85	
67.74/34.85	(187)
67.74/34.85	Obligation:
67.74/34.85	Q DP problem:
67.74/34.85	The TRS P consists of the following rules:
67.74/34.85	
67.74/34.85	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.85	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.85	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.85	   new_gcd0Gcd'(Neg(Succ(Succ(x1))), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, x1, x0, x1))), Neg(Succ(Succ(x1))), Pos(Succ(Succ(x0))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, x1, x0, x1))), Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS0(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS1, Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Zero))))
67.74/34.86	
67.74/34.86	The TRS R consists of the following rules:
67.74/34.86	
67.74/34.86	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.86	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.86	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.86	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.86	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.86	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.86	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.86	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.86	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.86	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.86	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.86	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.86	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.86	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.86	   new_error -> error([])
67.74/34.86	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.86	   new_primEqInt2 -> True
67.74/34.86	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.86	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.86	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.86	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.86	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.86	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.86	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.86	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.86	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.86	   new_primMinusNatS1 -> Zero
67.74/34.86	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.86	   new_primEqInt1 -> True
67.74/34.86	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.86	   new_primEqInt0(vuz3260) -> False
67.74/34.86	   new_primEqInt(vuz3250) -> False
67.74/34.86	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.86	
67.74/34.86	The set Q consists of the following terms:
67.74/34.86	
67.74/34.86	   new_rem(Neg(x0), Neg(Zero))
67.74/34.86	   new_primEqInt1
67.74/34.86	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.86	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.86	   new_primMinusNatS1
67.74/34.86	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.86	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.86	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.86	   new_primMinusNatS2(Zero, Zero)
67.74/34.86	   new_error
67.74/34.86	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.86	   new_rem(Pos(x0), Pos(Zero))
67.74/34.86	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.86	   new_primEqInt0(x0)
67.74/34.86	   new_esEs(Pos(Zero))
67.74/34.86	   new_esEs(Pos(Succ(x0)))
67.74/34.86	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.86	   new_primModNatS02(x0, x1)
67.74/34.86	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.86	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.86	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.86	   new_primModNatS1(Zero, x0)
67.74/34.86	   new_primEqInt(x0)
67.74/34.86	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.86	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.86	   new_rem(Pos(x0), Neg(Zero))
67.74/34.86	   new_rem(Neg(x0), Pos(Zero))
67.74/34.86	   new_primMinusNatS0(x0)
67.74/34.86	   new_primEqInt2
67.74/34.86	   new_esEs(Neg(Zero))
67.74/34.86	   new_esEs(Neg(Succ(x0)))
67.74/34.86	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.86	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.86	
67.74/34.86	We have to consider all minimal (P,Q,R)-chains.
67.74/34.86	----------------------------------------
67.74/34.86	
67.74/34.86	(188) TransformationProof (EQUIVALENT)
67.74/34.86	By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS0(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]:
67.74/34.86	
67.74/34.86	   (new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))),new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))))
67.74/34.86	
67.74/34.86	
67.74/34.86	----------------------------------------
67.74/34.86	
67.74/34.86	(189)
67.74/34.86	Obligation:
67.74/34.86	Q DP problem:
67.74/34.86	The TRS P consists of the following rules:
67.74/34.86	
67.74/34.86	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.86	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(x1))), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, x1, x0, x1))), Neg(Succ(Succ(x1))), Pos(Succ(Succ(x0))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, x1, x0, x1))), Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS1, Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Zero))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.86	
67.74/34.86	The TRS R consists of the following rules:
67.74/34.86	
67.74/34.86	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.86	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.86	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.86	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.86	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.86	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.86	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.86	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.86	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.86	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.86	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.86	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.86	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.86	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.86	   new_error -> error([])
67.74/34.86	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.86	   new_primEqInt2 -> True
67.74/34.86	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.86	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.86	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.86	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.86	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.86	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.86	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.86	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.86	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.86	   new_primMinusNatS1 -> Zero
67.74/34.86	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.86	   new_primEqInt1 -> True
67.74/34.86	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.86	   new_primEqInt0(vuz3260) -> False
67.74/34.86	   new_primEqInt(vuz3250) -> False
67.74/34.86	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.86	
67.74/34.86	The set Q consists of the following terms:
67.74/34.86	
67.74/34.86	   new_rem(Neg(x0), Neg(Zero))
67.74/34.86	   new_primEqInt1
67.74/34.86	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.86	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.86	   new_primMinusNatS1
67.74/34.86	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.86	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.86	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.86	   new_primMinusNatS2(Zero, Zero)
67.74/34.86	   new_error
67.74/34.86	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.86	   new_rem(Pos(x0), Pos(Zero))
67.74/34.86	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.86	   new_primEqInt0(x0)
67.74/34.86	   new_esEs(Pos(Zero))
67.74/34.86	   new_esEs(Pos(Succ(x0)))
67.74/34.86	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.86	   new_primModNatS02(x0, x1)
67.74/34.86	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.86	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.86	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.86	   new_primModNatS1(Zero, x0)
67.74/34.86	   new_primEqInt(x0)
67.74/34.86	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.86	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.86	   new_rem(Pos(x0), Neg(Zero))
67.74/34.86	   new_rem(Neg(x0), Pos(Zero))
67.74/34.86	   new_primMinusNatS0(x0)
67.74/34.86	   new_primEqInt2
67.74/34.86	   new_esEs(Neg(Zero))
67.74/34.86	   new_esEs(Neg(Succ(x0)))
67.74/34.86	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.86	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.86	
67.74/34.86	We have to consider all minimal (P,Q,R)-chains.
67.74/34.86	----------------------------------------
67.74/34.86	
67.74/34.86	(190) TransformationProof (EQUIVALENT)
67.74/34.86	By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS1, Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Zero)))) at position [0,0,0,0] we obtained the following new rules [LPAR04]:
67.74/34.86	
67.74/34.86	   (new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Zero, Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Zero)))),new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Zero, Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Zero)))))
67.74/34.86	
67.74/34.86	
67.74/34.86	----------------------------------------
67.74/34.86	
67.74/34.86	(191)
67.74/34.86	Obligation:
67.74/34.86	Q DP problem:
67.74/34.86	The TRS P consists of the following rules:
67.74/34.86	
67.74/34.86	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.86	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(x1))), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, x1, x0, x1))), Neg(Succ(Succ(x1))), Pos(Succ(Succ(x0))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, x1, x0, x1))), Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Zero, Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Zero))))
67.74/34.86	
67.74/34.86	The TRS R consists of the following rules:
67.74/34.86	
67.74/34.86	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.86	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.86	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.86	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.86	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.86	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.86	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.86	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.86	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.86	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.86	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.86	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.86	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.86	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.86	   new_error -> error([])
67.74/34.86	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.86	   new_primEqInt2 -> True
67.74/34.86	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.86	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.86	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.86	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.86	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.86	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.86	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.86	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.86	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.86	   new_primMinusNatS1 -> Zero
67.74/34.86	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.86	   new_primEqInt1 -> True
67.74/34.86	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.86	   new_primEqInt0(vuz3260) -> False
67.74/34.86	   new_primEqInt(vuz3250) -> False
67.74/34.86	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.86	
67.74/34.86	The set Q consists of the following terms:
67.74/34.86	
67.74/34.86	   new_rem(Neg(x0), Neg(Zero))
67.74/34.86	   new_primEqInt1
67.74/34.86	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.86	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.86	   new_primMinusNatS1
67.74/34.86	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.86	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.86	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.86	   new_primMinusNatS2(Zero, Zero)
67.74/34.86	   new_error
67.74/34.86	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.86	   new_rem(Pos(x0), Pos(Zero))
67.74/34.86	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.86	   new_primEqInt0(x0)
67.74/34.86	   new_esEs(Pos(Zero))
67.74/34.86	   new_esEs(Pos(Succ(x0)))
67.74/34.86	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.86	   new_primModNatS02(x0, x1)
67.74/34.86	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.86	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.86	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.86	   new_primModNatS1(Zero, x0)
67.74/34.86	   new_primEqInt(x0)
67.74/34.86	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.86	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.86	   new_rem(Pos(x0), Neg(Zero))
67.74/34.86	   new_rem(Neg(x0), Pos(Zero))
67.74/34.86	   new_primMinusNatS0(x0)
67.74/34.86	   new_primEqInt2
67.74/34.86	   new_esEs(Neg(Zero))
67.74/34.86	   new_esEs(Neg(Succ(x0)))
67.74/34.86	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.86	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.86	
67.74/34.86	We have to consider all minimal (P,Q,R)-chains.
67.74/34.86	----------------------------------------
67.74/34.86	
67.74/34.86	(192) TransformationProof (EQUIVALENT)
67.74/34.86	By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Zero, Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Zero)))) at position [0,0,0] we obtained the following new rules [LPAR04]:
67.74/34.86	
67.74/34.86	   (new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Pos(Zero)), Pos(Succ(Zero)), Pos(Succ(Succ(Zero)))),new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Pos(Zero)), Pos(Succ(Zero)), Pos(Succ(Succ(Zero)))))
67.74/34.86	
67.74/34.86	
67.74/34.86	----------------------------------------
67.74/34.86	
67.74/34.86	(193)
67.74/34.86	Obligation:
67.74/34.86	Q DP problem:
67.74/34.86	The TRS P consists of the following rules:
67.74/34.86	
67.74/34.86	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.86	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(x1))), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, x1, x0, x1))), Neg(Succ(Succ(x1))), Pos(Succ(Succ(x0))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, x1, x0, x1))), Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Pos(Zero)), Pos(Succ(Zero)), Pos(Succ(Succ(Zero))))
67.74/34.86	
67.74/34.86	The TRS R consists of the following rules:
67.74/34.86	
67.74/34.86	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.86	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.86	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.86	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.86	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.86	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.86	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.86	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.86	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.86	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.86	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.86	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.86	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.86	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.86	   new_error -> error([])
67.74/34.86	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.86	   new_primEqInt2 -> True
67.74/34.86	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.86	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.86	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.86	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.86	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.86	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.86	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.86	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.86	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.86	   new_primMinusNatS1 -> Zero
67.74/34.86	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.86	   new_primEqInt1 -> True
67.74/34.86	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.86	   new_primEqInt0(vuz3260) -> False
67.74/34.86	   new_primEqInt(vuz3250) -> False
67.74/34.86	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.86	
67.74/34.86	The set Q consists of the following terms:
67.74/34.86	
67.74/34.86	   new_rem(Neg(x0), Neg(Zero))
67.74/34.86	   new_primEqInt1
67.74/34.86	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.86	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.86	   new_primMinusNatS1
67.74/34.86	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.86	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.86	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.86	   new_primMinusNatS2(Zero, Zero)
67.74/34.86	   new_error
67.74/34.86	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.86	   new_rem(Pos(x0), Pos(Zero))
67.74/34.86	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.86	   new_primEqInt0(x0)
67.74/34.86	   new_esEs(Pos(Zero))
67.74/34.86	   new_esEs(Pos(Succ(x0)))
67.74/34.86	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.86	   new_primModNatS02(x0, x1)
67.74/34.86	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.86	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.86	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.86	   new_primModNatS1(Zero, x0)
67.74/34.86	   new_primEqInt(x0)
67.74/34.86	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.86	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.86	   new_rem(Pos(x0), Neg(Zero))
67.74/34.86	   new_rem(Neg(x0), Pos(Zero))
67.74/34.86	   new_primMinusNatS0(x0)
67.74/34.86	   new_primEqInt2
67.74/34.86	   new_esEs(Neg(Zero))
67.74/34.86	   new_esEs(Neg(Succ(x0)))
67.74/34.86	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.86	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.86	
67.74/34.86	We have to consider all minimal (P,Q,R)-chains.
67.74/34.86	----------------------------------------
67.74/34.86	
67.74/34.86	(194) DependencyGraphProof (EQUIVALENT)
67.74/34.86	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
67.74/34.86	----------------------------------------
67.74/34.86	
67.74/34.86	(195)
67.74/34.86	Obligation:
67.74/34.86	Q DP problem:
67.74/34.86	The TRS P consists of the following rules:
67.74/34.86	
67.74/34.86	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.86	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(x1))), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, x1, x0, x1))), Neg(Succ(Succ(x1))), Pos(Succ(Succ(x0))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, x1, x0, x1))), Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.86	
67.74/34.86	The TRS R consists of the following rules:
67.74/34.86	
67.74/34.86	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.86	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.86	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.86	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.86	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.86	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.86	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.86	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.86	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.86	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.86	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.86	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.86	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.86	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.86	   new_error -> error([])
67.74/34.86	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.86	   new_primEqInt2 -> True
67.74/34.86	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.86	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.86	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.86	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.86	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.86	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.86	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.86	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.86	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.86	   new_primMinusNatS1 -> Zero
67.74/34.86	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.86	   new_primEqInt1 -> True
67.74/34.86	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.86	   new_primEqInt0(vuz3260) -> False
67.74/34.86	   new_primEqInt(vuz3250) -> False
67.74/34.86	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.86	
67.74/34.86	The set Q consists of the following terms:
67.74/34.86	
67.74/34.86	   new_rem(Neg(x0), Neg(Zero))
67.74/34.86	   new_primEqInt1
67.74/34.86	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.86	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.86	   new_primMinusNatS1
67.74/34.86	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.86	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.86	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.86	   new_primMinusNatS2(Zero, Zero)
67.74/34.86	   new_error
67.74/34.86	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.86	   new_rem(Pos(x0), Pos(Zero))
67.74/34.86	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.86	   new_primEqInt0(x0)
67.74/34.86	   new_esEs(Pos(Zero))
67.74/34.86	   new_esEs(Pos(Succ(x0)))
67.74/34.86	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.86	   new_primModNatS02(x0, x1)
67.74/34.86	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.86	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.86	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.86	   new_primModNatS1(Zero, x0)
67.74/34.86	   new_primEqInt(x0)
67.74/34.86	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.86	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.86	   new_rem(Pos(x0), Neg(Zero))
67.74/34.86	   new_rem(Neg(x0), Pos(Zero))
67.74/34.86	   new_primMinusNatS0(x0)
67.74/34.86	   new_primEqInt2
67.74/34.86	   new_esEs(Neg(Zero))
67.74/34.86	   new_esEs(Neg(Succ(x0)))
67.74/34.86	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.86	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.86	
67.74/34.86	We have to consider all minimal (P,Q,R)-chains.
67.74/34.86	----------------------------------------
67.74/34.86	
67.74/34.86	(196) TransformationProof (EQUIVALENT)
67.74/34.86	By narrowing [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(x1))), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, x1, x0, x1))), Neg(Succ(Succ(x1))), Pos(Succ(Succ(x0)))) at position [0] we obtained the following new rules [LPAR04]:
67.74/34.86	
67.74/34.86	   (new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))))
67.74/34.86	   (new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Pos(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Pos(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))))
67.74/34.86	   (new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS02(Zero, Zero))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))),new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS02(Zero, Zero))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))))
67.74/34.86	   (new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS02(Succ(x2), Zero))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))),new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS02(Succ(x2), Zero))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))))
67.74/34.86	
67.74/34.86	
67.74/34.86	----------------------------------------
67.74/34.86	
67.74/34.86	(197)
67.74/34.86	Obligation:
67.74/34.86	Q DP problem:
67.74/34.86	The TRS P consists of the following rules:
67.74/34.86	
67.74/34.86	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.86	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, x1, x0, x1))), Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Pos(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS02(Zero, Zero))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Zero))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS02(Succ(x2), Zero))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.86	
67.74/34.86	The TRS R consists of the following rules:
67.74/34.86	
67.74/34.86	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.86	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.86	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.86	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.86	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.86	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.86	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.86	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.86	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.86	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.86	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.86	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.86	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.86	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.86	   new_error -> error([])
67.74/34.86	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.86	   new_primEqInt2 -> True
67.74/34.86	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.86	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.86	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.86	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.86	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.86	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.86	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.86	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.86	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.86	   new_primMinusNatS1 -> Zero
67.74/34.86	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.86	   new_primEqInt1 -> True
67.74/34.86	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.86	   new_primEqInt0(vuz3260) -> False
67.74/34.86	   new_primEqInt(vuz3250) -> False
67.74/34.86	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.86	
67.74/34.86	The set Q consists of the following terms:
67.74/34.86	
67.74/34.86	   new_rem(Neg(x0), Neg(Zero))
67.74/34.86	   new_primEqInt1
67.74/34.86	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.86	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.86	   new_primMinusNatS1
67.74/34.86	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.86	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.86	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.86	   new_primMinusNatS2(Zero, Zero)
67.74/34.86	   new_error
67.74/34.86	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.86	   new_rem(Pos(x0), Pos(Zero))
67.74/34.86	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.86	   new_primEqInt0(x0)
67.74/34.86	   new_esEs(Pos(Zero))
67.74/34.86	   new_esEs(Pos(Succ(x0)))
67.74/34.86	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.86	   new_primModNatS02(x0, x1)
67.74/34.86	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.86	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.86	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.86	   new_primModNatS1(Zero, x0)
67.74/34.86	   new_primEqInt(x0)
67.74/34.86	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.86	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.86	   new_rem(Pos(x0), Neg(Zero))
67.74/34.86	   new_rem(Neg(x0), Pos(Zero))
67.74/34.86	   new_primMinusNatS0(x0)
67.74/34.86	   new_primEqInt2
67.74/34.86	   new_esEs(Neg(Zero))
67.74/34.86	   new_esEs(Neg(Succ(x0)))
67.74/34.86	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.86	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.86	
67.74/34.86	We have to consider all minimal (P,Q,R)-chains.
67.74/34.86	----------------------------------------
67.74/34.86	
67.74/34.86	(198) TransformationProof (EQUIVALENT)
67.74/34.86	By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Pos(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) at position [0] we obtained the following new rules [LPAR04]:
67.74/34.86	
67.74/34.86	   (new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_primEqInt(Succ(Zero)), Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_primEqInt(Succ(Zero)), Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))))
67.74/34.86	
67.74/34.86	
67.74/34.86	----------------------------------------
67.74/34.86	
67.74/34.86	(199)
67.74/34.86	Obligation:
67.74/34.86	Q DP problem:
67.74/34.86	The TRS P consists of the following rules:
67.74/34.86	
67.74/34.86	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.86	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, x1, x0, x1))), Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS02(Zero, Zero))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Zero))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS02(Succ(x2), Zero))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_primEqInt(Succ(Zero)), Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.86	
67.74/34.86	The TRS R consists of the following rules:
67.74/34.86	
67.74/34.86	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.86	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.86	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.86	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.86	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.86	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.86	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.86	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.86	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.86	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.86	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.86	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.86	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.86	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.86	   new_error -> error([])
67.74/34.86	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.86	   new_primEqInt2 -> True
67.74/34.86	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.86	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.86	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.86	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.86	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.86	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.86	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.86	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.86	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.86	   new_primMinusNatS1 -> Zero
67.74/34.86	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.86	   new_primEqInt1 -> True
67.74/34.86	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.86	   new_primEqInt0(vuz3260) -> False
67.74/34.86	   new_primEqInt(vuz3250) -> False
67.74/34.86	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.86	
67.74/34.86	The set Q consists of the following terms:
67.74/34.86	
67.74/34.86	   new_rem(Neg(x0), Neg(Zero))
67.74/34.86	   new_primEqInt1
67.74/34.86	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.86	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.86	   new_primMinusNatS1
67.74/34.86	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.86	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.86	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.86	   new_primMinusNatS2(Zero, Zero)
67.74/34.86	   new_error
67.74/34.86	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.86	   new_rem(Pos(x0), Pos(Zero))
67.74/34.86	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.86	   new_primEqInt0(x0)
67.74/34.86	   new_esEs(Pos(Zero))
67.74/34.86	   new_esEs(Pos(Succ(x0)))
67.74/34.86	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.86	   new_primModNatS02(x0, x1)
67.74/34.86	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.86	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.86	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.86	   new_primModNatS1(Zero, x0)
67.74/34.86	   new_primEqInt(x0)
67.74/34.86	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.86	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.86	   new_rem(Pos(x0), Neg(Zero))
67.74/34.86	   new_rem(Neg(x0), Pos(Zero))
67.74/34.86	   new_primMinusNatS0(x0)
67.74/34.86	   new_primEqInt2
67.74/34.86	   new_esEs(Neg(Zero))
67.74/34.86	   new_esEs(Neg(Succ(x0)))
67.74/34.86	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.86	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.86	
67.74/34.86	We have to consider all minimal (P,Q,R)-chains.
67.74/34.86	----------------------------------------
67.74/34.86	
67.74/34.86	(200) TransformationProof (EQUIVALENT)
67.74/34.86	By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS02(Zero, Zero))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))) at position [0,0,0] we obtained the following new rules [LPAR04]:
67.74/34.86	
67.74/34.86	   (new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Succ(Zero), Succ(Zero)), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))),new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Succ(Zero), Succ(Zero)), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))))
67.74/34.86	
67.74/34.86	
67.74/34.86	----------------------------------------
67.74/34.86	
67.74/34.86	(201)
67.74/34.86	Obligation:
67.74/34.86	Q DP problem:
67.74/34.86	The TRS P consists of the following rules:
67.74/34.86	
67.74/34.86	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.86	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, x1, x0, x1))), Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS02(Succ(x2), Zero))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_primEqInt(Succ(Zero)), Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Succ(Zero), Succ(Zero)), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Zero))))
67.74/34.86	
67.74/34.86	The TRS R consists of the following rules:
67.74/34.86	
67.74/34.86	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.86	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.86	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.86	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.86	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.86	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.86	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.86	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.86	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.86	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.86	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.86	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.86	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.86	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.86	   new_error -> error([])
67.74/34.86	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.86	   new_primEqInt2 -> True
67.74/34.86	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.86	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.86	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.86	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.86	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.86	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.86	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.86	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.86	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.86	   new_primMinusNatS1 -> Zero
67.74/34.86	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.86	   new_primEqInt1 -> True
67.74/34.86	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.86	   new_primEqInt0(vuz3260) -> False
67.74/34.86	   new_primEqInt(vuz3250) -> False
67.74/34.86	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.86	
67.74/34.86	The set Q consists of the following terms:
67.74/34.86	
67.74/34.86	   new_rem(Neg(x0), Neg(Zero))
67.74/34.86	   new_primEqInt1
67.74/34.86	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.86	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.86	   new_primMinusNatS1
67.74/34.86	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.86	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.86	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.86	   new_primMinusNatS2(Zero, Zero)
67.74/34.86	   new_error
67.74/34.86	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.86	   new_rem(Pos(x0), Pos(Zero))
67.74/34.86	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.86	   new_primEqInt0(x0)
67.74/34.86	   new_esEs(Pos(Zero))
67.74/34.86	   new_esEs(Pos(Succ(x0)))
67.74/34.86	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.86	   new_primModNatS02(x0, x1)
67.74/34.86	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.86	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.86	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.86	   new_primModNatS1(Zero, x0)
67.74/34.86	   new_primEqInt(x0)
67.74/34.86	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.86	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.86	   new_rem(Pos(x0), Neg(Zero))
67.74/34.86	   new_rem(Neg(x0), Pos(Zero))
67.74/34.86	   new_primMinusNatS0(x0)
67.74/34.86	   new_primEqInt2
67.74/34.86	   new_esEs(Neg(Zero))
67.74/34.86	   new_esEs(Neg(Succ(x0)))
67.74/34.86	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.86	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.86	
67.74/34.86	We have to consider all minimal (P,Q,R)-chains.
67.74/34.86	----------------------------------------
67.74/34.86	
67.74/34.86	(202) TransformationProof (EQUIVALENT)
67.74/34.86	By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS02(Succ(x2), Zero))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) at position [0,0,0] we obtained the following new rules [LPAR04]:
67.74/34.86	
67.74/34.86	   (new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Succ(Succ(x2)), Succ(Zero)), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))),new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Succ(Succ(x2)), Succ(Zero)), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))))
67.74/34.86	
67.74/34.86	
67.74/34.86	----------------------------------------
67.74/34.86	
67.74/34.86	(203)
67.74/34.86	Obligation:
67.74/34.86	Q DP problem:
67.74/34.86	The TRS P consists of the following rules:
67.74/34.86	
67.74/34.86	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.86	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, x1, x0, x1))), Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_primEqInt(Succ(Zero)), Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Succ(Zero), Succ(Zero)), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Zero))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Succ(Succ(x2)), Succ(Zero)), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.86	
67.74/34.86	The TRS R consists of the following rules:
67.74/34.86	
67.74/34.86	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.86	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.86	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.86	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.86	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.86	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.86	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.86	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.86	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.86	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.86	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.86	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.86	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.86	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.86	   new_error -> error([])
67.74/34.86	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.86	   new_primEqInt2 -> True
67.74/34.86	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.86	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.86	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.86	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.86	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.86	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.86	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.86	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.86	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.86	   new_primMinusNatS1 -> Zero
67.74/34.86	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.86	   new_primEqInt1 -> True
67.74/34.86	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.86	   new_primEqInt0(vuz3260) -> False
67.74/34.86	   new_primEqInt(vuz3250) -> False
67.74/34.86	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.86	
67.74/34.86	The set Q consists of the following terms:
67.74/34.86	
67.74/34.86	   new_rem(Neg(x0), Neg(Zero))
67.74/34.86	   new_primEqInt1
67.74/34.86	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.86	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.86	   new_primMinusNatS1
67.74/34.86	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.86	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.86	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.86	   new_primMinusNatS2(Zero, Zero)
67.74/34.86	   new_error
67.74/34.86	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.86	   new_rem(Pos(x0), Pos(Zero))
67.74/34.86	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.86	   new_primEqInt0(x0)
67.74/34.86	   new_esEs(Pos(Zero))
67.74/34.86	   new_esEs(Pos(Succ(x0)))
67.74/34.86	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.86	   new_primModNatS02(x0, x1)
67.74/34.86	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.86	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.86	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.86	   new_primModNatS1(Zero, x0)
67.74/34.86	   new_primEqInt(x0)
67.74/34.86	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.86	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.86	   new_rem(Pos(x0), Neg(Zero))
67.74/34.86	   new_rem(Neg(x0), Pos(Zero))
67.74/34.86	   new_primMinusNatS0(x0)
67.74/34.86	   new_primEqInt2
67.74/34.86	   new_esEs(Neg(Zero))
67.74/34.86	   new_esEs(Neg(Succ(x0)))
67.74/34.86	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.86	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.86	
67.74/34.86	We have to consider all minimal (P,Q,R)-chains.
67.74/34.86	----------------------------------------
67.74/34.86	
67.74/34.86	(204) TransformationProof (EQUIVALENT)
67.74/34.86	By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_primEqInt(Succ(Zero)), Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) at position [0] we obtained the following new rules [LPAR04]:
67.74/34.86	
67.74/34.86	   (new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))))
67.74/34.86	
67.74/34.86	
67.74/34.86	----------------------------------------
67.74/34.86	
67.74/34.86	(205)
67.74/34.86	Obligation:
67.74/34.86	Q DP problem:
67.74/34.86	The TRS P consists of the following rules:
67.74/34.86	
67.74/34.86	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.86	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, x1, x0, x1))), Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Succ(Zero), Succ(Zero)), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Zero))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Succ(Succ(x2)), Succ(Zero)), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.86	
67.74/34.86	The TRS R consists of the following rules:
67.74/34.86	
67.74/34.86	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.86	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.86	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.86	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.86	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.86	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.86	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.86	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.86	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.86	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.86	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.86	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.86	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.86	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.86	   new_error -> error([])
67.74/34.86	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.86	   new_primEqInt2 -> True
67.74/34.86	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.86	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.86	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.86	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.86	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.86	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.86	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.86	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.86	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.86	   new_primMinusNatS1 -> Zero
67.74/34.86	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.86	   new_primEqInt1 -> True
67.74/34.86	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.86	   new_primEqInt0(vuz3260) -> False
67.74/34.86	   new_primEqInt(vuz3250) -> False
67.74/34.86	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.86	
67.74/34.86	The set Q consists of the following terms:
67.74/34.86	
67.74/34.86	   new_rem(Neg(x0), Neg(Zero))
67.74/34.86	   new_primEqInt1
67.74/34.86	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.86	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.86	   new_primMinusNatS1
67.74/34.86	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.86	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.86	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.86	   new_primMinusNatS2(Zero, Zero)
67.74/34.86	   new_error
67.74/34.86	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.86	   new_rem(Pos(x0), Pos(Zero))
67.74/34.86	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.86	   new_primEqInt0(x0)
67.74/34.86	   new_esEs(Pos(Zero))
67.74/34.86	   new_esEs(Pos(Succ(x0)))
67.74/34.86	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.86	   new_primModNatS02(x0, x1)
67.74/34.86	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.86	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.86	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.86	   new_primModNatS1(Zero, x0)
67.74/34.86	   new_primEqInt(x0)
67.74/34.86	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.86	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.86	   new_rem(Pos(x0), Neg(Zero))
67.74/34.86	   new_rem(Neg(x0), Pos(Zero))
67.74/34.86	   new_primMinusNatS0(x0)
67.74/34.86	   new_primEqInt2
67.74/34.86	   new_esEs(Neg(Zero))
67.74/34.86	   new_esEs(Neg(Succ(x0)))
67.74/34.86	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.86	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.86	
67.74/34.86	We have to consider all minimal (P,Q,R)-chains.
67.74/34.86	----------------------------------------
67.74/34.86	
67.74/34.86	(206) TransformationProof (EQUIVALENT)
67.74/34.86	By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Succ(Zero), Succ(Zero)), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))) at position [0,0,0,0] we obtained the following new rules [LPAR04]:
67.74/34.86	
67.74/34.86	   (new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Zero, Zero), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))),new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Zero, Zero), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))))
67.74/34.86	
67.74/34.86	
67.74/34.86	----------------------------------------
67.74/34.86	
67.74/34.86	(207)
67.74/34.86	Obligation:
67.74/34.86	Q DP problem:
67.74/34.86	The TRS P consists of the following rules:
67.74/34.86	
67.74/34.86	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.86	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, x1, x0, x1))), Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Succ(Succ(x2)), Succ(Zero)), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Zero, Zero), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Zero))))
67.74/34.86	
67.74/34.86	The TRS R consists of the following rules:
67.74/34.86	
67.74/34.86	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.86	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.86	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.86	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.86	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.86	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.86	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.86	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.86	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.86	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.86	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.86	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.86	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.86	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.86	   new_error -> error([])
67.74/34.86	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.86	   new_primEqInt2 -> True
67.74/34.86	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.86	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.86	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.86	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.86	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.86	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.86	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.86	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.86	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.86	   new_primMinusNatS1 -> Zero
67.74/34.86	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.86	   new_primEqInt1 -> True
67.74/34.86	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.86	   new_primEqInt0(vuz3260) -> False
67.74/34.86	   new_primEqInt(vuz3250) -> False
67.74/34.86	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.86	
67.74/34.86	The set Q consists of the following terms:
67.74/34.86	
67.74/34.86	   new_rem(Neg(x0), Neg(Zero))
67.74/34.86	   new_primEqInt1
67.74/34.86	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.86	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.86	   new_primMinusNatS1
67.74/34.86	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.86	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.86	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.86	   new_primMinusNatS2(Zero, Zero)
67.74/34.86	   new_error
67.74/34.86	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.86	   new_rem(Pos(x0), Pos(Zero))
67.74/34.86	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.86	   new_primEqInt0(x0)
67.74/34.86	   new_esEs(Pos(Zero))
67.74/34.86	   new_esEs(Pos(Succ(x0)))
67.74/34.86	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.86	   new_primModNatS02(x0, x1)
67.74/34.86	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.86	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.86	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.86	   new_primModNatS1(Zero, x0)
67.74/34.86	   new_primEqInt(x0)
67.74/34.86	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.86	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.86	   new_rem(Pos(x0), Neg(Zero))
67.74/34.86	   new_rem(Neg(x0), Pos(Zero))
67.74/34.86	   new_primMinusNatS0(x0)
67.74/34.86	   new_primEqInt2
67.74/34.86	   new_esEs(Neg(Zero))
67.74/34.86	   new_esEs(Neg(Succ(x0)))
67.74/34.86	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.86	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.86	
67.74/34.86	We have to consider all minimal (P,Q,R)-chains.
67.74/34.86	----------------------------------------
67.74/34.86	
67.74/34.86	(208) TransformationProof (EQUIVALENT)
67.74/34.86	By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Succ(Succ(x2)), Succ(Zero)), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]:
67.74/34.86	
67.74/34.86	   (new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Succ(x2), Zero), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))),new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Succ(x2), Zero), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))))
67.74/34.86	
67.74/34.86	
67.74/34.86	----------------------------------------
67.74/34.86	
67.74/34.86	(209)
67.74/34.86	Obligation:
67.74/34.86	Q DP problem:
67.74/34.86	The TRS P consists of the following rules:
67.74/34.86	
67.74/34.86	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.86	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, x1, x0, x1))), Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Zero, Zero), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Zero))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Succ(x2), Zero), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.86	
67.74/34.86	The TRS R consists of the following rules:
67.74/34.86	
67.74/34.86	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.86	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.86	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.86	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.86	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.86	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.86	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.86	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.86	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.86	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.86	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.86	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.86	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.86	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.86	   new_error -> error([])
67.74/34.86	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.86	   new_primEqInt2 -> True
67.74/34.86	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.86	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.86	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.86	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.86	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.86	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.86	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.86	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.86	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.86	   new_primMinusNatS1 -> Zero
67.74/34.86	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.86	   new_primEqInt1 -> True
67.74/34.86	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.86	   new_primEqInt0(vuz3260) -> False
67.74/34.86	   new_primEqInt(vuz3250) -> False
67.74/34.86	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.86	
67.74/34.86	The set Q consists of the following terms:
67.74/34.86	
67.74/34.86	   new_rem(Neg(x0), Neg(Zero))
67.74/34.86	   new_primEqInt1
67.74/34.86	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.86	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.86	   new_primMinusNatS1
67.74/34.86	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.86	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.86	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.86	   new_primMinusNatS2(Zero, Zero)
67.74/34.86	   new_error
67.74/34.86	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.86	   new_rem(Pos(x0), Pos(Zero))
67.74/34.86	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.86	   new_primEqInt0(x0)
67.74/34.86	   new_esEs(Pos(Zero))
67.74/34.86	   new_esEs(Pos(Succ(x0)))
67.74/34.86	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.86	   new_primModNatS02(x0, x1)
67.74/34.86	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.86	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.86	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.86	   new_primModNatS1(Zero, x0)
67.74/34.86	   new_primEqInt(x0)
67.74/34.86	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.86	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.86	   new_rem(Pos(x0), Neg(Zero))
67.74/34.86	   new_rem(Neg(x0), Pos(Zero))
67.74/34.86	   new_primMinusNatS0(x0)
67.74/34.86	   new_primEqInt2
67.74/34.86	   new_esEs(Neg(Zero))
67.74/34.86	   new_esEs(Neg(Succ(x0)))
67.74/34.86	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.86	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.86	
67.74/34.86	We have to consider all minimal (P,Q,R)-chains.
67.74/34.86	----------------------------------------
67.74/34.86	
67.74/34.86	(210) TransformationProof (EQUIVALENT)
67.74/34.86	By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Zero, Zero), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))) at position [0,0,0,0] we obtained the following new rules [LPAR04]:
67.74/34.86	
67.74/34.86	   (new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Zero, Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))),new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Zero, Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))))
67.74/34.86	
67.74/34.86	
67.74/34.86	----------------------------------------
67.74/34.86	
67.74/34.86	(211)
67.74/34.86	Obligation:
67.74/34.86	Q DP problem:
67.74/34.86	The TRS P consists of the following rules:
67.74/34.86	
67.74/34.86	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.86	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, x1, x0, x1))), Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Succ(x2), Zero), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Zero, Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Zero))))
67.74/34.86	
67.74/34.86	The TRS R consists of the following rules:
67.74/34.86	
67.74/34.86	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.86	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.86	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.86	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.86	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.86	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.86	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.86	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.86	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.86	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.86	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.86	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.86	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.86	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.86	   new_error -> error([])
67.74/34.86	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.86	   new_primEqInt2 -> True
67.74/34.86	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.86	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.86	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.86	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.86	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.86	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.86	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.86	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.86	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.86	   new_primMinusNatS1 -> Zero
67.74/34.86	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.86	   new_primEqInt1 -> True
67.74/34.86	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.86	   new_primEqInt0(vuz3260) -> False
67.74/34.86	   new_primEqInt(vuz3250) -> False
67.74/34.86	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.86	
67.74/34.86	The set Q consists of the following terms:
67.74/34.86	
67.74/34.86	   new_rem(Neg(x0), Neg(Zero))
67.74/34.86	   new_primEqInt1
67.74/34.86	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.86	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.86	   new_primMinusNatS1
67.74/34.86	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.86	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.86	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.86	   new_primMinusNatS2(Zero, Zero)
67.74/34.86	   new_error
67.74/34.86	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.86	   new_rem(Pos(x0), Pos(Zero))
67.74/34.86	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.86	   new_primEqInt0(x0)
67.74/34.86	   new_esEs(Pos(Zero))
67.74/34.86	   new_esEs(Pos(Succ(x0)))
67.74/34.86	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.86	   new_primModNatS02(x0, x1)
67.74/34.86	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.86	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.86	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.86	   new_primModNatS1(Zero, x0)
67.74/34.86	   new_primEqInt(x0)
67.74/34.86	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.86	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.86	   new_rem(Pos(x0), Neg(Zero))
67.74/34.86	   new_rem(Neg(x0), Pos(Zero))
67.74/34.86	   new_primMinusNatS0(x0)
67.74/34.86	   new_primEqInt2
67.74/34.86	   new_esEs(Neg(Zero))
67.74/34.86	   new_esEs(Neg(Succ(x0)))
67.74/34.86	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.86	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.86	
67.74/34.86	We have to consider all minimal (P,Q,R)-chains.
67.74/34.86	----------------------------------------
67.74/34.86	
67.74/34.86	(212) TransformationProof (EQUIVALENT)
67.74/34.86	By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Succ(x2), Zero), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]:
67.74/34.86	
67.74/34.86	   (new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))),new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))))
67.74/34.86	
67.74/34.86	
67.74/34.86	----------------------------------------
67.74/34.86	
67.74/34.86	(213)
67.74/34.86	Obligation:
67.74/34.86	Q DP problem:
67.74/34.86	The TRS P consists of the following rules:
67.74/34.86	
67.74/34.86	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.86	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, x1, x0, x1))), Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Zero, Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Zero))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.86	
67.74/34.86	The TRS R consists of the following rules:
67.74/34.86	
67.74/34.86	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.86	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.86	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.86	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.86	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.86	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.86	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.86	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.86	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.86	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.86	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.86	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.86	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.86	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.86	   new_error -> error([])
67.74/34.86	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.86	   new_primEqInt2 -> True
67.74/34.86	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.86	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.86	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.86	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.86	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.86	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.86	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.86	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.86	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.86	   new_primMinusNatS1 -> Zero
67.74/34.86	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.86	   new_primEqInt1 -> True
67.74/34.86	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.86	   new_primEqInt0(vuz3260) -> False
67.74/34.86	   new_primEqInt(vuz3250) -> False
67.74/34.86	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.86	
67.74/34.86	The set Q consists of the following terms:
67.74/34.86	
67.74/34.86	   new_rem(Neg(x0), Neg(Zero))
67.74/34.86	   new_primEqInt1
67.74/34.86	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.86	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.86	   new_primMinusNatS1
67.74/34.86	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.86	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.86	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.86	   new_primMinusNatS2(Zero, Zero)
67.74/34.86	   new_error
67.74/34.86	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.86	   new_rem(Pos(x0), Pos(Zero))
67.74/34.86	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.86	   new_primEqInt0(x0)
67.74/34.86	   new_esEs(Pos(Zero))
67.74/34.86	   new_esEs(Pos(Succ(x0)))
67.74/34.86	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.86	   new_primModNatS02(x0, x1)
67.74/34.86	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.86	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.86	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.86	   new_primModNatS1(Zero, x0)
67.74/34.86	   new_primEqInt(x0)
67.74/34.86	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.86	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.86	   new_rem(Pos(x0), Neg(Zero))
67.74/34.86	   new_rem(Neg(x0), Pos(Zero))
67.74/34.86	   new_primMinusNatS0(x0)
67.74/34.86	   new_primEqInt2
67.74/34.86	   new_esEs(Neg(Zero))
67.74/34.86	   new_esEs(Neg(Succ(x0)))
67.74/34.86	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.86	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.86	
67.74/34.86	We have to consider all minimal (P,Q,R)-chains.
67.74/34.86	----------------------------------------
67.74/34.86	
67.74/34.86	(214) TransformationProof (EQUIVALENT)
67.74/34.86	By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Zero, Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))) at position [0,0,0] we obtained the following new rules [LPAR04]:
67.74/34.86	
67.74/34.86	   (new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Pos(Zero)), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))),new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Pos(Zero)), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))))
67.74/34.86	
67.74/34.86	
67.74/34.86	----------------------------------------
67.74/34.86	
67.74/34.86	(215)
67.74/34.86	Obligation:
67.74/34.86	Q DP problem:
67.74/34.86	The TRS P consists of the following rules:
67.74/34.86	
67.74/34.86	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.86	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, x1, x0, x1))), Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Pos(Zero)), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Zero))))
67.74/34.86	
67.74/34.86	The TRS R consists of the following rules:
67.74/34.86	
67.74/34.86	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.86	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.86	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.86	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.86	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.86	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.86	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.86	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.86	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.86	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.86	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.86	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.86	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.86	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.86	   new_error -> error([])
67.74/34.86	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.86	   new_primEqInt2 -> True
67.74/34.86	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.86	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.86	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.86	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.86	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.86	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.86	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.86	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.86	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.86	   new_primMinusNatS1 -> Zero
67.74/34.86	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.86	   new_primEqInt1 -> True
67.74/34.86	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.86	   new_primEqInt0(vuz3260) -> False
67.74/34.86	   new_primEqInt(vuz3250) -> False
67.74/34.86	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.86	
67.74/34.86	The set Q consists of the following terms:
67.74/34.86	
67.74/34.86	   new_rem(Neg(x0), Neg(Zero))
67.74/34.86	   new_primEqInt1
67.74/34.86	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.86	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.86	   new_primMinusNatS1
67.74/34.86	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.86	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.86	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.86	   new_primMinusNatS2(Zero, Zero)
67.74/34.86	   new_error
67.74/34.86	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.86	   new_rem(Pos(x0), Pos(Zero))
67.74/34.86	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.86	   new_primEqInt0(x0)
67.74/34.86	   new_esEs(Pos(Zero))
67.74/34.86	   new_esEs(Pos(Succ(x0)))
67.74/34.86	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.86	   new_primModNatS02(x0, x1)
67.74/34.86	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.86	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.86	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.86	   new_primModNatS1(Zero, x0)
67.74/34.86	   new_primEqInt(x0)
67.74/34.86	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.86	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.86	   new_rem(Pos(x0), Neg(Zero))
67.74/34.86	   new_rem(Neg(x0), Pos(Zero))
67.74/34.86	   new_primMinusNatS0(x0)
67.74/34.86	   new_primEqInt2
67.74/34.86	   new_esEs(Neg(Zero))
67.74/34.86	   new_esEs(Neg(Succ(x0)))
67.74/34.86	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.86	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.86	
67.74/34.86	We have to consider all minimal (P,Q,R)-chains.
67.74/34.86	----------------------------------------
67.74/34.86	
67.74/34.86	(216) DependencyGraphProof (EQUIVALENT)
67.74/34.86	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
67.74/34.86	----------------------------------------
67.74/34.86	
67.74/34.86	(217)
67.74/34.86	Obligation:
67.74/34.86	Q DP problem:
67.74/34.86	The TRS P consists of the following rules:
67.74/34.86	
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.86	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.86	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(x0))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, x1, x0, x1))), Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.86	
67.74/34.86	The TRS R consists of the following rules:
67.74/34.86	
67.74/34.86	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.86	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.86	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.86	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.86	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.86	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.86	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.86	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.86	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.86	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.86	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.86	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.86	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.86	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.86	   new_error -> error([])
67.74/34.86	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.86	   new_primEqInt2 -> True
67.74/34.86	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.86	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.86	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.86	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.86	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.86	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.86	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.86	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.86	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.86	   new_primMinusNatS1 -> Zero
67.74/34.86	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.86	   new_primEqInt1 -> True
67.74/34.86	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.86	   new_primEqInt0(vuz3260) -> False
67.74/34.86	   new_primEqInt(vuz3250) -> False
67.74/34.86	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.86	
67.74/34.86	The set Q consists of the following terms:
67.74/34.86	
67.74/34.86	   new_rem(Neg(x0), Neg(Zero))
67.74/34.86	   new_primEqInt1
67.74/34.86	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.86	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.86	   new_primMinusNatS1
67.74/34.86	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.86	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.86	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.86	   new_primMinusNatS2(Zero, Zero)
67.74/34.86	   new_error
67.74/34.86	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.86	   new_rem(Pos(x0), Pos(Zero))
67.74/34.86	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.86	   new_primEqInt0(x0)
67.74/34.86	   new_esEs(Pos(Zero))
67.74/34.86	   new_esEs(Pos(Succ(x0)))
67.74/34.86	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.86	   new_primModNatS02(x0, x1)
67.74/34.86	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.86	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.86	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.86	   new_primModNatS1(Zero, x0)
67.74/34.86	   new_primEqInt(x0)
67.74/34.86	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.86	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.86	   new_rem(Pos(x0), Neg(Zero))
67.74/34.86	   new_rem(Neg(x0), Pos(Zero))
67.74/34.86	   new_primMinusNatS0(x0)
67.74/34.86	   new_primEqInt2
67.74/34.86	   new_esEs(Neg(Zero))
67.74/34.86	   new_esEs(Neg(Succ(x0)))
67.74/34.86	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.86	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.86	
67.74/34.86	We have to consider all minimal (P,Q,R)-chains.
67.74/34.86	----------------------------------------
67.74/34.86	
67.74/34.86	(218) TransformationProof (EQUIVALENT)
67.74/34.86	By narrowing [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(x0)))) at position [0] we obtained the following new rules [LPAR04]:
67.74/34.86	
67.74/34.86	   (new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS0(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))),new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS0(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))))
67.74/34.86	   (new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS1, Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Zero)))),new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS1, Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Zero)))))
67.74/34.86	
67.74/34.86	
67.74/34.86	----------------------------------------
67.74/34.86	
67.74/34.86	(219)
67.74/34.86	Obligation:
67.74/34.86	Q DP problem:
67.74/34.86	The TRS P consists of the following rules:
67.74/34.86	
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.86	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.86	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, x1, x0, x1))), Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS0(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS1, Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Zero))))
67.74/34.86	
67.74/34.86	The TRS R consists of the following rules:
67.74/34.86	
67.74/34.86	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.86	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.86	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.86	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.86	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.86	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.86	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.86	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.86	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.86	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.86	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.86	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.86	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.86	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.86	   new_error -> error([])
67.74/34.86	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.86	   new_primEqInt2 -> True
67.74/34.86	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.86	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.86	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.86	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.86	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.86	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.86	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.86	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.86	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.86	   new_primMinusNatS1 -> Zero
67.74/34.86	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.86	   new_primEqInt1 -> True
67.74/34.86	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.86	   new_primEqInt0(vuz3260) -> False
67.74/34.86	   new_primEqInt(vuz3250) -> False
67.74/34.86	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.86	
67.74/34.86	The set Q consists of the following terms:
67.74/34.86	
67.74/34.86	   new_rem(Neg(x0), Neg(Zero))
67.74/34.86	   new_primEqInt1
67.74/34.86	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.86	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.86	   new_primMinusNatS1
67.74/34.86	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.86	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.86	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.86	   new_primMinusNatS2(Zero, Zero)
67.74/34.86	   new_error
67.74/34.86	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.86	   new_rem(Pos(x0), Pos(Zero))
67.74/34.86	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.86	   new_primEqInt0(x0)
67.74/34.86	   new_esEs(Pos(Zero))
67.74/34.86	   new_esEs(Pos(Succ(x0)))
67.74/34.86	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.86	   new_primModNatS02(x0, x1)
67.74/34.86	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.86	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.86	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.86	   new_primModNatS1(Zero, x0)
67.74/34.86	   new_primEqInt(x0)
67.74/34.86	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.86	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.86	   new_rem(Pos(x0), Neg(Zero))
67.74/34.86	   new_rem(Neg(x0), Pos(Zero))
67.74/34.86	   new_primMinusNatS0(x0)
67.74/34.86	   new_primEqInt2
67.74/34.86	   new_esEs(Neg(Zero))
67.74/34.86	   new_esEs(Neg(Succ(x0)))
67.74/34.86	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.86	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.86	
67.74/34.86	We have to consider all minimal (P,Q,R)-chains.
67.74/34.86	----------------------------------------
67.74/34.86	
67.74/34.86	(220) TransformationProof (EQUIVALENT)
67.74/34.86	By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS0(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]:
67.74/34.86	
67.74/34.86	   (new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))),new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))))
67.74/34.86	
67.74/34.86	
67.74/34.86	----------------------------------------
67.74/34.86	
67.74/34.86	(221)
67.74/34.86	Obligation:
67.74/34.86	Q DP problem:
67.74/34.86	The TRS P consists of the following rules:
67.74/34.86	
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.86	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.86	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, x1, x0, x1))), Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.86	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.86	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS1, Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Zero))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.87	
67.74/34.87	The TRS R consists of the following rules:
67.74/34.87	
67.74/34.87	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.87	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.87	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.87	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.87	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.87	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.87	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.87	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.87	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.87	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.87	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.87	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.87	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.87	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.87	   new_error -> error([])
67.74/34.87	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.87	   new_primEqInt2 -> True
67.74/34.87	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.87	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.87	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.87	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.87	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.87	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.87	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.87	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.87	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.87	   new_primMinusNatS1 -> Zero
67.74/34.87	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.87	   new_primEqInt1 -> True
67.74/34.87	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.87	   new_primEqInt0(vuz3260) -> False
67.74/34.87	   new_primEqInt(vuz3250) -> False
67.74/34.87	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.87	
67.74/34.87	The set Q consists of the following terms:
67.74/34.87	
67.74/34.87	   new_rem(Neg(x0), Neg(Zero))
67.74/34.87	   new_primEqInt1
67.74/34.87	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.87	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.87	   new_primMinusNatS1
67.74/34.87	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.87	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.87	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.87	   new_primMinusNatS2(Zero, Zero)
67.74/34.87	   new_error
67.74/34.87	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.87	   new_rem(Pos(x0), Pos(Zero))
67.74/34.87	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.87	   new_primEqInt0(x0)
67.74/34.87	   new_esEs(Pos(Zero))
67.74/34.87	   new_esEs(Pos(Succ(x0)))
67.74/34.87	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.87	   new_primModNatS02(x0, x1)
67.74/34.87	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.87	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.87	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.87	   new_primModNatS1(Zero, x0)
67.74/34.87	   new_primEqInt(x0)
67.74/34.87	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.87	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.87	   new_rem(Pos(x0), Neg(Zero))
67.74/34.87	   new_rem(Neg(x0), Pos(Zero))
67.74/34.87	   new_primMinusNatS0(x0)
67.74/34.87	   new_primEqInt2
67.74/34.87	   new_esEs(Neg(Zero))
67.74/34.87	   new_esEs(Neg(Succ(x0)))
67.74/34.87	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.87	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.87	
67.74/34.87	We have to consider all minimal (P,Q,R)-chains.
67.74/34.87	----------------------------------------
67.74/34.87	
67.74/34.87	(222) TransformationProof (EQUIVALENT)
67.74/34.87	By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS1, Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Zero)))) at position [0,0,0,0] we obtained the following new rules [LPAR04]:
67.74/34.87	
67.74/34.87	   (new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Zero, Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Zero)))),new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Zero, Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Zero)))))
67.74/34.87	
67.74/34.87	
67.74/34.87	----------------------------------------
67.74/34.87	
67.74/34.87	(223)
67.74/34.87	Obligation:
67.74/34.87	Q DP problem:
67.74/34.87	The TRS P consists of the following rules:
67.74/34.87	
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.87	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.87	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, x1, x0, x1))), Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Zero, Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Zero))))
67.74/34.87	
67.74/34.87	The TRS R consists of the following rules:
67.74/34.87	
67.74/34.87	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.87	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.87	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.87	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.87	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.87	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.87	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.87	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.87	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.87	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.87	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.87	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.87	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.87	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.87	   new_error -> error([])
67.74/34.87	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.87	   new_primEqInt2 -> True
67.74/34.87	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.87	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.87	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.87	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.87	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.87	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.87	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.87	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.87	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.87	   new_primMinusNatS1 -> Zero
67.74/34.87	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.87	   new_primEqInt1 -> True
67.74/34.87	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.87	   new_primEqInt0(vuz3260) -> False
67.74/34.87	   new_primEqInt(vuz3250) -> False
67.74/34.87	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.87	
67.74/34.87	The set Q consists of the following terms:
67.74/34.87	
67.74/34.87	   new_rem(Neg(x0), Neg(Zero))
67.74/34.87	   new_primEqInt1
67.74/34.87	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.87	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.87	   new_primMinusNatS1
67.74/34.87	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.87	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.87	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.87	   new_primMinusNatS2(Zero, Zero)
67.74/34.87	   new_error
67.74/34.87	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.87	   new_rem(Pos(x0), Pos(Zero))
67.74/34.87	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.87	   new_primEqInt0(x0)
67.74/34.87	   new_esEs(Pos(Zero))
67.74/34.87	   new_esEs(Pos(Succ(x0)))
67.74/34.87	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.87	   new_primModNatS02(x0, x1)
67.74/34.87	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.87	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.87	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.87	   new_primModNatS1(Zero, x0)
67.74/34.87	   new_primEqInt(x0)
67.74/34.87	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.87	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.87	   new_rem(Pos(x0), Neg(Zero))
67.74/34.87	   new_rem(Neg(x0), Pos(Zero))
67.74/34.87	   new_primMinusNatS0(x0)
67.74/34.87	   new_primEqInt2
67.74/34.87	   new_esEs(Neg(Zero))
67.74/34.87	   new_esEs(Neg(Succ(x0)))
67.74/34.87	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.87	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.87	
67.74/34.87	We have to consider all minimal (P,Q,R)-chains.
67.74/34.87	----------------------------------------
67.74/34.87	
67.74/34.87	(224) TransformationProof (EQUIVALENT)
67.74/34.87	By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Zero, Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Zero)))) at position [0,0,0] we obtained the following new rules [LPAR04]:
67.74/34.87	
67.74/34.87	   (new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Pos(Zero)), Neg(Succ(Zero)), Pos(Succ(Succ(Zero)))),new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Pos(Zero)), Neg(Succ(Zero)), Pos(Succ(Succ(Zero)))))
67.74/34.87	
67.74/34.87	
67.74/34.87	----------------------------------------
67.74/34.87	
67.74/34.87	(225)
67.74/34.87	Obligation:
67.74/34.87	Q DP problem:
67.74/34.87	The TRS P consists of the following rules:
67.74/34.87	
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.87	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.87	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, x1, x0, x1))), Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Pos(Zero)), Neg(Succ(Zero)), Pos(Succ(Succ(Zero))))
67.74/34.87	
67.74/34.87	The TRS R consists of the following rules:
67.74/34.87	
67.74/34.87	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.87	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.87	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.87	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.87	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.87	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.87	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.87	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.87	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.87	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.87	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.87	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.87	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.87	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.87	   new_error -> error([])
67.74/34.87	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.87	   new_primEqInt2 -> True
67.74/34.87	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.87	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.87	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.87	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.87	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.87	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.87	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.87	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.87	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.87	   new_primMinusNatS1 -> Zero
67.74/34.87	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.87	   new_primEqInt1 -> True
67.74/34.87	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.87	   new_primEqInt0(vuz3260) -> False
67.74/34.87	   new_primEqInt(vuz3250) -> False
67.74/34.87	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.87	
67.74/34.87	The set Q consists of the following terms:
67.74/34.87	
67.74/34.87	   new_rem(Neg(x0), Neg(Zero))
67.74/34.87	   new_primEqInt1
67.74/34.87	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.87	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.87	   new_primMinusNatS1
67.74/34.87	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.87	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.87	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.87	   new_primMinusNatS2(Zero, Zero)
67.74/34.87	   new_error
67.74/34.87	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.87	   new_rem(Pos(x0), Pos(Zero))
67.74/34.87	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.87	   new_primEqInt0(x0)
67.74/34.87	   new_esEs(Pos(Zero))
67.74/34.87	   new_esEs(Pos(Succ(x0)))
67.74/34.87	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.87	   new_primModNatS02(x0, x1)
67.74/34.87	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.87	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.87	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.87	   new_primModNatS1(Zero, x0)
67.74/34.87	   new_primEqInt(x0)
67.74/34.87	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.87	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.87	   new_rem(Pos(x0), Neg(Zero))
67.74/34.87	   new_rem(Neg(x0), Pos(Zero))
67.74/34.87	   new_primMinusNatS0(x0)
67.74/34.87	   new_primEqInt2
67.74/34.87	   new_esEs(Neg(Zero))
67.74/34.87	   new_esEs(Neg(Succ(x0)))
67.74/34.87	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.87	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.87	
67.74/34.87	We have to consider all minimal (P,Q,R)-chains.
67.74/34.87	----------------------------------------
67.74/34.87	
67.74/34.87	(226) DependencyGraphProof (EQUIVALENT)
67.74/34.87	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
67.74/34.87	----------------------------------------
67.74/34.87	
67.74/34.87	(227)
67.74/34.87	Obligation:
67.74/34.87	Q DP problem:
67.74/34.87	The TRS P consists of the following rules:
67.74/34.87	
67.74/34.87	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.87	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, x1, x0, x1))), Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.87	
67.74/34.87	The TRS R consists of the following rules:
67.74/34.87	
67.74/34.87	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.87	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.87	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.87	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.87	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.87	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.87	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.87	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.87	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.87	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.87	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.87	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.87	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.87	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.87	   new_error -> error([])
67.74/34.87	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.87	   new_primEqInt2 -> True
67.74/34.87	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.87	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.87	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.87	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.87	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.87	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.87	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.87	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.87	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.87	   new_primMinusNatS1 -> Zero
67.74/34.87	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.87	   new_primEqInt1 -> True
67.74/34.87	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.87	   new_primEqInt0(vuz3260) -> False
67.74/34.87	   new_primEqInt(vuz3250) -> False
67.74/34.87	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.87	
67.74/34.87	The set Q consists of the following terms:
67.74/34.87	
67.74/34.87	   new_rem(Neg(x0), Neg(Zero))
67.74/34.87	   new_primEqInt1
67.74/34.87	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.87	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.87	   new_primMinusNatS1
67.74/34.87	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.87	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.87	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.87	   new_primMinusNatS2(Zero, Zero)
67.74/34.87	   new_error
67.74/34.87	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.87	   new_rem(Pos(x0), Pos(Zero))
67.74/34.87	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.87	   new_primEqInt0(x0)
67.74/34.87	   new_esEs(Pos(Zero))
67.74/34.87	   new_esEs(Pos(Succ(x0)))
67.74/34.87	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.87	   new_primModNatS02(x0, x1)
67.74/34.87	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.87	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.87	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.87	   new_primModNatS1(Zero, x0)
67.74/34.87	   new_primEqInt(x0)
67.74/34.87	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.87	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.87	   new_rem(Pos(x0), Neg(Zero))
67.74/34.87	   new_rem(Neg(x0), Pos(Zero))
67.74/34.87	   new_primMinusNatS0(x0)
67.74/34.87	   new_primEqInt2
67.74/34.87	   new_esEs(Neg(Zero))
67.74/34.87	   new_esEs(Neg(Succ(x0)))
67.74/34.87	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.87	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.87	
67.74/34.87	We have to consider all minimal (P,Q,R)-chains.
67.74/34.87	----------------------------------------
67.74/34.87	
67.74/34.87	(228) TransformationProof (EQUIVALENT)
67.74/34.87	By narrowing [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, x1, x0, x1))), Pos(Succ(Succ(x1))), Neg(Succ(Succ(x0)))) at position [0] we obtained the following new rules [LPAR04]:
67.74/34.87	
67.74/34.87	   (new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))))
67.74/34.87	   (new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Neg(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Neg(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))))
67.74/34.87	   (new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS02(Zero, Zero))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))),new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS02(Zero, Zero))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))))
67.74/34.87	   (new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS02(Succ(x2), Zero))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))),new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS02(Succ(x2), Zero))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))))
67.74/34.87	
67.74/34.87	
67.74/34.87	----------------------------------------
67.74/34.87	
67.74/34.87	(229)
67.74/34.87	Obligation:
67.74/34.87	Q DP problem:
67.74/34.87	The TRS P consists of the following rules:
67.74/34.87	
67.74/34.87	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.87	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Neg(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS02(Zero, Zero))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Zero))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS02(Succ(x2), Zero))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.87	
67.74/34.87	The TRS R consists of the following rules:
67.74/34.87	
67.74/34.87	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.87	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.87	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.87	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.87	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.87	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.87	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.87	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.87	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.87	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.87	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.87	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.87	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.87	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.87	   new_error -> error([])
67.74/34.87	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.87	   new_primEqInt2 -> True
67.74/34.87	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.87	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.87	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.87	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.87	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.87	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.87	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.87	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.87	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.87	   new_primMinusNatS1 -> Zero
67.74/34.87	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.87	   new_primEqInt1 -> True
67.74/34.87	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.87	   new_primEqInt0(vuz3260) -> False
67.74/34.87	   new_primEqInt(vuz3250) -> False
67.74/34.87	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.87	
67.74/34.87	The set Q consists of the following terms:
67.74/34.87	
67.74/34.87	   new_rem(Neg(x0), Neg(Zero))
67.74/34.87	   new_primEqInt1
67.74/34.87	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.87	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.87	   new_primMinusNatS1
67.74/34.87	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.87	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.87	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.87	   new_primMinusNatS2(Zero, Zero)
67.74/34.87	   new_error
67.74/34.87	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.87	   new_rem(Pos(x0), Pos(Zero))
67.74/34.87	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.87	   new_primEqInt0(x0)
67.74/34.87	   new_esEs(Pos(Zero))
67.74/34.87	   new_esEs(Pos(Succ(x0)))
67.74/34.87	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.87	   new_primModNatS02(x0, x1)
67.74/34.87	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.87	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.87	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.87	   new_primModNatS1(Zero, x0)
67.74/34.87	   new_primEqInt(x0)
67.74/34.87	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.87	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.87	   new_rem(Pos(x0), Neg(Zero))
67.74/34.87	   new_rem(Neg(x0), Pos(Zero))
67.74/34.87	   new_primMinusNatS0(x0)
67.74/34.87	   new_primEqInt2
67.74/34.87	   new_esEs(Neg(Zero))
67.74/34.87	   new_esEs(Neg(Succ(x0)))
67.74/34.87	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.87	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.87	
67.74/34.87	We have to consider all minimal (P,Q,R)-chains.
67.74/34.87	----------------------------------------
67.74/34.87	
67.74/34.87	(230) TransformationProof (EQUIVALENT)
67.74/34.87	By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Neg(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) at position [0] we obtained the following new rules [LPAR04]:
67.74/34.87	
67.74/34.87	   (new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_primEqInt0(Succ(Zero)), Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_primEqInt0(Succ(Zero)), Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))))
67.74/34.87	
67.74/34.87	
67.74/34.87	----------------------------------------
67.74/34.87	
67.74/34.87	(231)
67.74/34.87	Obligation:
67.74/34.87	Q DP problem:
67.74/34.87	The TRS P consists of the following rules:
67.74/34.87	
67.74/34.87	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.87	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS02(Zero, Zero))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Zero))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS02(Succ(x2), Zero))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_primEqInt0(Succ(Zero)), Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.87	
67.74/34.87	The TRS R consists of the following rules:
67.74/34.87	
67.74/34.87	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.87	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.87	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.87	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.87	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.87	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.87	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.87	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.87	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.87	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.87	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.87	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.87	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.87	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.87	   new_error -> error([])
67.74/34.87	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.87	   new_primEqInt2 -> True
67.74/34.87	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.87	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.87	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.87	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.87	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.87	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.87	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.87	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.87	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.87	   new_primMinusNatS1 -> Zero
67.74/34.87	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.87	   new_primEqInt1 -> True
67.74/34.87	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.87	   new_primEqInt0(vuz3260) -> False
67.74/34.87	   new_primEqInt(vuz3250) -> False
67.74/34.87	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.87	
67.74/34.87	The set Q consists of the following terms:
67.74/34.87	
67.74/34.87	   new_rem(Neg(x0), Neg(Zero))
67.74/34.87	   new_primEqInt1
67.74/34.87	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.87	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.87	   new_primMinusNatS1
67.74/34.87	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.87	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.87	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.87	   new_primMinusNatS2(Zero, Zero)
67.74/34.87	   new_error
67.74/34.87	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.87	   new_rem(Pos(x0), Pos(Zero))
67.74/34.87	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.87	   new_primEqInt0(x0)
67.74/34.87	   new_esEs(Pos(Zero))
67.74/34.87	   new_esEs(Pos(Succ(x0)))
67.74/34.87	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.87	   new_primModNatS02(x0, x1)
67.74/34.87	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.87	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.87	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.87	   new_primModNatS1(Zero, x0)
67.74/34.87	   new_primEqInt(x0)
67.74/34.87	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.87	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.87	   new_rem(Pos(x0), Neg(Zero))
67.74/34.87	   new_rem(Neg(x0), Pos(Zero))
67.74/34.87	   new_primMinusNatS0(x0)
67.74/34.87	   new_primEqInt2
67.74/34.87	   new_esEs(Neg(Zero))
67.74/34.87	   new_esEs(Neg(Succ(x0)))
67.74/34.87	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.87	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.87	
67.74/34.87	We have to consider all minimal (P,Q,R)-chains.
67.74/34.87	----------------------------------------
67.74/34.87	
67.74/34.87	(232) TransformationProof (EQUIVALENT)
67.74/34.87	By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS02(Zero, Zero))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) at position [0,0,0] we obtained the following new rules [LPAR04]:
67.74/34.87	
67.74/34.87	   (new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Succ(Zero), Succ(Zero)), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))),new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Succ(Zero), Succ(Zero)), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))))
67.74/34.87	
67.74/34.87	
67.74/34.87	----------------------------------------
67.74/34.87	
67.74/34.87	(233)
67.74/34.87	Obligation:
67.74/34.87	Q DP problem:
67.74/34.87	The TRS P consists of the following rules:
67.74/34.87	
67.74/34.87	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.87	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS02(Succ(x2), Zero))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_primEqInt0(Succ(Zero)), Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Succ(Zero), Succ(Zero)), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Zero))))
67.74/34.87	
67.74/34.87	The TRS R consists of the following rules:
67.74/34.87	
67.74/34.87	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.87	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.87	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.87	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.87	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.87	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.87	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.87	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.87	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.87	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.87	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.87	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.87	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.87	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.87	   new_error -> error([])
67.74/34.87	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.87	   new_primEqInt2 -> True
67.74/34.87	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.87	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.87	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.87	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.87	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.87	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.87	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.87	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.87	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.87	   new_primMinusNatS1 -> Zero
67.74/34.87	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.87	   new_primEqInt1 -> True
67.74/34.87	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.87	   new_primEqInt0(vuz3260) -> False
67.74/34.87	   new_primEqInt(vuz3250) -> False
67.74/34.87	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.87	
67.74/34.87	The set Q consists of the following terms:
67.74/34.87	
67.74/34.87	   new_rem(Neg(x0), Neg(Zero))
67.74/34.87	   new_primEqInt1
67.74/34.87	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.87	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.87	   new_primMinusNatS1
67.74/34.87	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.87	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.87	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.87	   new_primMinusNatS2(Zero, Zero)
67.74/34.87	   new_error
67.74/34.87	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.87	   new_rem(Pos(x0), Pos(Zero))
67.74/34.87	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.87	   new_primEqInt0(x0)
67.74/34.87	   new_esEs(Pos(Zero))
67.74/34.87	   new_esEs(Pos(Succ(x0)))
67.74/34.87	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.87	   new_primModNatS02(x0, x1)
67.74/34.87	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.87	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.87	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.87	   new_primModNatS1(Zero, x0)
67.74/34.87	   new_primEqInt(x0)
67.74/34.87	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.87	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.87	   new_rem(Pos(x0), Neg(Zero))
67.74/34.87	   new_rem(Neg(x0), Pos(Zero))
67.74/34.87	   new_primMinusNatS0(x0)
67.74/34.87	   new_primEqInt2
67.74/34.87	   new_esEs(Neg(Zero))
67.74/34.87	   new_esEs(Neg(Succ(x0)))
67.74/34.87	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.87	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.87	
67.74/34.87	We have to consider all minimal (P,Q,R)-chains.
67.74/34.87	----------------------------------------
67.74/34.87	
67.74/34.87	(234) TransformationProof (EQUIVALENT)
67.74/34.87	By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS02(Succ(x2), Zero))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) at position [0,0,0] we obtained the following new rules [LPAR04]:
67.74/34.87	
67.74/34.87	   (new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Succ(Succ(x2)), Succ(Zero)), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))),new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Succ(Succ(x2)), Succ(Zero)), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))))
67.74/34.87	
67.74/34.87	
67.74/34.87	----------------------------------------
67.74/34.87	
67.74/34.87	(235)
67.74/34.87	Obligation:
67.74/34.87	Q DP problem:
67.74/34.87	The TRS P consists of the following rules:
67.74/34.87	
67.74/34.87	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.87	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_primEqInt0(Succ(Zero)), Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Succ(Zero), Succ(Zero)), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Zero))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Succ(Succ(x2)), Succ(Zero)), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.87	
67.74/34.87	The TRS R consists of the following rules:
67.74/34.87	
67.74/34.87	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.87	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.87	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.87	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.87	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.87	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.87	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.87	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.87	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.87	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.87	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.87	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.87	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.87	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.87	   new_error -> error([])
67.74/34.87	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.87	   new_primEqInt2 -> True
67.74/34.87	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.87	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.87	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.87	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.87	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.87	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.87	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.87	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.87	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.87	   new_primMinusNatS1 -> Zero
67.74/34.87	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.87	   new_primEqInt1 -> True
67.74/34.87	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.87	   new_primEqInt0(vuz3260) -> False
67.74/34.87	   new_primEqInt(vuz3250) -> False
67.74/34.87	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.87	
67.74/34.87	The set Q consists of the following terms:
67.74/34.87	
67.74/34.87	   new_rem(Neg(x0), Neg(Zero))
67.74/34.87	   new_primEqInt1
67.74/34.87	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.87	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.87	   new_primMinusNatS1
67.74/34.87	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.87	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.87	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.87	   new_primMinusNatS2(Zero, Zero)
67.74/34.87	   new_error
67.74/34.87	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.87	   new_rem(Pos(x0), Pos(Zero))
67.74/34.87	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.87	   new_primEqInt0(x0)
67.74/34.87	   new_esEs(Pos(Zero))
67.74/34.87	   new_esEs(Pos(Succ(x0)))
67.74/34.87	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.87	   new_primModNatS02(x0, x1)
67.74/34.87	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.87	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.87	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.87	   new_primModNatS1(Zero, x0)
67.74/34.87	   new_primEqInt(x0)
67.74/34.87	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.87	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.87	   new_rem(Pos(x0), Neg(Zero))
67.74/34.87	   new_rem(Neg(x0), Pos(Zero))
67.74/34.87	   new_primMinusNatS0(x0)
67.74/34.87	   new_primEqInt2
67.74/34.87	   new_esEs(Neg(Zero))
67.74/34.87	   new_esEs(Neg(Succ(x0)))
67.74/34.87	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.87	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.87	
67.74/34.87	We have to consider all minimal (P,Q,R)-chains.
67.74/34.87	----------------------------------------
67.74/34.87	
67.74/34.87	(236) TransformationProof (EQUIVALENT)
67.74/34.87	By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_primEqInt0(Succ(Zero)), Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) at position [0] we obtained the following new rules [LPAR04]:
67.74/34.87	
67.74/34.87	   (new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))))
67.74/34.87	
67.74/34.87	
67.74/34.87	----------------------------------------
67.74/34.87	
67.74/34.87	(237)
67.74/34.87	Obligation:
67.74/34.87	Q DP problem:
67.74/34.87	The TRS P consists of the following rules:
67.74/34.87	
67.74/34.87	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.87	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Succ(Zero), Succ(Zero)), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Zero))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Succ(Succ(x2)), Succ(Zero)), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.87	
67.74/34.87	The TRS R consists of the following rules:
67.74/34.87	
67.74/34.87	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.87	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.87	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.87	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.87	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.87	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.87	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.87	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.87	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.87	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.87	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.87	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.87	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.87	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.87	   new_error -> error([])
67.74/34.87	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.87	   new_primEqInt2 -> True
67.74/34.87	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.87	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.87	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.87	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.87	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.87	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.87	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.87	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.87	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.87	   new_primMinusNatS1 -> Zero
67.74/34.87	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.87	   new_primEqInt1 -> True
67.74/34.87	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.87	   new_primEqInt0(vuz3260) -> False
67.74/34.87	   new_primEqInt(vuz3250) -> False
67.74/34.87	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.87	
67.74/34.87	The set Q consists of the following terms:
67.74/34.87	
67.74/34.87	   new_rem(Neg(x0), Neg(Zero))
67.74/34.87	   new_primEqInt1
67.74/34.87	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.87	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.87	   new_primMinusNatS1
67.74/34.87	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.87	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.87	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.87	   new_primMinusNatS2(Zero, Zero)
67.74/34.87	   new_error
67.74/34.87	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.87	   new_rem(Pos(x0), Pos(Zero))
67.74/34.87	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.87	   new_primEqInt0(x0)
67.74/34.87	   new_esEs(Pos(Zero))
67.74/34.87	   new_esEs(Pos(Succ(x0)))
67.74/34.87	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.87	   new_primModNatS02(x0, x1)
67.74/34.87	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.87	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.87	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.87	   new_primModNatS1(Zero, x0)
67.74/34.87	   new_primEqInt(x0)
67.74/34.87	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.87	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.87	   new_rem(Pos(x0), Neg(Zero))
67.74/34.87	   new_rem(Neg(x0), Pos(Zero))
67.74/34.87	   new_primMinusNatS0(x0)
67.74/34.87	   new_primEqInt2
67.74/34.87	   new_esEs(Neg(Zero))
67.74/34.87	   new_esEs(Neg(Succ(x0)))
67.74/34.87	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.87	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.87	
67.74/34.87	We have to consider all minimal (P,Q,R)-chains.
67.74/34.87	----------------------------------------
67.74/34.87	
67.74/34.87	(238) TransformationProof (EQUIVALENT)
67.74/34.87	By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Succ(Zero), Succ(Zero)), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) at position [0,0,0,0] we obtained the following new rules [LPAR04]:
67.74/34.87	
67.74/34.87	   (new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Zero, Zero), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))),new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Zero, Zero), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))))
67.74/34.87	
67.74/34.87	
67.74/34.87	----------------------------------------
67.74/34.87	
67.74/34.87	(239)
67.74/34.87	Obligation:
67.74/34.87	Q DP problem:
67.74/34.87	The TRS P consists of the following rules:
67.74/34.87	
67.74/34.87	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.87	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Succ(Succ(x2)), Succ(Zero)), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Zero, Zero), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Zero))))
67.74/34.87	
67.74/34.87	The TRS R consists of the following rules:
67.74/34.87	
67.74/34.87	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.87	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.87	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.87	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.87	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.87	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.87	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.87	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.87	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.87	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.87	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.87	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.87	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.87	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.87	   new_error -> error([])
67.74/34.87	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.87	   new_primEqInt2 -> True
67.74/34.87	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.87	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.87	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.87	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.87	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.87	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.87	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.87	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.87	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.87	   new_primMinusNatS1 -> Zero
67.74/34.87	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.87	   new_primEqInt1 -> True
67.74/34.87	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.87	   new_primEqInt0(vuz3260) -> False
67.74/34.87	   new_primEqInt(vuz3250) -> False
67.74/34.87	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.87	
67.74/34.87	The set Q consists of the following terms:
67.74/34.87	
67.74/34.87	   new_rem(Neg(x0), Neg(Zero))
67.74/34.87	   new_primEqInt1
67.74/34.87	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.87	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.87	   new_primMinusNatS1
67.74/34.87	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.87	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.87	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.87	   new_primMinusNatS2(Zero, Zero)
67.74/34.87	   new_error
67.74/34.87	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.87	   new_rem(Pos(x0), Pos(Zero))
67.74/34.87	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.87	   new_primEqInt0(x0)
67.74/34.87	   new_esEs(Pos(Zero))
67.74/34.87	   new_esEs(Pos(Succ(x0)))
67.74/34.87	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.87	   new_primModNatS02(x0, x1)
67.74/34.87	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.87	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.87	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.87	   new_primModNatS1(Zero, x0)
67.74/34.87	   new_primEqInt(x0)
67.74/34.87	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.87	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.87	   new_rem(Pos(x0), Neg(Zero))
67.74/34.87	   new_rem(Neg(x0), Pos(Zero))
67.74/34.87	   new_primMinusNatS0(x0)
67.74/34.87	   new_primEqInt2
67.74/34.87	   new_esEs(Neg(Zero))
67.74/34.87	   new_esEs(Neg(Succ(x0)))
67.74/34.87	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.87	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.87	
67.74/34.87	We have to consider all minimal (P,Q,R)-chains.
67.74/34.87	----------------------------------------
67.74/34.87	
67.74/34.87	(240) TransformationProof (EQUIVALENT)
67.74/34.87	By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Succ(Succ(x2)), Succ(Zero)), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]:
67.74/34.87	
67.74/34.87	   (new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Succ(x2), Zero), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))),new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Succ(x2), Zero), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))))
67.74/34.87	
67.74/34.87	
67.74/34.87	----------------------------------------
67.74/34.87	
67.74/34.87	(241)
67.74/34.87	Obligation:
67.74/34.87	Q DP problem:
67.74/34.87	The TRS P consists of the following rules:
67.74/34.87	
67.74/34.87	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.87	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Zero, Zero), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Zero))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Succ(x2), Zero), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.87	
67.74/34.87	The TRS R consists of the following rules:
67.74/34.87	
67.74/34.87	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.87	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.87	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.87	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.87	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.87	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.87	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.87	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.87	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.87	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.87	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.87	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.87	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.87	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.87	   new_error -> error([])
67.74/34.87	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.87	   new_primEqInt2 -> True
67.74/34.87	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.87	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.87	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.87	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.87	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.87	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.87	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.87	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.87	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.87	   new_primMinusNatS1 -> Zero
67.74/34.87	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.87	   new_primEqInt1 -> True
67.74/34.87	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.87	   new_primEqInt0(vuz3260) -> False
67.74/34.87	   new_primEqInt(vuz3250) -> False
67.74/34.87	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.87	
67.74/34.87	The set Q consists of the following terms:
67.74/34.87	
67.74/34.87	   new_rem(Neg(x0), Neg(Zero))
67.74/34.87	   new_primEqInt1
67.74/34.87	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.87	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.87	   new_primMinusNatS1
67.74/34.87	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.87	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.87	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.87	   new_primMinusNatS2(Zero, Zero)
67.74/34.87	   new_error
67.74/34.87	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.87	   new_rem(Pos(x0), Pos(Zero))
67.74/34.87	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.87	   new_primEqInt0(x0)
67.74/34.87	   new_esEs(Pos(Zero))
67.74/34.87	   new_esEs(Pos(Succ(x0)))
67.74/34.87	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.87	   new_primModNatS02(x0, x1)
67.74/34.87	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.87	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.87	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.87	   new_primModNatS1(Zero, x0)
67.74/34.87	   new_primEqInt(x0)
67.74/34.87	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.87	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.87	   new_rem(Pos(x0), Neg(Zero))
67.74/34.87	   new_rem(Neg(x0), Pos(Zero))
67.74/34.87	   new_primMinusNatS0(x0)
67.74/34.87	   new_primEqInt2
67.74/34.87	   new_esEs(Neg(Zero))
67.74/34.87	   new_esEs(Neg(Succ(x0)))
67.74/34.87	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.87	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.87	
67.74/34.87	We have to consider all minimal (P,Q,R)-chains.
67.74/34.87	----------------------------------------
67.74/34.87	
67.74/34.87	(242) TransformationProof (EQUIVALENT)
67.74/34.87	By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Zero, Zero), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) at position [0,0,0,0] we obtained the following new rules [LPAR04]:
67.74/34.87	
67.74/34.87	   (new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Zero, Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))),new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Zero, Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))))
67.74/34.87	
67.74/34.87	
67.74/34.87	----------------------------------------
67.74/34.87	
67.74/34.87	(243)
67.74/34.87	Obligation:
67.74/34.87	Q DP problem:
67.74/34.87	The TRS P consists of the following rules:
67.74/34.87	
67.74/34.87	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.87	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Succ(x2), Zero), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Zero, Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Zero))))
67.74/34.87	
67.74/34.87	The TRS R consists of the following rules:
67.74/34.87	
67.74/34.87	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.87	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.87	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.87	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.87	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.87	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.87	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.87	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.87	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.87	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.87	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.87	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.87	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.87	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.87	   new_error -> error([])
67.74/34.87	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.87	   new_primEqInt2 -> True
67.74/34.87	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.87	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.87	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.87	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.87	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.87	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.87	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.87	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.87	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.87	   new_primMinusNatS1 -> Zero
67.74/34.87	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.87	   new_primEqInt1 -> True
67.74/34.87	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.87	   new_primEqInt0(vuz3260) -> False
67.74/34.87	   new_primEqInt(vuz3250) -> False
67.74/34.87	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.87	
67.74/34.87	The set Q consists of the following terms:
67.74/34.87	
67.74/34.87	   new_rem(Neg(x0), Neg(Zero))
67.74/34.87	   new_primEqInt1
67.74/34.87	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.87	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.87	   new_primMinusNatS1
67.74/34.87	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.87	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.87	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.87	   new_primMinusNatS2(Zero, Zero)
67.74/34.87	   new_error
67.74/34.87	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.87	   new_rem(Pos(x0), Pos(Zero))
67.74/34.87	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.87	   new_primEqInt0(x0)
67.74/34.87	   new_esEs(Pos(Zero))
67.74/34.87	   new_esEs(Pos(Succ(x0)))
67.74/34.87	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.87	   new_primModNatS02(x0, x1)
67.74/34.87	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.87	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.87	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.87	   new_primModNatS1(Zero, x0)
67.74/34.87	   new_primEqInt(x0)
67.74/34.87	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.87	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.87	   new_rem(Pos(x0), Neg(Zero))
67.74/34.87	   new_rem(Neg(x0), Pos(Zero))
67.74/34.87	   new_primMinusNatS0(x0)
67.74/34.87	   new_primEqInt2
67.74/34.87	   new_esEs(Neg(Zero))
67.74/34.87	   new_esEs(Neg(Succ(x0)))
67.74/34.87	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.87	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.87	
67.74/34.87	We have to consider all minimal (P,Q,R)-chains.
67.74/34.87	----------------------------------------
67.74/34.87	
67.74/34.87	(244) TransformationProof (EQUIVALENT)
67.74/34.87	By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Succ(x2), Zero), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]:
67.74/34.87	
67.74/34.87	   (new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))),new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))))
67.74/34.87	
67.74/34.87	
67.74/34.87	----------------------------------------
67.74/34.87	
67.74/34.87	(245)
67.74/34.87	Obligation:
67.74/34.87	Q DP problem:
67.74/34.87	The TRS P consists of the following rules:
67.74/34.87	
67.74/34.87	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.87	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Zero, Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Zero))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.87	
67.74/34.87	The TRS R consists of the following rules:
67.74/34.87	
67.74/34.87	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.87	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.87	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.87	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.87	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.87	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.87	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.87	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.87	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.87	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.87	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.87	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.87	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.87	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.87	   new_error -> error([])
67.74/34.87	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.87	   new_primEqInt2 -> True
67.74/34.87	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.87	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.87	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.87	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.87	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.87	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.87	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.87	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.87	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.87	   new_primMinusNatS1 -> Zero
67.74/34.87	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.87	   new_primEqInt1 -> True
67.74/34.87	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.87	   new_primEqInt0(vuz3260) -> False
67.74/34.87	   new_primEqInt(vuz3250) -> False
67.74/34.87	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.87	
67.74/34.87	The set Q consists of the following terms:
67.74/34.87	
67.74/34.87	   new_rem(Neg(x0), Neg(Zero))
67.74/34.87	   new_primEqInt1
67.74/34.87	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.87	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.87	   new_primMinusNatS1
67.74/34.87	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.87	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.87	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.87	   new_primMinusNatS2(Zero, Zero)
67.74/34.87	   new_error
67.74/34.87	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.87	   new_rem(Pos(x0), Pos(Zero))
67.74/34.87	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.87	   new_primEqInt0(x0)
67.74/34.87	   new_esEs(Pos(Zero))
67.74/34.87	   new_esEs(Pos(Succ(x0)))
67.74/34.87	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.87	   new_primModNatS02(x0, x1)
67.74/34.87	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.87	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.87	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.87	   new_primModNatS1(Zero, x0)
67.74/34.87	   new_primEqInt(x0)
67.74/34.87	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.87	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.87	   new_rem(Pos(x0), Neg(Zero))
67.74/34.87	   new_rem(Neg(x0), Pos(Zero))
67.74/34.87	   new_primMinusNatS0(x0)
67.74/34.87	   new_primEqInt2
67.74/34.87	   new_esEs(Neg(Zero))
67.74/34.87	   new_esEs(Neg(Succ(x0)))
67.74/34.87	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.87	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.87	
67.74/34.87	We have to consider all minimal (P,Q,R)-chains.
67.74/34.87	----------------------------------------
67.74/34.87	
67.74/34.87	(246) TransformationProof (EQUIVALENT)
67.74/34.87	By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Zero, Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) at position [0,0,0] we obtained the following new rules [LPAR04]:
67.74/34.87	
67.74/34.87	   (new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Neg(Zero)), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))),new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Neg(Zero)), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))))
67.74/34.87	
67.74/34.87	
67.74/34.87	----------------------------------------
67.74/34.87	
67.74/34.87	(247)
67.74/34.87	Obligation:
67.74/34.87	Q DP problem:
67.74/34.87	The TRS P consists of the following rules:
67.74/34.87	
67.74/34.87	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.87	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Neg(Zero)), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Zero))))
67.74/34.87	
67.74/34.87	The TRS R consists of the following rules:
67.74/34.87	
67.74/34.87	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.87	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.87	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.87	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.87	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.87	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.87	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.87	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.87	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.87	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.87	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.87	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.87	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.87	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.87	   new_error -> error([])
67.74/34.87	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.87	   new_primEqInt2 -> True
67.74/34.87	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.87	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.87	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.87	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.87	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.87	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.87	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.87	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.87	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.87	   new_primMinusNatS1 -> Zero
67.74/34.87	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.87	   new_primEqInt1 -> True
67.74/34.87	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.87	   new_primEqInt0(vuz3260) -> False
67.74/34.87	   new_primEqInt(vuz3250) -> False
67.74/34.87	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.87	
67.74/34.87	The set Q consists of the following terms:
67.74/34.87	
67.74/34.87	   new_rem(Neg(x0), Neg(Zero))
67.74/34.87	   new_primEqInt1
67.74/34.87	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.87	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.87	   new_primMinusNatS1
67.74/34.87	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.87	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.87	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.87	   new_primMinusNatS2(Zero, Zero)
67.74/34.87	   new_error
67.74/34.87	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.87	   new_rem(Pos(x0), Pos(Zero))
67.74/34.87	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.87	   new_primEqInt0(x0)
67.74/34.87	   new_esEs(Pos(Zero))
67.74/34.87	   new_esEs(Pos(Succ(x0)))
67.74/34.87	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.87	   new_primModNatS02(x0, x1)
67.74/34.87	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.87	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.87	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.87	   new_primModNatS1(Zero, x0)
67.74/34.87	   new_primEqInt(x0)
67.74/34.87	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.87	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.87	   new_rem(Pos(x0), Neg(Zero))
67.74/34.87	   new_rem(Neg(x0), Pos(Zero))
67.74/34.87	   new_primMinusNatS0(x0)
67.74/34.87	   new_primEqInt2
67.74/34.87	   new_esEs(Neg(Zero))
67.74/34.87	   new_esEs(Neg(Succ(x0)))
67.74/34.87	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.87	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.87	
67.74/34.87	We have to consider all minimal (P,Q,R)-chains.
67.74/34.87	----------------------------------------
67.74/34.87	
67.74/34.87	(248) DependencyGraphProof (EQUIVALENT)
67.74/34.87	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
67.74/34.87	----------------------------------------
67.74/34.87	
67.74/34.87	(249)
67.74/34.87	Obligation:
67.74/34.87	Q DP problem:
67.74/34.87	The TRS P consists of the following rules:
67.74/34.87	
67.74/34.87	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.87	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(x0))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.87	
67.74/34.87	The TRS R consists of the following rules:
67.74/34.87	
67.74/34.87	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.87	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.87	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.87	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.87	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.87	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.87	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.87	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.87	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.87	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.87	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.87	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.87	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.87	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.87	   new_error -> error([])
67.74/34.87	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.87	   new_primEqInt2 -> True
67.74/34.87	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.87	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.87	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.87	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.87	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.87	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.87	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.87	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.87	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.87	   new_primMinusNatS1 -> Zero
67.74/34.87	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.87	   new_primEqInt1 -> True
67.74/34.87	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.87	   new_primEqInt0(vuz3260) -> False
67.74/34.87	   new_primEqInt(vuz3250) -> False
67.74/34.87	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.87	
67.74/34.87	The set Q consists of the following terms:
67.74/34.87	
67.74/34.87	   new_rem(Neg(x0), Neg(Zero))
67.74/34.87	   new_primEqInt1
67.74/34.87	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.87	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.87	   new_primMinusNatS1
67.74/34.87	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.87	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.87	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.87	   new_primMinusNatS2(Zero, Zero)
67.74/34.87	   new_error
67.74/34.87	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.87	   new_rem(Pos(x0), Pos(Zero))
67.74/34.87	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.87	   new_primEqInt0(x0)
67.74/34.87	   new_esEs(Pos(Zero))
67.74/34.87	   new_esEs(Pos(Succ(x0)))
67.74/34.87	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.87	   new_primModNatS02(x0, x1)
67.74/34.87	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.87	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.87	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.87	   new_primModNatS1(Zero, x0)
67.74/34.87	   new_primEqInt(x0)
67.74/34.87	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.87	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.87	   new_rem(Pos(x0), Neg(Zero))
67.74/34.87	   new_rem(Neg(x0), Pos(Zero))
67.74/34.87	   new_primMinusNatS0(x0)
67.74/34.87	   new_primEqInt2
67.74/34.87	   new_esEs(Neg(Zero))
67.74/34.87	   new_esEs(Neg(Succ(x0)))
67.74/34.87	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.87	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.87	
67.74/34.87	We have to consider all minimal (P,Q,R)-chains.
67.74/34.87	----------------------------------------
67.74/34.87	
67.74/34.87	(250) TransformationProof (EQUIVALENT)
67.74/34.87	By narrowing [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(x0)))) at position [0] we obtained the following new rules [LPAR04]:
67.74/34.87	
67.74/34.87	   (new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS0(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))),new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS0(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))))
67.74/34.87	   (new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS1, Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Zero)))),new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS1, Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Zero)))))
67.74/34.87	
67.74/34.87	
67.74/34.87	----------------------------------------
67.74/34.87	
67.74/34.87	(251)
67.74/34.87	Obligation:
67.74/34.87	Q DP problem:
67.74/34.87	The TRS P consists of the following rules:
67.74/34.87	
67.74/34.87	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.87	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS0(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS1, Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Zero))))
67.74/34.87	
67.74/34.87	The TRS R consists of the following rules:
67.74/34.87	
67.74/34.87	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.87	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.87	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.87	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.87	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.87	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.87	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.87	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.87	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.87	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.87	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.87	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.87	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.87	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.87	   new_error -> error([])
67.74/34.87	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.87	   new_primEqInt2 -> True
67.74/34.87	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.87	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.87	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.87	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.87	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.87	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.87	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.87	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.87	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.87	   new_primMinusNatS1 -> Zero
67.74/34.87	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.87	   new_primEqInt1 -> True
67.74/34.87	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.87	   new_primEqInt0(vuz3260) -> False
67.74/34.87	   new_primEqInt(vuz3250) -> False
67.74/34.87	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.87	
67.74/34.87	The set Q consists of the following terms:
67.74/34.87	
67.74/34.87	   new_rem(Neg(x0), Neg(Zero))
67.74/34.87	   new_primEqInt1
67.74/34.87	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.87	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.87	   new_primMinusNatS1
67.74/34.87	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.87	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.87	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.87	   new_primMinusNatS2(Zero, Zero)
67.74/34.87	   new_error
67.74/34.87	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.87	   new_rem(Pos(x0), Pos(Zero))
67.74/34.87	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.87	   new_primEqInt0(x0)
67.74/34.87	   new_esEs(Pos(Zero))
67.74/34.87	   new_esEs(Pos(Succ(x0)))
67.74/34.87	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.87	   new_primModNatS02(x0, x1)
67.74/34.87	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.87	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.87	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.87	   new_primModNatS1(Zero, x0)
67.74/34.87	   new_primEqInt(x0)
67.74/34.87	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.87	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.87	   new_rem(Pos(x0), Neg(Zero))
67.74/34.87	   new_rem(Neg(x0), Pos(Zero))
67.74/34.87	   new_primMinusNatS0(x0)
67.74/34.87	   new_primEqInt2
67.74/34.87	   new_esEs(Neg(Zero))
67.74/34.87	   new_esEs(Neg(Succ(x0)))
67.74/34.87	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.87	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.87	
67.74/34.87	We have to consider all minimal (P,Q,R)-chains.
67.74/34.87	----------------------------------------
67.74/34.87	
67.74/34.87	(252) TransformationProof (EQUIVALENT)
67.74/34.87	By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS0(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]:
67.74/34.87	
67.74/34.87	   (new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))),new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))))
67.74/34.87	
67.74/34.87	
67.74/34.87	----------------------------------------
67.74/34.87	
67.74/34.87	(253)
67.74/34.87	Obligation:
67.74/34.87	Q DP problem:
67.74/34.87	The TRS P consists of the following rules:
67.74/34.87	
67.74/34.87	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.87	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS1, Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Zero))))
67.74/34.87	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.87	
67.74/34.87	The TRS R consists of the following rules:
67.74/34.87	
67.74/34.87	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.87	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.87	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.87	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.87	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.87	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.87	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.87	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.87	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.87	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.87	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.87	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.87	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.87	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.87	   new_error -> error([])
67.74/34.87	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.87	   new_primEqInt2 -> True
67.74/34.87	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.87	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.87	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.87	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.87	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.87	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.87	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.87	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.87	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.87	   new_primMinusNatS1 -> Zero
67.74/34.87	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.87	   new_primEqInt1 -> True
67.74/34.87	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.87	   new_primEqInt0(vuz3260) -> False
67.74/34.87	   new_primEqInt(vuz3250) -> False
67.74/34.87	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.87	
67.74/34.87	The set Q consists of the following terms:
67.74/34.87	
67.74/34.87	   new_rem(Neg(x0), Neg(Zero))
67.74/34.87	   new_primEqInt1
67.74/34.87	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.87	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.87	   new_primMinusNatS1
67.74/34.87	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.87	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.87	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.87	   new_primMinusNatS2(Zero, Zero)
67.74/34.87	   new_error
67.74/34.87	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.87	   new_rem(Pos(x0), Pos(Zero))
67.74/34.87	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.87	   new_primEqInt0(x0)
67.74/34.87	   new_esEs(Pos(Zero))
67.74/34.87	   new_esEs(Pos(Succ(x0)))
67.74/34.87	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.87	   new_primModNatS02(x0, x1)
67.74/34.87	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.87	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.87	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.87	   new_primModNatS1(Zero, x0)
67.74/34.87	   new_primEqInt(x0)
67.74/34.87	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.87	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.88	   new_rem(Pos(x0), Neg(Zero))
67.74/34.88	   new_rem(Neg(x0), Pos(Zero))
67.74/34.88	   new_primMinusNatS0(x0)
67.74/34.88	   new_primEqInt2
67.74/34.88	   new_esEs(Neg(Zero))
67.74/34.88	   new_esEs(Neg(Succ(x0)))
67.74/34.88	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.88	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.88	
67.74/34.88	We have to consider all minimal (P,Q,R)-chains.
67.74/34.88	----------------------------------------
67.74/34.88	
67.74/34.88	(254) TransformationProof (EQUIVALENT)
67.74/34.88	By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS1, Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Zero)))) at position [0,0,0,0] we obtained the following new rules [LPAR04]:
67.74/34.88	
67.74/34.88	   (new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Zero, Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Zero)))),new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Zero, Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Zero)))))
67.74/34.88	
67.74/34.88	
67.74/34.88	----------------------------------------
67.74/34.88	
67.74/34.88	(255)
67.74/34.88	Obligation:
67.74/34.88	Q DP problem:
67.74/34.88	The TRS P consists of the following rules:
67.74/34.88	
67.74/34.88	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.88	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Zero, Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Zero))))
67.74/34.88	
67.74/34.88	The TRS R consists of the following rules:
67.74/34.88	
67.74/34.88	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.88	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.88	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.88	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.88	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.88	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.88	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.88	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.88	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.88	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.88	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.88	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.88	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.88	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.88	   new_error -> error([])
67.74/34.88	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.88	   new_primEqInt2 -> True
67.74/34.88	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.88	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.88	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.88	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.88	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.88	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.88	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.88	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.88	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.88	   new_primMinusNatS1 -> Zero
67.74/34.88	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.88	   new_primEqInt1 -> True
67.74/34.88	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.88	   new_primEqInt0(vuz3260) -> False
67.74/34.88	   new_primEqInt(vuz3250) -> False
67.74/34.88	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.88	
67.74/34.88	The set Q consists of the following terms:
67.74/34.88	
67.74/34.88	   new_rem(Neg(x0), Neg(Zero))
67.74/34.88	   new_primEqInt1
67.74/34.88	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.88	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.88	   new_primMinusNatS1
67.74/34.88	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.88	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.88	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.88	   new_primMinusNatS2(Zero, Zero)
67.74/34.88	   new_error
67.74/34.88	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.88	   new_rem(Pos(x0), Pos(Zero))
67.74/34.88	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.88	   new_primEqInt0(x0)
67.74/34.88	   new_esEs(Pos(Zero))
67.74/34.88	   new_esEs(Pos(Succ(x0)))
67.74/34.88	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.88	   new_primModNatS02(x0, x1)
67.74/34.88	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.88	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.88	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.88	   new_primModNatS1(Zero, x0)
67.74/34.88	   new_primEqInt(x0)
67.74/34.88	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.88	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.88	   new_rem(Pos(x0), Neg(Zero))
67.74/34.88	   new_rem(Neg(x0), Pos(Zero))
67.74/34.88	   new_primMinusNatS0(x0)
67.74/34.88	   new_primEqInt2
67.74/34.88	   new_esEs(Neg(Zero))
67.74/34.88	   new_esEs(Neg(Succ(x0)))
67.74/34.88	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.88	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.88	
67.74/34.88	We have to consider all minimal (P,Q,R)-chains.
67.74/34.88	----------------------------------------
67.74/34.88	
67.74/34.88	(256) TransformationProof (EQUIVALENT)
67.74/34.88	By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Zero, Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Zero)))) at position [0,0,0] we obtained the following new rules [LPAR04]:
67.74/34.88	
67.74/34.88	   (new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Neg(Zero)), Pos(Succ(Zero)), Neg(Succ(Succ(Zero)))),new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Neg(Zero)), Pos(Succ(Zero)), Neg(Succ(Succ(Zero)))))
67.74/34.88	
67.74/34.88	
67.74/34.88	----------------------------------------
67.74/34.88	
67.74/34.88	(257)
67.74/34.88	Obligation:
67.74/34.88	Q DP problem:
67.74/34.88	The TRS P consists of the following rules:
67.74/34.88	
67.74/34.88	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.88	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(new_esEs(Neg(Zero)), Pos(Succ(Zero)), Neg(Succ(Succ(Zero))))
67.74/34.88	
67.74/34.88	The TRS R consists of the following rules:
67.74/34.88	
67.74/34.88	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.88	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.88	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.88	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.88	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.88	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.88	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.88	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.88	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.88	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.88	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.88	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.88	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.88	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.88	   new_error -> error([])
67.74/34.88	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.88	   new_primEqInt2 -> True
67.74/34.88	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.88	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.88	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.88	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.88	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.88	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.88	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.88	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.88	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.88	   new_primMinusNatS1 -> Zero
67.74/34.88	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.88	   new_primEqInt1 -> True
67.74/34.88	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.88	   new_primEqInt0(vuz3260) -> False
67.74/34.88	   new_primEqInt(vuz3250) -> False
67.74/34.88	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.88	
67.74/34.88	The set Q consists of the following terms:
67.74/34.88	
67.74/34.88	   new_rem(Neg(x0), Neg(Zero))
67.74/34.88	   new_primEqInt1
67.74/34.88	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.88	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.88	   new_primMinusNatS1
67.74/34.88	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.88	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.88	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.88	   new_primMinusNatS2(Zero, Zero)
67.74/34.88	   new_error
67.74/34.88	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.88	   new_rem(Pos(x0), Pos(Zero))
67.74/34.88	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.88	   new_primEqInt0(x0)
67.74/34.88	   new_esEs(Pos(Zero))
67.74/34.88	   new_esEs(Pos(Succ(x0)))
67.74/34.88	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.88	   new_primModNatS02(x0, x1)
67.74/34.88	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.88	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.88	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.88	   new_primModNatS1(Zero, x0)
67.74/34.88	   new_primEqInt(x0)
67.74/34.88	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.88	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.88	   new_rem(Pos(x0), Neg(Zero))
67.74/34.88	   new_rem(Neg(x0), Pos(Zero))
67.74/34.88	   new_primMinusNatS0(x0)
67.74/34.88	   new_primEqInt2
67.74/34.88	   new_esEs(Neg(Zero))
67.74/34.88	   new_esEs(Neg(Succ(x0)))
67.74/34.88	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.88	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.88	
67.74/34.88	We have to consider all minimal (P,Q,R)-chains.
67.74/34.88	----------------------------------------
67.74/34.88	
67.74/34.88	(258) DependencyGraphProof (EQUIVALENT)
67.74/34.88	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
67.74/34.88	----------------------------------------
67.74/34.88	
67.74/34.88	(259)
67.74/34.88	Obligation:
67.74/34.88	Q DP problem:
67.74/34.88	The TRS P consists of the following rules:
67.74/34.88	
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.88	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.88	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.88	
67.74/34.88	The TRS R consists of the following rules:
67.74/34.88	
67.74/34.88	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.88	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.88	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.88	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.88	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.88	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.88	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.88	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.88	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.88	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.88	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.88	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.88	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.88	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.88	   new_error -> error([])
67.74/34.88	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.88	   new_primEqInt2 -> True
67.74/34.88	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.88	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.88	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.88	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.88	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.88	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.88	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.88	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.88	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.88	   new_primMinusNatS1 -> Zero
67.74/34.88	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.88	   new_primEqInt1 -> True
67.74/34.88	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.88	   new_primEqInt0(vuz3260) -> False
67.74/34.88	   new_primEqInt(vuz3250) -> False
67.74/34.88	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.88	
67.74/34.88	The set Q consists of the following terms:
67.74/34.88	
67.74/34.88	   new_rem(Neg(x0), Neg(Zero))
67.74/34.88	   new_primEqInt1
67.74/34.88	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.88	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.88	   new_primMinusNatS1
67.74/34.88	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.88	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.88	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.88	   new_primMinusNatS2(Zero, Zero)
67.74/34.88	   new_error
67.74/34.88	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.88	   new_rem(Pos(x0), Pos(Zero))
67.74/34.88	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.88	   new_primEqInt0(x0)
67.74/34.88	   new_esEs(Pos(Zero))
67.74/34.88	   new_esEs(Pos(Succ(x0)))
67.74/34.88	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.88	   new_primModNatS02(x0, x1)
67.74/34.88	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.88	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.88	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.88	   new_primModNatS1(Zero, x0)
67.74/34.88	   new_primEqInt(x0)
67.74/34.88	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.88	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.88	   new_rem(Pos(x0), Neg(Zero))
67.74/34.88	   new_rem(Neg(x0), Pos(Zero))
67.74/34.88	   new_primMinusNatS0(x0)
67.74/34.88	   new_primEqInt2
67.74/34.88	   new_esEs(Neg(Zero))
67.74/34.88	   new_esEs(Neg(Succ(x0)))
67.74/34.88	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.88	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.88	
67.74/34.88	We have to consider all minimal (P,Q,R)-chains.
67.74/34.88	----------------------------------------
67.74/34.88	
67.74/34.88	(260) TransformationProof (EQUIVALENT)
67.74/34.88	By narrowing [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) at position [0] we obtained the following new rules [LPAR04]:
67.74/34.88	
67.74/34.88	   (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))))
67.74/34.88	   (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Neg(Succ(Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Neg(Succ(Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))))
67.74/34.88	   (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS02(Succ(Zero), Succ(Zero)))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS02(Succ(Zero), Succ(Zero)))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))))
67.74/34.88	   (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS02(Succ(Succ(x2)), Succ(Zero)))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS02(Succ(Succ(x2)), Succ(Zero)))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))))
67.74/34.88	
67.74/34.88	
67.74/34.88	----------------------------------------
67.74/34.88	
67.74/34.88	(261)
67.74/34.88	Obligation:
67.74/34.88	Q DP problem:
67.74/34.88	The TRS P consists of the following rules:
67.74/34.88	
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.88	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.88	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Neg(Succ(Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS02(Succ(Zero), Succ(Zero)))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero)))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS02(Succ(Succ(x2)), Succ(Zero)))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.74/34.88	
67.74/34.88	The TRS R consists of the following rules:
67.74/34.88	
67.74/34.88	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.88	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.88	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.88	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.88	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.88	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.88	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.88	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.88	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.88	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.88	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.88	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.88	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.88	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.88	   new_error -> error([])
67.74/34.88	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.88	   new_primEqInt2 -> True
67.74/34.88	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.88	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.88	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.88	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.88	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.88	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.88	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.88	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.88	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.88	   new_primMinusNatS1 -> Zero
67.74/34.88	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.88	   new_primEqInt1 -> True
67.74/34.88	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.88	   new_primEqInt0(vuz3260) -> False
67.74/34.88	   new_primEqInt(vuz3250) -> False
67.74/34.88	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.88	
67.74/34.88	The set Q consists of the following terms:
67.74/34.88	
67.74/34.88	   new_rem(Neg(x0), Neg(Zero))
67.74/34.88	   new_primEqInt1
67.74/34.88	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.88	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.88	   new_primMinusNatS1
67.74/34.88	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.88	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.88	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.88	   new_primMinusNatS2(Zero, Zero)
67.74/34.88	   new_error
67.74/34.88	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.88	   new_rem(Pos(x0), Pos(Zero))
67.74/34.88	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.88	   new_primEqInt0(x0)
67.74/34.88	   new_esEs(Pos(Zero))
67.74/34.88	   new_esEs(Pos(Succ(x0)))
67.74/34.88	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.88	   new_primModNatS02(x0, x1)
67.74/34.88	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.88	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.88	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.88	   new_primModNatS1(Zero, x0)
67.74/34.88	   new_primEqInt(x0)
67.74/34.88	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.88	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.88	   new_rem(Pos(x0), Neg(Zero))
67.74/34.88	   new_rem(Neg(x0), Pos(Zero))
67.74/34.88	   new_primMinusNatS0(x0)
67.74/34.88	   new_primEqInt2
67.74/34.88	   new_esEs(Neg(Zero))
67.74/34.88	   new_esEs(Neg(Succ(x0)))
67.74/34.88	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.88	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.88	
67.74/34.88	We have to consider all minimal (P,Q,R)-chains.
67.74/34.88	----------------------------------------
67.74/34.88	
67.74/34.88	(262) TransformationProof (EQUIVALENT)
67.74/34.88	By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Neg(Succ(Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) at position [0] we obtained the following new rules [LPAR04]:
67.74/34.88	
67.74/34.88	   (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_primEqInt0(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_primEqInt0(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))))
67.74/34.88	
67.74/34.88	
67.74/34.88	----------------------------------------
67.74/34.88	
67.74/34.88	(263)
67.74/34.88	Obligation:
67.74/34.88	Q DP problem:
67.74/34.88	The TRS P consists of the following rules:
67.74/34.88	
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.88	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.88	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS02(Succ(Zero), Succ(Zero)))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero)))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS02(Succ(Succ(x2)), Succ(Zero)))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_primEqInt0(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.74/34.88	
67.74/34.88	The TRS R consists of the following rules:
67.74/34.88	
67.74/34.88	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.88	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.88	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.88	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.88	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.88	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.88	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.88	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.88	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.88	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.88	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.88	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.88	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.88	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.88	   new_error -> error([])
67.74/34.88	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.88	   new_primEqInt2 -> True
67.74/34.88	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.88	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.88	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.88	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.88	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.88	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.88	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.88	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.88	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.88	   new_primMinusNatS1 -> Zero
67.74/34.88	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.88	   new_primEqInt1 -> True
67.74/34.88	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.88	   new_primEqInt0(vuz3260) -> False
67.74/34.88	   new_primEqInt(vuz3250) -> False
67.74/34.88	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.88	
67.74/34.88	The set Q consists of the following terms:
67.74/34.88	
67.74/34.88	   new_rem(Neg(x0), Neg(Zero))
67.74/34.88	   new_primEqInt1
67.74/34.88	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.88	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.88	   new_primMinusNatS1
67.74/34.88	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.88	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.88	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.88	   new_primMinusNatS2(Zero, Zero)
67.74/34.88	   new_error
67.74/34.88	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.88	   new_rem(Pos(x0), Pos(Zero))
67.74/34.88	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.88	   new_primEqInt0(x0)
67.74/34.88	   new_esEs(Pos(Zero))
67.74/34.88	   new_esEs(Pos(Succ(x0)))
67.74/34.88	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.88	   new_primModNatS02(x0, x1)
67.74/34.88	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.88	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.88	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.88	   new_primModNatS1(Zero, x0)
67.74/34.88	   new_primEqInt(x0)
67.74/34.88	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.88	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.88	   new_rem(Pos(x0), Neg(Zero))
67.74/34.88	   new_rem(Neg(x0), Pos(Zero))
67.74/34.88	   new_primMinusNatS0(x0)
67.74/34.88	   new_primEqInt2
67.74/34.88	   new_esEs(Neg(Zero))
67.74/34.88	   new_esEs(Neg(Succ(x0)))
67.74/34.88	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.88	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.88	
67.74/34.88	We have to consider all minimal (P,Q,R)-chains.
67.74/34.88	----------------------------------------
67.74/34.88	
67.74/34.88	(264) TransformationProof (EQUIVALENT)
67.74/34.88	By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS02(Succ(Zero), Succ(Zero)))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) at position [0,0,0] we obtained the following new rules [LPAR04]:
67.74/34.88	
67.74/34.88	   (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Succ(Succ(Zero)), Succ(Succ(Zero))), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Succ(Succ(Zero)), Succ(Succ(Zero))), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))))
67.74/34.88	
67.74/34.88	
67.74/34.88	----------------------------------------
67.74/34.88	
67.74/34.88	(265)
67.74/34.88	Obligation:
67.74/34.88	Q DP problem:
67.74/34.88	The TRS P consists of the following rules:
67.74/34.88	
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.88	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.88	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS02(Succ(Succ(x2)), Succ(Zero)))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_primEqInt0(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Succ(Succ(Zero)), Succ(Succ(Zero))), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero)))))
67.74/34.88	
67.74/34.88	The TRS R consists of the following rules:
67.74/34.88	
67.74/34.88	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.88	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.88	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.88	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.88	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.88	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.88	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.88	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.88	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.88	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.88	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.88	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.88	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.88	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.88	   new_error -> error([])
67.74/34.88	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.88	   new_primEqInt2 -> True
67.74/34.88	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.88	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.88	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.88	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.88	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.88	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.88	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.88	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.88	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.88	   new_primMinusNatS1 -> Zero
67.74/34.88	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.88	   new_primEqInt1 -> True
67.74/34.88	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.88	   new_primEqInt0(vuz3260) -> False
67.74/34.88	   new_primEqInt(vuz3250) -> False
67.74/34.88	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.88	
67.74/34.88	The set Q consists of the following terms:
67.74/34.88	
67.74/34.88	   new_rem(Neg(x0), Neg(Zero))
67.74/34.88	   new_primEqInt1
67.74/34.88	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.88	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.88	   new_primMinusNatS1
67.74/34.88	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.88	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.88	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.88	   new_primMinusNatS2(Zero, Zero)
67.74/34.88	   new_error
67.74/34.88	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.88	   new_rem(Pos(x0), Pos(Zero))
67.74/34.88	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.88	   new_primEqInt0(x0)
67.74/34.88	   new_esEs(Pos(Zero))
67.74/34.88	   new_esEs(Pos(Succ(x0)))
67.74/34.88	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.88	   new_primModNatS02(x0, x1)
67.74/34.88	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.88	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.88	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.88	   new_primModNatS1(Zero, x0)
67.74/34.88	   new_primEqInt(x0)
67.74/34.88	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.88	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.88	   new_rem(Pos(x0), Neg(Zero))
67.74/34.88	   new_rem(Neg(x0), Pos(Zero))
67.74/34.88	   new_primMinusNatS0(x0)
67.74/34.88	   new_primEqInt2
67.74/34.88	   new_esEs(Neg(Zero))
67.74/34.88	   new_esEs(Neg(Succ(x0)))
67.74/34.88	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.88	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.88	
67.74/34.88	We have to consider all minimal (P,Q,R)-chains.
67.74/34.88	----------------------------------------
67.74/34.88	
67.74/34.88	(266) TransformationProof (EQUIVALENT)
67.74/34.88	By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS02(Succ(Succ(x2)), Succ(Zero)))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) at position [0,0,0] we obtained the following new rules [LPAR04]:
67.74/34.88	
67.74/34.88	   (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Succ(Succ(Succ(x2))), Succ(Succ(Zero))), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Succ(Succ(Succ(x2))), Succ(Succ(Zero))), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))))
67.74/34.88	
67.74/34.88	
67.74/34.88	----------------------------------------
67.74/34.88	
67.74/34.88	(267)
67.74/34.88	Obligation:
67.74/34.88	Q DP problem:
67.74/34.88	The TRS P consists of the following rules:
67.74/34.88	
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.88	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.88	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_primEqInt0(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Succ(Succ(Zero)), Succ(Succ(Zero))), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero)))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Succ(Succ(Succ(x2))), Succ(Succ(Zero))), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.74/34.88	
67.74/34.88	The TRS R consists of the following rules:
67.74/34.88	
67.74/34.88	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.88	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.88	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.88	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.88	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.88	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.88	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.88	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.88	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.88	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.88	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.88	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.88	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.88	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.88	   new_error -> error([])
67.74/34.88	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.88	   new_primEqInt2 -> True
67.74/34.88	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.88	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.88	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.88	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.88	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.88	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.88	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.88	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.88	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.88	   new_primMinusNatS1 -> Zero
67.74/34.88	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.88	   new_primEqInt1 -> True
67.74/34.88	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.88	   new_primEqInt0(vuz3260) -> False
67.74/34.88	   new_primEqInt(vuz3250) -> False
67.74/34.88	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.88	
67.74/34.88	The set Q consists of the following terms:
67.74/34.88	
67.74/34.88	   new_rem(Neg(x0), Neg(Zero))
67.74/34.88	   new_primEqInt1
67.74/34.88	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.88	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.88	   new_primMinusNatS1
67.74/34.88	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.88	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.88	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.88	   new_primMinusNatS2(Zero, Zero)
67.74/34.88	   new_error
67.74/34.88	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.88	   new_rem(Pos(x0), Pos(Zero))
67.74/34.88	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.88	   new_primEqInt0(x0)
67.74/34.88	   new_esEs(Pos(Zero))
67.74/34.88	   new_esEs(Pos(Succ(x0)))
67.74/34.88	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.88	   new_primModNatS02(x0, x1)
67.74/34.88	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.88	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.88	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.88	   new_primModNatS1(Zero, x0)
67.74/34.88	   new_primEqInt(x0)
67.74/34.88	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.88	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.88	   new_rem(Pos(x0), Neg(Zero))
67.74/34.88	   new_rem(Neg(x0), Pos(Zero))
67.74/34.88	   new_primMinusNatS0(x0)
67.74/34.88	   new_primEqInt2
67.74/34.88	   new_esEs(Neg(Zero))
67.74/34.88	   new_esEs(Neg(Succ(x0)))
67.74/34.88	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.88	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.88	
67.74/34.88	We have to consider all minimal (P,Q,R)-chains.
67.74/34.88	----------------------------------------
67.74/34.88	
67.74/34.88	(268) TransformationProof (EQUIVALENT)
67.74/34.88	By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_primEqInt0(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) at position [0] we obtained the following new rules [LPAR04]:
67.74/34.88	
67.74/34.88	   (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))))
67.74/34.88	
67.74/34.88	
67.74/34.88	----------------------------------------
67.74/34.88	
67.74/34.88	(269)
67.74/34.88	Obligation:
67.74/34.88	Q DP problem:
67.74/34.88	The TRS P consists of the following rules:
67.74/34.88	
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.88	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.88	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Succ(Succ(Zero)), Succ(Succ(Zero))), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero)))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Succ(Succ(Succ(x2))), Succ(Succ(Zero))), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.74/34.88	
67.74/34.88	The TRS R consists of the following rules:
67.74/34.88	
67.74/34.88	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.88	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.88	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.88	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.88	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.88	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.88	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.88	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.88	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.88	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.88	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.88	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.88	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.88	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.88	   new_error -> error([])
67.74/34.88	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.88	   new_primEqInt2 -> True
67.74/34.88	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.88	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.88	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.88	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.88	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.88	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.88	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.88	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.88	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.88	   new_primMinusNatS1 -> Zero
67.74/34.88	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.88	   new_primEqInt1 -> True
67.74/34.88	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.88	   new_primEqInt0(vuz3260) -> False
67.74/34.88	   new_primEqInt(vuz3250) -> False
67.74/34.88	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.88	
67.74/34.88	The set Q consists of the following terms:
67.74/34.88	
67.74/34.88	   new_rem(Neg(x0), Neg(Zero))
67.74/34.88	   new_primEqInt1
67.74/34.88	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.88	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.88	   new_primMinusNatS1
67.74/34.88	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.88	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.88	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.88	   new_primMinusNatS2(Zero, Zero)
67.74/34.88	   new_error
67.74/34.88	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.88	   new_rem(Pos(x0), Pos(Zero))
67.74/34.88	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.88	   new_primEqInt0(x0)
67.74/34.88	   new_esEs(Pos(Zero))
67.74/34.88	   new_esEs(Pos(Succ(x0)))
67.74/34.88	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.88	   new_primModNatS02(x0, x1)
67.74/34.88	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.88	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.88	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.88	   new_primModNatS1(Zero, x0)
67.74/34.88	   new_primEqInt(x0)
67.74/34.88	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.88	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.88	   new_rem(Pos(x0), Neg(Zero))
67.74/34.88	   new_rem(Neg(x0), Pos(Zero))
67.74/34.88	   new_primMinusNatS0(x0)
67.74/34.88	   new_primEqInt2
67.74/34.88	   new_esEs(Neg(Zero))
67.74/34.88	   new_esEs(Neg(Succ(x0)))
67.74/34.88	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.88	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.88	
67.74/34.88	We have to consider all minimal (P,Q,R)-chains.
67.74/34.88	----------------------------------------
67.74/34.88	
67.74/34.88	(270) TransformationProof (EQUIVALENT)
67.74/34.88	By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Succ(Succ(Zero)), Succ(Succ(Zero))), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]:
67.74/34.88	
67.74/34.88	   (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Succ(Zero), Succ(Zero)), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Succ(Zero), Succ(Zero)), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))))
67.74/34.88	
67.74/34.88	
67.74/34.88	----------------------------------------
67.74/34.88	
67.74/34.88	(271)
67.74/34.88	Obligation:
67.74/34.88	Q DP problem:
67.74/34.88	The TRS P consists of the following rules:
67.74/34.88	
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.88	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.88	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Succ(Succ(Succ(x2))), Succ(Succ(Zero))), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Succ(Zero), Succ(Zero)), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero)))))
67.74/34.88	
67.74/34.88	The TRS R consists of the following rules:
67.74/34.88	
67.74/34.88	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.88	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.88	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.88	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.88	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.88	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.88	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.88	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.88	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.88	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.88	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.88	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.88	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.88	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.88	   new_error -> error([])
67.74/34.88	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.88	   new_primEqInt2 -> True
67.74/34.88	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.88	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.88	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.88	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.88	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.88	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.88	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.88	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.88	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.88	   new_primMinusNatS1 -> Zero
67.74/34.88	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.88	   new_primEqInt1 -> True
67.74/34.88	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.88	   new_primEqInt0(vuz3260) -> False
67.74/34.88	   new_primEqInt(vuz3250) -> False
67.74/34.88	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.88	
67.74/34.88	The set Q consists of the following terms:
67.74/34.88	
67.74/34.88	   new_rem(Neg(x0), Neg(Zero))
67.74/34.88	   new_primEqInt1
67.74/34.88	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.88	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.88	   new_primMinusNatS1
67.74/34.88	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.88	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.88	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.88	   new_primMinusNatS2(Zero, Zero)
67.74/34.88	   new_error
67.74/34.88	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.88	   new_rem(Pos(x0), Pos(Zero))
67.74/34.88	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.88	   new_primEqInt0(x0)
67.74/34.88	   new_esEs(Pos(Zero))
67.74/34.88	   new_esEs(Pos(Succ(x0)))
67.74/34.88	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.88	   new_primModNatS02(x0, x1)
67.74/34.88	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.88	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.88	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.88	   new_primModNatS1(Zero, x0)
67.74/34.88	   new_primEqInt(x0)
67.74/34.88	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.88	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.88	   new_rem(Pos(x0), Neg(Zero))
67.74/34.88	   new_rem(Neg(x0), Pos(Zero))
67.74/34.88	   new_primMinusNatS0(x0)
67.74/34.88	   new_primEqInt2
67.74/34.88	   new_esEs(Neg(Zero))
67.74/34.88	   new_esEs(Neg(Succ(x0)))
67.74/34.88	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.88	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.88	
67.74/34.88	We have to consider all minimal (P,Q,R)-chains.
67.74/34.88	----------------------------------------
67.74/34.88	
67.74/34.88	(272) TransformationProof (EQUIVALENT)
67.74/34.88	By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Succ(Succ(Succ(x2))), Succ(Succ(Zero))), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]:
67.74/34.88	
67.74/34.88	   (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Succ(Succ(x2)), Succ(Zero)), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Succ(Succ(x2)), Succ(Zero)), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))))
67.74/34.88	
67.74/34.88	
67.74/34.88	----------------------------------------
67.74/34.88	
67.74/34.88	(273)
67.74/34.88	Obligation:
67.74/34.88	Q DP problem:
67.74/34.88	The TRS P consists of the following rules:
67.74/34.88	
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.88	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.88	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Succ(Zero), Succ(Zero)), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero)))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Succ(Succ(x2)), Succ(Zero)), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.74/34.88	
67.74/34.88	The TRS R consists of the following rules:
67.74/34.88	
67.74/34.88	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.88	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.88	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.88	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.88	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.88	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.88	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.88	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.88	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.88	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.88	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.88	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.88	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.88	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.88	   new_error -> error([])
67.74/34.88	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.88	   new_primEqInt2 -> True
67.74/34.88	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.88	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.88	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.88	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.88	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.88	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.88	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.88	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.88	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.88	   new_primMinusNatS1 -> Zero
67.74/34.88	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.88	   new_primEqInt1 -> True
67.74/34.88	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.88	   new_primEqInt0(vuz3260) -> False
67.74/34.88	   new_primEqInt(vuz3250) -> False
67.74/34.88	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.88	
67.74/34.88	The set Q consists of the following terms:
67.74/34.88	
67.74/34.88	   new_rem(Neg(x0), Neg(Zero))
67.74/34.88	   new_primEqInt1
67.74/34.88	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.88	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.88	   new_primMinusNatS1
67.74/34.88	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.88	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.88	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.88	   new_primMinusNatS2(Zero, Zero)
67.74/34.88	   new_error
67.74/34.88	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.88	   new_rem(Pos(x0), Pos(Zero))
67.74/34.88	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.88	   new_primEqInt0(x0)
67.74/34.88	   new_esEs(Pos(Zero))
67.74/34.88	   new_esEs(Pos(Succ(x0)))
67.74/34.88	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.88	   new_primModNatS02(x0, x1)
67.74/34.88	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.88	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.88	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.88	   new_primModNatS1(Zero, x0)
67.74/34.88	   new_primEqInt(x0)
67.74/34.88	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.88	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.88	   new_rem(Pos(x0), Neg(Zero))
67.74/34.88	   new_rem(Neg(x0), Pos(Zero))
67.74/34.88	   new_primMinusNatS0(x0)
67.74/34.88	   new_primEqInt2
67.74/34.88	   new_esEs(Neg(Zero))
67.74/34.88	   new_esEs(Neg(Succ(x0)))
67.74/34.88	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.88	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.88	
67.74/34.88	We have to consider all minimal (P,Q,R)-chains.
67.74/34.88	----------------------------------------
67.74/34.88	
67.74/34.88	(274) TransformationProof (EQUIVALENT)
67.74/34.88	By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Succ(Zero), Succ(Zero)), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]:
67.74/34.88	
67.74/34.88	   (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Zero, Zero), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Zero, Zero), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))))
67.74/34.88	
67.74/34.88	
67.74/34.88	----------------------------------------
67.74/34.88	
67.74/34.88	(275)
67.74/34.88	Obligation:
67.74/34.88	Q DP problem:
67.74/34.88	The TRS P consists of the following rules:
67.74/34.88	
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.88	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.88	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Succ(Succ(x2)), Succ(Zero)), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Zero, Zero), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero)))))
67.74/34.88	
67.74/34.88	The TRS R consists of the following rules:
67.74/34.88	
67.74/34.88	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.88	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.88	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.88	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.88	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.88	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.88	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.88	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.88	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.88	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.88	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.88	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.88	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.88	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.88	   new_error -> error([])
67.74/34.88	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.88	   new_primEqInt2 -> True
67.74/34.88	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.88	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.88	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.88	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.88	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.88	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.88	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.88	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.88	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.88	   new_primMinusNatS1 -> Zero
67.74/34.88	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.88	   new_primEqInt1 -> True
67.74/34.88	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.88	   new_primEqInt0(vuz3260) -> False
67.74/34.88	   new_primEqInt(vuz3250) -> False
67.74/34.88	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.88	
67.74/34.88	The set Q consists of the following terms:
67.74/34.88	
67.74/34.88	   new_rem(Neg(x0), Neg(Zero))
67.74/34.88	   new_primEqInt1
67.74/34.88	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.88	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.88	   new_primMinusNatS1
67.74/34.88	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.88	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.88	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.88	   new_primMinusNatS2(Zero, Zero)
67.74/34.88	   new_error
67.74/34.88	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.88	   new_rem(Pos(x0), Pos(Zero))
67.74/34.88	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.88	   new_primEqInt0(x0)
67.74/34.88	   new_esEs(Pos(Zero))
67.74/34.88	   new_esEs(Pos(Succ(x0)))
67.74/34.88	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.88	   new_primModNatS02(x0, x1)
67.74/34.88	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.88	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.88	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.88	   new_primModNatS1(Zero, x0)
67.74/34.88	   new_primEqInt(x0)
67.74/34.88	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.88	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.88	   new_rem(Pos(x0), Neg(Zero))
67.74/34.88	   new_rem(Neg(x0), Pos(Zero))
67.74/34.88	   new_primMinusNatS0(x0)
67.74/34.88	   new_primEqInt2
67.74/34.88	   new_esEs(Neg(Zero))
67.74/34.88	   new_esEs(Neg(Succ(x0)))
67.74/34.88	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.88	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.88	
67.74/34.88	We have to consider all minimal (P,Q,R)-chains.
67.74/34.88	----------------------------------------
67.74/34.88	
67.74/34.88	(276) TransformationProof (EQUIVALENT)
67.74/34.88	By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Succ(Succ(x2)), Succ(Zero)), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]:
67.74/34.88	
67.74/34.88	   (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Succ(x2), Zero), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Succ(x2), Zero), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))))
67.74/34.88	
67.74/34.88	
67.74/34.88	----------------------------------------
67.74/34.88	
67.74/34.88	(277)
67.74/34.88	Obligation:
67.74/34.88	Q DP problem:
67.74/34.88	The TRS P consists of the following rules:
67.74/34.88	
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.88	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.88	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Zero, Zero), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero)))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Succ(x2), Zero), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.74/34.88	
67.74/34.88	The TRS R consists of the following rules:
67.74/34.88	
67.74/34.88	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.88	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.88	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.88	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.88	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.88	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.88	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.88	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.88	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.88	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.88	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.88	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.88	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.88	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.88	   new_error -> error([])
67.74/34.88	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.88	   new_primEqInt2 -> True
67.74/34.88	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.88	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.88	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.88	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.88	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.88	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.88	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.88	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.88	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.88	   new_primMinusNatS1 -> Zero
67.74/34.88	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.88	   new_primEqInt1 -> True
67.74/34.88	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.88	   new_primEqInt0(vuz3260) -> False
67.74/34.88	   new_primEqInt(vuz3250) -> False
67.74/34.88	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.88	
67.74/34.88	The set Q consists of the following terms:
67.74/34.88	
67.74/34.88	   new_rem(Neg(x0), Neg(Zero))
67.74/34.88	   new_primEqInt1
67.74/34.88	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.88	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.88	   new_primMinusNatS1
67.74/34.88	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.88	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.88	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.88	   new_primMinusNatS2(Zero, Zero)
67.74/34.88	   new_error
67.74/34.88	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.88	   new_rem(Pos(x0), Pos(Zero))
67.74/34.88	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.88	   new_primEqInt0(x0)
67.74/34.88	   new_esEs(Pos(Zero))
67.74/34.88	   new_esEs(Pos(Succ(x0)))
67.74/34.88	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.88	   new_primModNatS02(x0, x1)
67.74/34.88	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.88	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.88	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.88	   new_primModNatS1(Zero, x0)
67.74/34.88	   new_primEqInt(x0)
67.74/34.88	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.88	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.88	   new_rem(Pos(x0), Neg(Zero))
67.74/34.88	   new_rem(Neg(x0), Pos(Zero))
67.74/34.88	   new_primMinusNatS0(x0)
67.74/34.88	   new_primEqInt2
67.74/34.88	   new_esEs(Neg(Zero))
67.74/34.88	   new_esEs(Neg(Succ(x0)))
67.74/34.88	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.88	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.88	
67.74/34.88	We have to consider all minimal (P,Q,R)-chains.
67.74/34.88	----------------------------------------
67.74/34.88	
67.74/34.88	(278) TransformationProof (EQUIVALENT)
67.74/34.88	By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Zero, Zero), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]:
67.74/34.88	
67.74/34.88	   (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Zero, Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Zero, Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))))
67.74/34.88	
67.74/34.88	
67.74/34.88	----------------------------------------
67.74/34.88	
67.74/34.88	(279)
67.74/34.88	Obligation:
67.74/34.88	Q DP problem:
67.74/34.88	The TRS P consists of the following rules:
67.74/34.88	
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.88	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.88	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Succ(x2), Zero), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Zero, Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero)))))
67.74/34.88	
67.74/34.88	The TRS R consists of the following rules:
67.74/34.88	
67.74/34.88	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.88	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.88	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.88	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.88	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.88	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.88	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.88	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.88	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.88	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.88	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.88	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.88	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.88	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.88	   new_error -> error([])
67.74/34.88	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.88	   new_primEqInt2 -> True
67.74/34.88	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.88	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.88	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.88	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.88	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.88	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.88	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.88	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.88	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.88	   new_primMinusNatS1 -> Zero
67.74/34.88	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.88	   new_primEqInt1 -> True
67.74/34.88	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.88	   new_primEqInt0(vuz3260) -> False
67.74/34.88	   new_primEqInt(vuz3250) -> False
67.74/34.88	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.88	
67.74/34.88	The set Q consists of the following terms:
67.74/34.88	
67.74/34.88	   new_rem(Neg(x0), Neg(Zero))
67.74/34.88	   new_primEqInt1
67.74/34.88	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.88	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.88	   new_primMinusNatS1
67.74/34.88	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.88	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.88	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.88	   new_primMinusNatS2(Zero, Zero)
67.74/34.88	   new_error
67.74/34.88	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.88	   new_rem(Pos(x0), Pos(Zero))
67.74/34.88	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.88	   new_primEqInt0(x0)
67.74/34.88	   new_esEs(Pos(Zero))
67.74/34.88	   new_esEs(Pos(Succ(x0)))
67.74/34.88	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.88	   new_primModNatS02(x0, x1)
67.74/34.88	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.88	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.88	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.88	   new_primModNatS1(Zero, x0)
67.74/34.88	   new_primEqInt(x0)
67.74/34.88	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.88	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.88	   new_rem(Pos(x0), Neg(Zero))
67.74/34.88	   new_rem(Neg(x0), Pos(Zero))
67.74/34.88	   new_primMinusNatS0(x0)
67.74/34.88	   new_primEqInt2
67.74/34.88	   new_esEs(Neg(Zero))
67.74/34.88	   new_esEs(Neg(Succ(x0)))
67.74/34.88	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.88	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.88	
67.74/34.88	We have to consider all minimal (P,Q,R)-chains.
67.74/34.88	----------------------------------------
67.74/34.88	
67.74/34.88	(280) TransformationProof (EQUIVALENT)
67.74/34.88	By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Succ(x2), Zero), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]:
67.74/34.88	
67.74/34.88	   (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))))
67.74/34.88	
67.74/34.88	
67.74/34.88	----------------------------------------
67.74/34.88	
67.74/34.88	(281)
67.74/34.88	Obligation:
67.74/34.88	Q DP problem:
67.74/34.88	The TRS P consists of the following rules:
67.74/34.88	
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.88	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.88	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Zero, Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero)))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.74/34.88	
67.74/34.88	The TRS R consists of the following rules:
67.74/34.88	
67.74/34.88	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.88	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.88	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.88	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.88	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.88	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.88	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.88	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.88	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.88	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.88	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.88	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.88	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.88	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.88	   new_error -> error([])
67.74/34.88	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.88	   new_primEqInt2 -> True
67.74/34.88	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.88	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.88	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.88	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.88	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.88	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.88	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.88	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.88	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.88	   new_primMinusNatS1 -> Zero
67.74/34.88	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.88	   new_primEqInt1 -> True
67.74/34.88	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.88	   new_primEqInt0(vuz3260) -> False
67.74/34.88	   new_primEqInt(vuz3250) -> False
67.74/34.88	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.88	
67.74/34.88	The set Q consists of the following terms:
67.74/34.88	
67.74/34.88	   new_rem(Neg(x0), Neg(Zero))
67.74/34.88	   new_primEqInt1
67.74/34.88	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.88	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.88	   new_primMinusNatS1
67.74/34.88	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.88	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.88	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.88	   new_primMinusNatS2(Zero, Zero)
67.74/34.88	   new_error
67.74/34.88	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.88	   new_rem(Pos(x0), Pos(Zero))
67.74/34.88	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.88	   new_primEqInt0(x0)
67.74/34.88	   new_esEs(Pos(Zero))
67.74/34.88	   new_esEs(Pos(Succ(x0)))
67.74/34.88	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.88	   new_primModNatS02(x0, x1)
67.74/34.88	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.88	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.88	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.88	   new_primModNatS1(Zero, x0)
67.74/34.88	   new_primEqInt(x0)
67.74/34.88	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.88	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.88	   new_rem(Pos(x0), Neg(Zero))
67.74/34.88	   new_rem(Neg(x0), Pos(Zero))
67.74/34.88	   new_primMinusNatS0(x0)
67.74/34.88	   new_primEqInt2
67.74/34.88	   new_esEs(Neg(Zero))
67.74/34.88	   new_esEs(Neg(Succ(x0)))
67.74/34.88	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.88	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.88	
67.74/34.88	We have to consider all minimal (P,Q,R)-chains.
67.74/34.88	----------------------------------------
67.74/34.88	
67.74/34.88	(282) TransformationProof (EQUIVALENT)
67.74/34.88	By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Zero, Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) at position [0,0,0] we obtained the following new rules [LPAR04]:
67.74/34.88	
67.74/34.88	   (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Neg(Zero)), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Neg(Zero)), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))))
67.74/34.88	
67.74/34.88	
67.74/34.88	----------------------------------------
67.74/34.88	
67.74/34.88	(283)
67.74/34.88	Obligation:
67.74/34.88	Q DP problem:
67.74/34.88	The TRS P consists of the following rules:
67.74/34.88	
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.88	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.88	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Neg(Zero)), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero)))))
67.74/34.88	
67.74/34.88	The TRS R consists of the following rules:
67.74/34.88	
67.74/34.88	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.88	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.88	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.88	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.88	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.88	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.88	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.88	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.88	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.88	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.88	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.88	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.88	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.88	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.88	   new_error -> error([])
67.74/34.88	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.88	   new_primEqInt2 -> True
67.74/34.88	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.88	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.88	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.88	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.88	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.88	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.88	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.88	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.88	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.88	   new_primMinusNatS1 -> Zero
67.74/34.88	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.88	   new_primEqInt1 -> True
67.74/34.88	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.88	   new_primEqInt0(vuz3260) -> False
67.74/34.88	   new_primEqInt(vuz3250) -> False
67.74/34.88	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.88	
67.74/34.88	The set Q consists of the following terms:
67.74/34.88	
67.74/34.88	   new_rem(Neg(x0), Neg(Zero))
67.74/34.88	   new_primEqInt1
67.74/34.88	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.88	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.88	   new_primMinusNatS1
67.74/34.88	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.88	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.88	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.88	   new_primMinusNatS2(Zero, Zero)
67.74/34.88	   new_error
67.74/34.88	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.88	   new_rem(Pos(x0), Pos(Zero))
67.74/34.88	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.88	   new_primEqInt0(x0)
67.74/34.88	   new_esEs(Pos(Zero))
67.74/34.88	   new_esEs(Pos(Succ(x0)))
67.74/34.88	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.88	   new_primModNatS02(x0, x1)
67.74/34.88	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.88	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.88	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.88	   new_primModNatS1(Zero, x0)
67.74/34.88	   new_primEqInt(x0)
67.74/34.88	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.88	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.88	   new_rem(Pos(x0), Neg(Zero))
67.74/34.88	   new_rem(Neg(x0), Pos(Zero))
67.74/34.88	   new_primMinusNatS0(x0)
67.74/34.88	   new_primEqInt2
67.74/34.88	   new_esEs(Neg(Zero))
67.74/34.88	   new_esEs(Neg(Succ(x0)))
67.74/34.88	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.88	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.88	
67.74/34.88	We have to consider all minimal (P,Q,R)-chains.
67.74/34.88	----------------------------------------
67.74/34.88	
67.74/34.88	(284) DependencyGraphProof (EQUIVALENT)
67.74/34.88	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
67.74/34.88	----------------------------------------
67.74/34.88	
67.74/34.88	(285)
67.74/34.88	Obligation:
67.74/34.88	Q DP problem:
67.74/34.88	The TRS P consists of the following rules:
67.74/34.88	
67.74/34.88	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.88	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.74/34.88	
67.74/34.88	The TRS R consists of the following rules:
67.74/34.88	
67.74/34.88	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.88	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.88	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.88	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.88	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.88	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.88	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.88	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.88	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.88	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.88	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.88	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.88	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.88	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.88	   new_error -> error([])
67.74/34.88	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.88	   new_primEqInt2 -> True
67.74/34.88	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.88	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.88	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.88	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.88	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.88	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.88	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.88	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.88	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.88	   new_primMinusNatS1 -> Zero
67.74/34.88	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.88	   new_primEqInt1 -> True
67.74/34.88	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.88	   new_primEqInt0(vuz3260) -> False
67.74/34.88	   new_primEqInt(vuz3250) -> False
67.74/34.88	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.88	
67.74/34.88	The set Q consists of the following terms:
67.74/34.88	
67.74/34.88	   new_rem(Neg(x0), Neg(Zero))
67.74/34.88	   new_primEqInt1
67.74/34.88	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.88	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.88	   new_primMinusNatS1
67.74/34.88	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.88	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.88	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.88	   new_primMinusNatS2(Zero, Zero)
67.74/34.88	   new_error
67.74/34.88	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.88	   new_rem(Pos(x0), Pos(Zero))
67.74/34.88	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.88	   new_primEqInt0(x0)
67.74/34.88	   new_esEs(Pos(Zero))
67.74/34.88	   new_esEs(Pos(Succ(x0)))
67.74/34.88	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.88	   new_primModNatS02(x0, x1)
67.74/34.88	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.88	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.88	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.88	   new_primModNatS1(Zero, x0)
67.74/34.88	   new_primEqInt(x0)
67.74/34.88	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.88	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.88	   new_rem(Pos(x0), Neg(Zero))
67.74/34.88	   new_rem(Neg(x0), Pos(Zero))
67.74/34.88	   new_primMinusNatS0(x0)
67.74/34.88	   new_primEqInt2
67.74/34.88	   new_esEs(Neg(Zero))
67.74/34.88	   new_esEs(Neg(Succ(x0)))
67.74/34.88	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.88	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.88	
67.74/34.88	We have to consider all minimal (P,Q,R)-chains.
67.74/34.88	----------------------------------------
67.74/34.88	
67.74/34.88	(286) TransformationProof (EQUIVALENT)
67.74/34.88	By narrowing [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) at position [0] we obtained the following new rules [LPAR04]:
67.74/34.88	
67.74/34.88	   (new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Neg(Succ(Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))),new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Neg(Succ(Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))))
67.74/34.88	   (new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0)))))),new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0)))))))
67.74/34.88	
67.74/34.88	
67.74/34.88	----------------------------------------
67.74/34.88	
67.74/34.88	(287)
67.74/34.88	Obligation:
67.74/34.88	Q DP problem:
67.74/34.88	The TRS P consists of the following rules:
67.74/34.88	
67.74/34.88	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.88	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.88	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.88	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Neg(Succ(Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero)))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0))))))
67.74/34.89	
67.74/34.89	The TRS R consists of the following rules:
67.74/34.89	
67.74/34.89	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.89	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.89	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.89	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.89	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.89	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.89	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.89	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.89	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.89	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.89	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.89	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.89	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.89	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.89	   new_error -> error([])
67.74/34.89	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.89	   new_primEqInt2 -> True
67.74/34.89	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.89	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.89	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.89	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.89	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.89	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.89	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.89	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.89	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.89	   new_primMinusNatS1 -> Zero
67.74/34.89	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.89	   new_primEqInt1 -> True
67.74/34.89	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.89	   new_primEqInt0(vuz3260) -> False
67.74/34.89	   new_primEqInt(vuz3250) -> False
67.74/34.89	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.89	
67.74/34.89	The set Q consists of the following terms:
67.74/34.89	
67.74/34.89	   new_rem(Neg(x0), Neg(Zero))
67.74/34.89	   new_primEqInt1
67.74/34.89	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.89	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.89	   new_primMinusNatS1
67.74/34.89	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.89	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.89	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.89	   new_primMinusNatS2(Zero, Zero)
67.74/34.89	   new_error
67.74/34.89	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.89	   new_rem(Pos(x0), Pos(Zero))
67.74/34.89	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.89	   new_primEqInt0(x0)
67.74/34.89	   new_esEs(Pos(Zero))
67.74/34.89	   new_esEs(Pos(Succ(x0)))
67.74/34.89	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.89	   new_primModNatS02(x0, x1)
67.74/34.89	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.89	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.89	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.89	   new_primModNatS1(Zero, x0)
67.74/34.89	   new_primEqInt(x0)
67.74/34.89	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.89	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.89	   new_rem(Pos(x0), Neg(Zero))
67.74/34.89	   new_rem(Neg(x0), Pos(Zero))
67.74/34.89	   new_primMinusNatS0(x0)
67.74/34.89	   new_primEqInt2
67.74/34.89	   new_esEs(Neg(Zero))
67.74/34.89	   new_esEs(Neg(Succ(x0)))
67.74/34.89	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.89	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.89	
67.74/34.89	We have to consider all minimal (P,Q,R)-chains.
67.74/34.89	----------------------------------------
67.74/34.89	
67.74/34.89	(288) TransformationProof (EQUIVALENT)
67.74/34.89	By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Neg(Succ(Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) at position [0] we obtained the following new rules [LPAR04]:
67.74/34.89	
67.74/34.89	   (new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_primEqInt0(Zero), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))),new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_primEqInt0(Zero), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))))
67.74/34.89	
67.74/34.89	
67.74/34.89	----------------------------------------
67.74/34.89	
67.74/34.89	(289)
67.74/34.89	Obligation:
67.74/34.89	Q DP problem:
67.74/34.89	The TRS P consists of the following rules:
67.74/34.89	
67.74/34.89	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.89	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0))))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_primEqInt0(Zero), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero)))))
67.74/34.89	
67.74/34.89	The TRS R consists of the following rules:
67.74/34.89	
67.74/34.89	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.89	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.89	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.89	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.89	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.89	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.89	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.89	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.89	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.89	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.89	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.89	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.89	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.89	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.89	   new_error -> error([])
67.74/34.89	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.89	   new_primEqInt2 -> True
67.74/34.89	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.89	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.89	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.89	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.89	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.89	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.89	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.89	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.89	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.89	   new_primMinusNatS1 -> Zero
67.74/34.89	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.89	   new_primEqInt1 -> True
67.74/34.89	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.89	   new_primEqInt0(vuz3260) -> False
67.74/34.89	   new_primEqInt(vuz3250) -> False
67.74/34.89	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.89	
67.74/34.89	The set Q consists of the following terms:
67.74/34.89	
67.74/34.89	   new_rem(Neg(x0), Neg(Zero))
67.74/34.89	   new_primEqInt1
67.74/34.89	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.89	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.89	   new_primMinusNatS1
67.74/34.89	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.89	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.89	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.89	   new_primMinusNatS2(Zero, Zero)
67.74/34.89	   new_error
67.74/34.89	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.89	   new_rem(Pos(x0), Pos(Zero))
67.74/34.89	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.89	   new_primEqInt0(x0)
67.74/34.89	   new_esEs(Pos(Zero))
67.74/34.89	   new_esEs(Pos(Succ(x0)))
67.74/34.89	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.89	   new_primModNatS02(x0, x1)
67.74/34.89	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.89	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.89	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.89	   new_primModNatS1(Zero, x0)
67.74/34.89	   new_primEqInt(x0)
67.74/34.89	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.89	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.89	   new_rem(Pos(x0), Neg(Zero))
67.74/34.89	   new_rem(Neg(x0), Pos(Zero))
67.74/34.89	   new_primMinusNatS0(x0)
67.74/34.89	   new_primEqInt2
67.74/34.89	   new_esEs(Neg(Zero))
67.74/34.89	   new_esEs(Neg(Succ(x0)))
67.74/34.89	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.89	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.89	
67.74/34.89	We have to consider all minimal (P,Q,R)-chains.
67.74/34.89	----------------------------------------
67.74/34.89	
67.74/34.89	(290) TransformationProof (EQUIVALENT)
67.74/34.89	By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_primEqInt0(Zero), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) at position [0] we obtained the following new rules [LPAR04]:
67.74/34.89	
67.74/34.89	   (new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))),new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))))
67.74/34.89	
67.74/34.89	
67.74/34.89	----------------------------------------
67.74/34.89	
67.74/34.89	(291)
67.74/34.89	Obligation:
67.74/34.89	Q DP problem:
67.74/34.89	The TRS P consists of the following rules:
67.74/34.89	
67.74/34.89	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.89	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0))))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero)))))
67.74/34.89	
67.74/34.89	The TRS R consists of the following rules:
67.74/34.89	
67.74/34.89	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.89	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.89	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.89	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.89	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.89	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.89	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.89	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.89	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.89	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.89	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.89	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.89	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.89	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.89	   new_error -> error([])
67.74/34.89	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.89	   new_primEqInt2 -> True
67.74/34.89	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.89	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.89	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.89	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.89	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.89	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.89	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.89	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.89	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.89	   new_primMinusNatS1 -> Zero
67.74/34.89	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.89	   new_primEqInt1 -> True
67.74/34.89	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.89	   new_primEqInt0(vuz3260) -> False
67.74/34.89	   new_primEqInt(vuz3250) -> False
67.74/34.89	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.89	
67.74/34.89	The set Q consists of the following terms:
67.74/34.89	
67.74/34.89	   new_rem(Neg(x0), Neg(Zero))
67.74/34.89	   new_primEqInt1
67.74/34.89	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.89	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.89	   new_primMinusNatS1
67.74/34.89	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.89	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.89	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.89	   new_primMinusNatS2(Zero, Zero)
67.74/34.89	   new_error
67.74/34.89	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.89	   new_rem(Pos(x0), Pos(Zero))
67.74/34.89	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.89	   new_primEqInt0(x0)
67.74/34.89	   new_esEs(Pos(Zero))
67.74/34.89	   new_esEs(Pos(Succ(x0)))
67.74/34.89	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.89	   new_primModNatS02(x0, x1)
67.74/34.89	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.89	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.89	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.89	   new_primModNatS1(Zero, x0)
67.74/34.89	   new_primEqInt(x0)
67.74/34.89	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.89	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.89	   new_rem(Pos(x0), Neg(Zero))
67.74/34.89	   new_rem(Neg(x0), Pos(Zero))
67.74/34.89	   new_primMinusNatS0(x0)
67.74/34.89	   new_primEqInt2
67.74/34.89	   new_esEs(Neg(Zero))
67.74/34.89	   new_esEs(Neg(Succ(x0)))
67.74/34.89	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.89	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.89	
67.74/34.89	We have to consider all minimal (P,Q,R)-chains.
67.74/34.89	----------------------------------------
67.74/34.89	
67.74/34.89	(292) TransformationProof (EQUIVALENT)
67.74/34.89	By narrowing [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) at position [0] we obtained the following new rules [LPAR04]:
67.74/34.89	
67.74/34.89	   (new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS0(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0)))))),new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS0(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0)))))))
67.74/34.89	   (new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS1, Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Zero))))),new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS1, Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Zero))))))
67.74/34.89	
67.74/34.89	
67.74/34.89	----------------------------------------
67.74/34.89	
67.74/34.89	(293)
67.74/34.89	Obligation:
67.74/34.89	Q DP problem:
67.74/34.89	The TRS P consists of the following rules:
67.74/34.89	
67.74/34.89	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.89	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0))))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero)))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS0(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0))))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS1, Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Zero)))))
67.74/34.89	
67.74/34.89	The TRS R consists of the following rules:
67.74/34.89	
67.74/34.89	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.89	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.89	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.89	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.89	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.89	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.89	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.89	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.89	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.89	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.89	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.89	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.89	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.89	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.89	   new_error -> error([])
67.74/34.89	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.89	   new_primEqInt2 -> True
67.74/34.89	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.89	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.89	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.89	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.89	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.89	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.89	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.89	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.89	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.89	   new_primMinusNatS1 -> Zero
67.74/34.89	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.89	   new_primEqInt1 -> True
67.74/34.89	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.89	   new_primEqInt0(vuz3260) -> False
67.74/34.89	   new_primEqInt(vuz3250) -> False
67.74/34.89	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.89	
67.74/34.89	The set Q consists of the following terms:
67.74/34.89	
67.74/34.89	   new_rem(Neg(x0), Neg(Zero))
67.74/34.89	   new_primEqInt1
67.74/34.89	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.89	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.89	   new_primMinusNatS1
67.74/34.89	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.89	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.89	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.89	   new_primMinusNatS2(Zero, Zero)
67.74/34.89	   new_error
67.74/34.89	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.89	   new_rem(Pos(x0), Pos(Zero))
67.74/34.89	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.89	   new_primEqInt0(x0)
67.74/34.89	   new_esEs(Pos(Zero))
67.74/34.89	   new_esEs(Pos(Succ(x0)))
67.74/34.89	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.89	   new_primModNatS02(x0, x1)
67.74/34.89	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.89	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.89	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.89	   new_primModNatS1(Zero, x0)
67.74/34.89	   new_primEqInt(x0)
67.74/34.89	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.89	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.89	   new_rem(Pos(x0), Neg(Zero))
67.74/34.89	   new_rem(Neg(x0), Pos(Zero))
67.74/34.89	   new_primMinusNatS0(x0)
67.74/34.89	   new_primEqInt2
67.74/34.89	   new_esEs(Neg(Zero))
67.74/34.89	   new_esEs(Neg(Succ(x0)))
67.74/34.89	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.89	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.89	
67.74/34.89	We have to consider all minimal (P,Q,R)-chains.
67.74/34.89	----------------------------------------
67.74/34.89	
67.74/34.89	(294) TransformationProof (EQUIVALENT)
67.74/34.89	By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS0(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0)))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]:
67.74/34.89	
67.74/34.89	   (new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0)))))),new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0)))))))
67.74/34.89	
67.74/34.89	
67.74/34.89	----------------------------------------
67.74/34.89	
67.74/34.89	(295)
67.74/34.89	Obligation:
67.74/34.89	Q DP problem:
67.74/34.89	The TRS P consists of the following rules:
67.74/34.89	
67.74/34.89	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.89	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0))))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero)))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS1, Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Zero)))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0))))))
67.74/34.89	
67.74/34.89	The TRS R consists of the following rules:
67.74/34.89	
67.74/34.89	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.89	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.89	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.89	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.89	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.89	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.89	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.89	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.89	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.89	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.89	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.89	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.89	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.89	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.89	   new_error -> error([])
67.74/34.89	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.89	   new_primEqInt2 -> True
67.74/34.89	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.89	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.89	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.89	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.89	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.89	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.89	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.89	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.89	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.89	   new_primMinusNatS1 -> Zero
67.74/34.89	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.89	   new_primEqInt1 -> True
67.74/34.89	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.89	   new_primEqInt0(vuz3260) -> False
67.74/34.89	   new_primEqInt(vuz3250) -> False
67.74/34.89	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.89	
67.74/34.89	The set Q consists of the following terms:
67.74/34.89	
67.74/34.89	   new_rem(Neg(x0), Neg(Zero))
67.74/34.89	   new_primEqInt1
67.74/34.89	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.89	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.89	   new_primMinusNatS1
67.74/34.89	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.89	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.89	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.89	   new_primMinusNatS2(Zero, Zero)
67.74/34.89	   new_error
67.74/34.89	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.89	   new_rem(Pos(x0), Pos(Zero))
67.74/34.89	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.89	   new_primEqInt0(x0)
67.74/34.89	   new_esEs(Pos(Zero))
67.74/34.89	   new_esEs(Pos(Succ(x0)))
67.74/34.89	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.89	   new_primModNatS02(x0, x1)
67.74/34.89	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.89	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.89	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.89	   new_primModNatS1(Zero, x0)
67.74/34.89	   new_primEqInt(x0)
67.74/34.89	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.89	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.89	   new_rem(Pos(x0), Neg(Zero))
67.74/34.89	   new_rem(Neg(x0), Pos(Zero))
67.74/34.89	   new_primMinusNatS0(x0)
67.74/34.89	   new_primEqInt2
67.74/34.89	   new_esEs(Neg(Zero))
67.74/34.89	   new_esEs(Neg(Succ(x0)))
67.74/34.89	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.89	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.89	
67.74/34.89	We have to consider all minimal (P,Q,R)-chains.
67.74/34.89	----------------------------------------
67.74/34.89	
67.74/34.89	(296) TransformationProof (EQUIVALENT)
67.74/34.89	By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS1, Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Zero))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]:
67.74/34.89	
67.74/34.89	   (new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Zero, Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Zero))))),new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Zero, Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Zero))))))
67.74/34.89	
67.74/34.89	
67.74/34.89	----------------------------------------
67.74/34.89	
67.74/34.89	(297)
67.74/34.89	Obligation:
67.74/34.89	Q DP problem:
67.74/34.89	The TRS P consists of the following rules:
67.74/34.89	
67.74/34.89	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.89	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0))))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero)))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0))))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Zero, Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Zero)))))
67.74/34.89	
67.74/34.89	The TRS R consists of the following rules:
67.74/34.89	
67.74/34.89	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.89	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.89	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.89	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.89	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.89	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.89	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.89	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.89	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.89	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.89	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.89	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.89	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.89	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.89	   new_error -> error([])
67.74/34.89	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.89	   new_primEqInt2 -> True
67.74/34.89	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.89	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.89	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.89	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.89	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.89	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.89	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.89	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.89	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.89	   new_primMinusNatS1 -> Zero
67.74/34.89	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.89	   new_primEqInt1 -> True
67.74/34.89	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.89	   new_primEqInt0(vuz3260) -> False
67.74/34.89	   new_primEqInt(vuz3250) -> False
67.74/34.89	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.89	
67.74/34.89	The set Q consists of the following terms:
67.74/34.89	
67.74/34.89	   new_rem(Neg(x0), Neg(Zero))
67.74/34.89	   new_primEqInt1
67.74/34.89	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.89	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.89	   new_primMinusNatS1
67.74/34.89	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.89	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.89	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.89	   new_primMinusNatS2(Zero, Zero)
67.74/34.89	   new_error
67.74/34.89	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.89	   new_rem(Pos(x0), Pos(Zero))
67.74/34.89	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.89	   new_primEqInt0(x0)
67.74/34.89	   new_esEs(Pos(Zero))
67.74/34.89	   new_esEs(Pos(Succ(x0)))
67.74/34.89	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.89	   new_primModNatS02(x0, x1)
67.74/34.89	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.89	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.89	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.89	   new_primModNatS1(Zero, x0)
67.74/34.89	   new_primEqInt(x0)
67.74/34.89	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.89	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.89	   new_rem(Pos(x0), Neg(Zero))
67.74/34.89	   new_rem(Neg(x0), Pos(Zero))
67.74/34.89	   new_primMinusNatS0(x0)
67.74/34.89	   new_primEqInt2
67.74/34.89	   new_esEs(Neg(Zero))
67.74/34.89	   new_esEs(Neg(Succ(x0)))
67.74/34.89	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.89	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.89	
67.74/34.89	We have to consider all minimal (P,Q,R)-chains.
67.74/34.89	----------------------------------------
67.74/34.89	
67.74/34.89	(298) TransformationProof (EQUIVALENT)
67.74/34.89	By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Zero, Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Zero))))) at position [0,0,0] we obtained the following new rules [LPAR04]:
67.74/34.89	
67.74/34.89	   (new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Neg(Zero)), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Zero))))),new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Neg(Zero)), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Zero))))))
67.74/34.89	
67.74/34.89	
67.74/34.89	----------------------------------------
67.74/34.89	
67.74/34.89	(299)
67.74/34.89	Obligation:
67.74/34.89	Q DP problem:
67.74/34.89	The TRS P consists of the following rules:
67.74/34.89	
67.74/34.89	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.89	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0))))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero)))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0))))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Neg(Zero)), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Zero)))))
67.74/34.89	
67.74/34.89	The TRS R consists of the following rules:
67.74/34.89	
67.74/34.89	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.89	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.89	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.89	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.89	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.89	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.89	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.89	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.89	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.89	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.89	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.89	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.89	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.89	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.89	   new_error -> error([])
67.74/34.89	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.89	   new_primEqInt2 -> True
67.74/34.89	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.89	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.89	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.89	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.89	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.89	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.89	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.89	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.89	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.89	   new_primMinusNatS1 -> Zero
67.74/34.89	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.89	   new_primEqInt1 -> True
67.74/34.89	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.89	   new_primEqInt0(vuz3260) -> False
67.74/34.89	   new_primEqInt(vuz3250) -> False
67.74/34.89	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.89	
67.74/34.89	The set Q consists of the following terms:
67.74/34.89	
67.74/34.89	   new_rem(Neg(x0), Neg(Zero))
67.74/34.89	   new_primEqInt1
67.74/34.89	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.89	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.89	   new_primMinusNatS1
67.74/34.89	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.89	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.89	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.89	   new_primMinusNatS2(Zero, Zero)
67.74/34.89	   new_error
67.74/34.89	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.89	   new_rem(Pos(x0), Pos(Zero))
67.74/34.89	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.89	   new_primEqInt0(x0)
67.74/34.89	   new_esEs(Pos(Zero))
67.74/34.89	   new_esEs(Pos(Succ(x0)))
67.74/34.89	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.89	   new_primModNatS02(x0, x1)
67.74/34.89	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.89	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.89	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.89	   new_primModNatS1(Zero, x0)
67.74/34.89	   new_primEqInt(x0)
67.74/34.89	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.89	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.89	   new_rem(Pos(x0), Neg(Zero))
67.74/34.89	   new_rem(Neg(x0), Pos(Zero))
67.74/34.89	   new_primMinusNatS0(x0)
67.74/34.89	   new_primEqInt2
67.74/34.89	   new_esEs(Neg(Zero))
67.74/34.89	   new_esEs(Neg(Succ(x0)))
67.74/34.89	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.89	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.89	
67.74/34.89	We have to consider all minimal (P,Q,R)-chains.
67.74/34.89	----------------------------------------
67.74/34.89	
67.74/34.89	(300) DependencyGraphProof (EQUIVALENT)
67.74/34.89	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
67.74/34.89	----------------------------------------
67.74/34.89	
67.74/34.89	(301)
67.74/34.89	Obligation:
67.74/34.89	Q DP problem:
67.74/34.89	The TRS P consists of the following rules:
67.74/34.89	
67.74/34.89	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.89	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0))))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero)))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0))))))
67.74/34.89	
67.74/34.89	The TRS R consists of the following rules:
67.74/34.89	
67.74/34.89	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.89	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.89	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.89	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.89	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.89	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.89	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.89	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.89	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.89	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.89	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.89	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.89	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.89	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.89	   new_error -> error([])
67.74/34.89	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.89	   new_primEqInt2 -> True
67.74/34.89	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.89	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.89	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.89	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.89	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.89	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.89	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.89	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.89	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.89	   new_primMinusNatS1 -> Zero
67.74/34.89	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.89	   new_primEqInt1 -> True
67.74/34.89	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.89	   new_primEqInt0(vuz3260) -> False
67.74/34.89	   new_primEqInt(vuz3250) -> False
67.74/34.89	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.89	
67.74/34.89	The set Q consists of the following terms:
67.74/34.89	
67.74/34.89	   new_rem(Neg(x0), Neg(Zero))
67.74/34.89	   new_primEqInt1
67.74/34.89	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.89	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.89	   new_primMinusNatS1
67.74/34.89	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.89	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.89	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.89	   new_primMinusNatS2(Zero, Zero)
67.74/34.89	   new_error
67.74/34.89	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.89	   new_rem(Pos(x0), Pos(Zero))
67.74/34.89	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.89	   new_primEqInt0(x0)
67.74/34.89	   new_esEs(Pos(Zero))
67.74/34.89	   new_esEs(Pos(Succ(x0)))
67.74/34.89	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.89	   new_primModNatS02(x0, x1)
67.74/34.89	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.89	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.89	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.89	   new_primModNatS1(Zero, x0)
67.74/34.89	   new_primEqInt(x0)
67.74/34.89	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.89	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.89	   new_rem(Pos(x0), Neg(Zero))
67.74/34.89	   new_rem(Neg(x0), Pos(Zero))
67.74/34.89	   new_primMinusNatS0(x0)
67.74/34.89	   new_primEqInt2
67.74/34.89	   new_esEs(Neg(Zero))
67.74/34.89	   new_esEs(Neg(Succ(x0)))
67.74/34.89	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.89	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.89	
67.74/34.89	We have to consider all minimal (P,Q,R)-chains.
67.74/34.89	----------------------------------------
67.74/34.89	
67.74/34.89	(302) TransformationProof (EQUIVALENT)
67.74/34.89	By narrowing [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) at position [0] we obtained the following new rules [LPAR04]:
67.74/34.89	
67.74/34.89	   (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))))
67.74/34.89	   (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Pos(Succ(Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Pos(Succ(Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))))
67.74/34.89	   (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS02(Succ(Zero), Succ(Zero)))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS02(Succ(Zero), Succ(Zero)))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))))
67.74/34.89	   (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS02(Succ(Succ(x2)), Succ(Zero)))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS02(Succ(Succ(x2)), Succ(Zero)))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))))
67.74/34.89	
67.74/34.89	
67.74/34.89	----------------------------------------
67.74/34.89	
67.74/34.89	(303)
67.74/34.89	Obligation:
67.74/34.89	Q DP problem:
67.74/34.89	The TRS P consists of the following rules:
67.74/34.89	
67.74/34.89	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.89	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0))))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero)))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0))))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Pos(Succ(Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS02(Succ(Zero), Succ(Zero)))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero)))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS02(Succ(Succ(x2)), Succ(Zero)))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.74/34.89	
67.74/34.89	The TRS R consists of the following rules:
67.74/34.89	
67.74/34.89	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.89	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.89	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.89	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.89	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.89	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.89	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.89	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.89	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.89	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.89	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.89	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.89	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.89	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.89	   new_error -> error([])
67.74/34.89	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.89	   new_primEqInt2 -> True
67.74/34.89	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.89	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.89	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.89	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.89	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.89	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.89	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.89	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.89	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.89	   new_primMinusNatS1 -> Zero
67.74/34.89	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.89	   new_primEqInt1 -> True
67.74/34.89	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.89	   new_primEqInt0(vuz3260) -> False
67.74/34.89	   new_primEqInt(vuz3250) -> False
67.74/34.89	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.89	
67.74/34.89	The set Q consists of the following terms:
67.74/34.89	
67.74/34.89	   new_rem(Neg(x0), Neg(Zero))
67.74/34.89	   new_primEqInt1
67.74/34.89	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.89	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.89	   new_primMinusNatS1
67.74/34.89	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.89	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.89	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.89	   new_primMinusNatS2(Zero, Zero)
67.74/34.89	   new_error
67.74/34.89	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.89	   new_rem(Pos(x0), Pos(Zero))
67.74/34.89	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.89	   new_primEqInt0(x0)
67.74/34.89	   new_esEs(Pos(Zero))
67.74/34.89	   new_esEs(Pos(Succ(x0)))
67.74/34.89	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.89	   new_primModNatS02(x0, x1)
67.74/34.89	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.89	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.89	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.89	   new_primModNatS1(Zero, x0)
67.74/34.89	   new_primEqInt(x0)
67.74/34.89	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.89	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.89	   new_rem(Pos(x0), Neg(Zero))
67.74/34.89	   new_rem(Neg(x0), Pos(Zero))
67.74/34.89	   new_primMinusNatS0(x0)
67.74/34.89	   new_primEqInt2
67.74/34.89	   new_esEs(Neg(Zero))
67.74/34.89	   new_esEs(Neg(Succ(x0)))
67.74/34.89	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.89	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.89	
67.74/34.89	We have to consider all minimal (P,Q,R)-chains.
67.74/34.89	----------------------------------------
67.74/34.89	
67.74/34.89	(304) TransformationProof (EQUIVALENT)
67.74/34.89	By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Pos(Succ(Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) at position [0] we obtained the following new rules [LPAR04]:
67.74/34.89	
67.74/34.89	   (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_primEqInt(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_primEqInt(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))))
67.74/34.89	
67.74/34.89	
67.74/34.89	----------------------------------------
67.74/34.89	
67.74/34.89	(305)
67.74/34.89	Obligation:
67.74/34.89	Q DP problem:
67.74/34.89	The TRS P consists of the following rules:
67.74/34.89	
67.74/34.89	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.89	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0))))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero)))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0))))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS02(Succ(Zero), Succ(Zero)))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero)))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS02(Succ(Succ(x2)), Succ(Zero)))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_primEqInt(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.74/34.89	
67.74/34.89	The TRS R consists of the following rules:
67.74/34.89	
67.74/34.89	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.89	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.89	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.89	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.89	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.89	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.89	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.89	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.89	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.89	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.89	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.89	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.89	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.89	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.89	   new_error -> error([])
67.74/34.89	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.89	   new_primEqInt2 -> True
67.74/34.89	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.89	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.89	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.89	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.89	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.89	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.89	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.89	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.89	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.89	   new_primMinusNatS1 -> Zero
67.74/34.89	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.89	   new_primEqInt1 -> True
67.74/34.89	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.89	   new_primEqInt0(vuz3260) -> False
67.74/34.89	   new_primEqInt(vuz3250) -> False
67.74/34.89	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.89	
67.74/34.89	The set Q consists of the following terms:
67.74/34.89	
67.74/34.89	   new_rem(Neg(x0), Neg(Zero))
67.74/34.89	   new_primEqInt1
67.74/34.89	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.89	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.89	   new_primMinusNatS1
67.74/34.89	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.89	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.89	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.89	   new_primMinusNatS2(Zero, Zero)
67.74/34.89	   new_error
67.74/34.89	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.89	   new_rem(Pos(x0), Pos(Zero))
67.74/34.89	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.89	   new_primEqInt0(x0)
67.74/34.89	   new_esEs(Pos(Zero))
67.74/34.89	   new_esEs(Pos(Succ(x0)))
67.74/34.89	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.89	   new_primModNatS02(x0, x1)
67.74/34.89	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.89	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.89	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.89	   new_primModNatS1(Zero, x0)
67.74/34.89	   new_primEqInt(x0)
67.74/34.89	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.89	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.89	   new_rem(Pos(x0), Neg(Zero))
67.74/34.89	   new_rem(Neg(x0), Pos(Zero))
67.74/34.89	   new_primMinusNatS0(x0)
67.74/34.89	   new_primEqInt2
67.74/34.89	   new_esEs(Neg(Zero))
67.74/34.89	   new_esEs(Neg(Succ(x0)))
67.74/34.89	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.89	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.89	
67.74/34.89	We have to consider all minimal (P,Q,R)-chains.
67.74/34.89	----------------------------------------
67.74/34.89	
67.74/34.89	(306) TransformationProof (EQUIVALENT)
67.74/34.89	By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS02(Succ(Zero), Succ(Zero)))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) at position [0,0,0] we obtained the following new rules [LPAR04]:
67.74/34.89	
67.74/34.89	   (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Succ(Succ(Zero)), Succ(Succ(Zero))), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Succ(Succ(Zero)), Succ(Succ(Zero))), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))))
67.74/34.89	
67.74/34.89	
67.74/34.89	----------------------------------------
67.74/34.89	
67.74/34.89	(307)
67.74/34.89	Obligation:
67.74/34.89	Q DP problem:
67.74/34.89	The TRS P consists of the following rules:
67.74/34.89	
67.74/34.89	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.89	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0))))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero)))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0))))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS02(Succ(Succ(x2)), Succ(Zero)))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_primEqInt(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Succ(Succ(Zero)), Succ(Succ(Zero))), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero)))))
67.74/34.89	
67.74/34.89	The TRS R consists of the following rules:
67.74/34.89	
67.74/34.89	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.89	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.89	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.89	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.89	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.89	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.89	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.89	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.89	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.89	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.89	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.89	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.89	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.89	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.89	   new_error -> error([])
67.74/34.89	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.89	   new_primEqInt2 -> True
67.74/34.89	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.89	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.89	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.89	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.89	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.89	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.89	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.89	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.89	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.89	   new_primMinusNatS1 -> Zero
67.74/34.89	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.89	   new_primEqInt1 -> True
67.74/34.89	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.89	   new_primEqInt0(vuz3260) -> False
67.74/34.89	   new_primEqInt(vuz3250) -> False
67.74/34.89	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.89	
67.74/34.89	The set Q consists of the following terms:
67.74/34.89	
67.74/34.89	   new_rem(Neg(x0), Neg(Zero))
67.74/34.89	   new_primEqInt1
67.74/34.89	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.89	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.89	   new_primMinusNatS1
67.74/34.89	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.89	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.89	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.89	   new_primMinusNatS2(Zero, Zero)
67.74/34.89	   new_error
67.74/34.89	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.89	   new_rem(Pos(x0), Pos(Zero))
67.74/34.89	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.89	   new_primEqInt0(x0)
67.74/34.89	   new_esEs(Pos(Zero))
67.74/34.89	   new_esEs(Pos(Succ(x0)))
67.74/34.89	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.89	   new_primModNatS02(x0, x1)
67.74/34.89	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.89	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.89	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.89	   new_primModNatS1(Zero, x0)
67.74/34.89	   new_primEqInt(x0)
67.74/34.89	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.89	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.89	   new_rem(Pos(x0), Neg(Zero))
67.74/34.89	   new_rem(Neg(x0), Pos(Zero))
67.74/34.89	   new_primMinusNatS0(x0)
67.74/34.89	   new_primEqInt2
67.74/34.89	   new_esEs(Neg(Zero))
67.74/34.89	   new_esEs(Neg(Succ(x0)))
67.74/34.89	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.89	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.89	
67.74/34.89	We have to consider all minimal (P,Q,R)-chains.
67.74/34.89	----------------------------------------
67.74/34.89	
67.74/34.89	(308) TransformationProof (EQUIVALENT)
67.74/34.89	By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS02(Succ(Succ(x2)), Succ(Zero)))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) at position [0,0,0] we obtained the following new rules [LPAR04]:
67.74/34.89	
67.74/34.89	   (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Succ(Succ(Succ(x2))), Succ(Succ(Zero))), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Succ(Succ(Succ(x2))), Succ(Succ(Zero))), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))))
67.74/34.89	
67.74/34.89	
67.74/34.89	----------------------------------------
67.74/34.89	
67.74/34.89	(309)
67.74/34.89	Obligation:
67.74/34.89	Q DP problem:
67.74/34.89	The TRS P consists of the following rules:
67.74/34.89	
67.74/34.89	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.89	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0))))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero)))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0))))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_primEqInt(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Succ(Succ(Zero)), Succ(Succ(Zero))), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero)))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Succ(Succ(Succ(x2))), Succ(Succ(Zero))), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.74/34.89	
67.74/34.89	The TRS R consists of the following rules:
67.74/34.89	
67.74/34.89	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.89	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.89	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.89	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.89	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.89	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.89	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.89	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.89	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.89	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.89	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.89	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.89	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.89	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.89	   new_error -> error([])
67.74/34.89	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.89	   new_primEqInt2 -> True
67.74/34.89	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.89	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.89	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.89	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.89	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.89	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.89	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.89	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.89	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.89	   new_primMinusNatS1 -> Zero
67.74/34.89	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.89	   new_primEqInt1 -> True
67.74/34.89	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.89	   new_primEqInt0(vuz3260) -> False
67.74/34.89	   new_primEqInt(vuz3250) -> False
67.74/34.89	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.89	
67.74/34.89	The set Q consists of the following terms:
67.74/34.89	
67.74/34.89	   new_rem(Neg(x0), Neg(Zero))
67.74/34.89	   new_primEqInt1
67.74/34.89	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.89	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.89	   new_primMinusNatS1
67.74/34.89	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.89	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.89	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.89	   new_primMinusNatS2(Zero, Zero)
67.74/34.89	   new_error
67.74/34.89	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.89	   new_rem(Pos(x0), Pos(Zero))
67.74/34.89	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.89	   new_primEqInt0(x0)
67.74/34.89	   new_esEs(Pos(Zero))
67.74/34.89	   new_esEs(Pos(Succ(x0)))
67.74/34.89	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.89	   new_primModNatS02(x0, x1)
67.74/34.89	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.89	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.89	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.89	   new_primModNatS1(Zero, x0)
67.74/34.89	   new_primEqInt(x0)
67.74/34.89	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.89	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.89	   new_rem(Pos(x0), Neg(Zero))
67.74/34.89	   new_rem(Neg(x0), Pos(Zero))
67.74/34.89	   new_primMinusNatS0(x0)
67.74/34.89	   new_primEqInt2
67.74/34.89	   new_esEs(Neg(Zero))
67.74/34.89	   new_esEs(Neg(Succ(x0)))
67.74/34.89	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.89	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.89	
67.74/34.89	We have to consider all minimal (P,Q,R)-chains.
67.74/34.89	----------------------------------------
67.74/34.89	
67.74/34.89	(310) TransformationProof (EQUIVALENT)
67.74/34.89	By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_primEqInt(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) at position [0] we obtained the following new rules [LPAR04]:
67.74/34.89	
67.74/34.89	   (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))))
67.74/34.89	
67.74/34.89	
67.74/34.89	----------------------------------------
67.74/34.89	
67.74/34.89	(311)
67.74/34.89	Obligation:
67.74/34.89	Q DP problem:
67.74/34.89	The TRS P consists of the following rules:
67.74/34.89	
67.74/34.89	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.89	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0))))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero)))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0))))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Succ(Succ(Zero)), Succ(Succ(Zero))), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero)))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Succ(Succ(Succ(x2))), Succ(Succ(Zero))), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.74/34.89	
67.74/34.89	The TRS R consists of the following rules:
67.74/34.89	
67.74/34.89	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.89	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.89	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.89	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.89	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.89	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.89	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.89	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.89	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.89	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.89	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.89	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.89	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.89	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.89	   new_error -> error([])
67.74/34.89	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.89	   new_primEqInt2 -> True
67.74/34.89	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.89	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.89	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.89	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.89	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.89	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.89	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.89	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.89	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.89	   new_primMinusNatS1 -> Zero
67.74/34.89	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.89	   new_primEqInt1 -> True
67.74/34.89	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.89	   new_primEqInt0(vuz3260) -> False
67.74/34.89	   new_primEqInt(vuz3250) -> False
67.74/34.89	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.89	
67.74/34.89	The set Q consists of the following terms:
67.74/34.89	
67.74/34.89	   new_rem(Neg(x0), Neg(Zero))
67.74/34.89	   new_primEqInt1
67.74/34.89	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.89	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.89	   new_primMinusNatS1
67.74/34.89	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.89	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.89	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.89	   new_primMinusNatS2(Zero, Zero)
67.74/34.89	   new_error
67.74/34.89	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.89	   new_rem(Pos(x0), Pos(Zero))
67.74/34.89	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.89	   new_primEqInt0(x0)
67.74/34.89	   new_esEs(Pos(Zero))
67.74/34.89	   new_esEs(Pos(Succ(x0)))
67.74/34.89	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.89	   new_primModNatS02(x0, x1)
67.74/34.89	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.89	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.89	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.89	   new_primModNatS1(Zero, x0)
67.74/34.89	   new_primEqInt(x0)
67.74/34.89	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.89	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.89	   new_rem(Pos(x0), Neg(Zero))
67.74/34.89	   new_rem(Neg(x0), Pos(Zero))
67.74/34.89	   new_primMinusNatS0(x0)
67.74/34.89	   new_primEqInt2
67.74/34.89	   new_esEs(Neg(Zero))
67.74/34.89	   new_esEs(Neg(Succ(x0)))
67.74/34.89	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.89	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.89	
67.74/34.89	We have to consider all minimal (P,Q,R)-chains.
67.74/34.89	----------------------------------------
67.74/34.89	
67.74/34.89	(312) TransformationProof (EQUIVALENT)
67.74/34.89	By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Succ(Succ(Zero)), Succ(Succ(Zero))), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]:
67.74/34.89	
67.74/34.89	   (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Succ(Zero), Succ(Zero)), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Succ(Zero), Succ(Zero)), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))))
67.74/34.89	
67.74/34.89	
67.74/34.89	----------------------------------------
67.74/34.89	
67.74/34.89	(313)
67.74/34.89	Obligation:
67.74/34.89	Q DP problem:
67.74/34.89	The TRS P consists of the following rules:
67.74/34.89	
67.74/34.89	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.89	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0))))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero)))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0))))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Succ(Succ(Succ(x2))), Succ(Succ(Zero))), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Succ(Zero), Succ(Zero)), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero)))))
67.74/34.89	
67.74/34.89	The TRS R consists of the following rules:
67.74/34.89	
67.74/34.89	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.89	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.89	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.89	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.89	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.89	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.89	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.89	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.89	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.89	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.89	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.89	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.89	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.89	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.89	   new_error -> error([])
67.74/34.89	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.89	   new_primEqInt2 -> True
67.74/34.89	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.89	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.89	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.89	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.89	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.89	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.89	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.89	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.89	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.89	   new_primMinusNatS1 -> Zero
67.74/34.89	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.89	   new_primEqInt1 -> True
67.74/34.89	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.89	   new_primEqInt0(vuz3260) -> False
67.74/34.89	   new_primEqInt(vuz3250) -> False
67.74/34.89	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.89	
67.74/34.89	The set Q consists of the following terms:
67.74/34.89	
67.74/34.89	   new_rem(Neg(x0), Neg(Zero))
67.74/34.89	   new_primEqInt1
67.74/34.89	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.89	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.89	   new_primMinusNatS1
67.74/34.89	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.89	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.89	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.89	   new_primMinusNatS2(Zero, Zero)
67.74/34.89	   new_error
67.74/34.89	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.89	   new_rem(Pos(x0), Pos(Zero))
67.74/34.89	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.89	   new_primEqInt0(x0)
67.74/34.89	   new_esEs(Pos(Zero))
67.74/34.89	   new_esEs(Pos(Succ(x0)))
67.74/34.89	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.89	   new_primModNatS02(x0, x1)
67.74/34.89	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.89	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.89	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.89	   new_primModNatS1(Zero, x0)
67.74/34.89	   new_primEqInt(x0)
67.74/34.89	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.89	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.89	   new_rem(Pos(x0), Neg(Zero))
67.74/34.89	   new_rem(Neg(x0), Pos(Zero))
67.74/34.89	   new_primMinusNatS0(x0)
67.74/34.89	   new_primEqInt2
67.74/34.89	   new_esEs(Neg(Zero))
67.74/34.89	   new_esEs(Neg(Succ(x0)))
67.74/34.89	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.89	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.89	
67.74/34.89	We have to consider all minimal (P,Q,R)-chains.
67.74/34.89	----------------------------------------
67.74/34.89	
67.74/34.89	(314) TransformationProof (EQUIVALENT)
67.74/34.89	By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Succ(Succ(Succ(x2))), Succ(Succ(Zero))), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]:
67.74/34.89	
67.74/34.89	   (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Succ(Succ(x2)), Succ(Zero)), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Succ(Succ(x2)), Succ(Zero)), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))))
67.74/34.89	
67.74/34.89	
67.74/34.89	----------------------------------------
67.74/34.89	
67.74/34.89	(315)
67.74/34.89	Obligation:
67.74/34.89	Q DP problem:
67.74/34.89	The TRS P consists of the following rules:
67.74/34.89	
67.74/34.89	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.89	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0))))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero)))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0))))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Succ(Zero), Succ(Zero)), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero)))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Succ(Succ(x2)), Succ(Zero)), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.74/34.89	
67.74/34.89	The TRS R consists of the following rules:
67.74/34.89	
67.74/34.89	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.89	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.89	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.89	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.89	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.89	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.89	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.89	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.89	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.89	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.89	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.89	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.89	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.89	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.89	   new_error -> error([])
67.74/34.89	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.89	   new_primEqInt2 -> True
67.74/34.89	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.89	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.89	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.89	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.89	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.89	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.89	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.89	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.89	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.89	   new_primMinusNatS1 -> Zero
67.74/34.89	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.89	   new_primEqInt1 -> True
67.74/34.89	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.89	   new_primEqInt0(vuz3260) -> False
67.74/34.89	   new_primEqInt(vuz3250) -> False
67.74/34.89	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.89	
67.74/34.89	The set Q consists of the following terms:
67.74/34.89	
67.74/34.89	   new_rem(Neg(x0), Neg(Zero))
67.74/34.89	   new_primEqInt1
67.74/34.89	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.89	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.89	   new_primMinusNatS1
67.74/34.89	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.89	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.89	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.89	   new_primMinusNatS2(Zero, Zero)
67.74/34.89	   new_error
67.74/34.89	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.89	   new_rem(Pos(x0), Pos(Zero))
67.74/34.89	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.89	   new_primEqInt0(x0)
67.74/34.89	   new_esEs(Pos(Zero))
67.74/34.89	   new_esEs(Pos(Succ(x0)))
67.74/34.89	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.89	   new_primModNatS02(x0, x1)
67.74/34.89	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.89	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.89	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.89	   new_primModNatS1(Zero, x0)
67.74/34.89	   new_primEqInt(x0)
67.74/34.89	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.89	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.89	   new_rem(Pos(x0), Neg(Zero))
67.74/34.89	   new_rem(Neg(x0), Pos(Zero))
67.74/34.89	   new_primMinusNatS0(x0)
67.74/34.89	   new_primEqInt2
67.74/34.89	   new_esEs(Neg(Zero))
67.74/34.89	   new_esEs(Neg(Succ(x0)))
67.74/34.89	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.89	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.89	
67.74/34.89	We have to consider all minimal (P,Q,R)-chains.
67.74/34.89	----------------------------------------
67.74/34.89	
67.74/34.89	(316) TransformationProof (EQUIVALENT)
67.74/34.89	By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Succ(Zero), Succ(Zero)), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]:
67.74/34.89	
67.74/34.89	   (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Zero, Zero), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Zero, Zero), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))))
67.74/34.89	
67.74/34.89	
67.74/34.89	----------------------------------------
67.74/34.89	
67.74/34.89	(317)
67.74/34.89	Obligation:
67.74/34.89	Q DP problem:
67.74/34.89	The TRS P consists of the following rules:
67.74/34.89	
67.74/34.89	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.89	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0))))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero)))))
67.74/34.89	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0))))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Succ(Succ(x2)), Succ(Zero)), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.74/34.89	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Zero, Zero), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero)))))
67.74/34.89	
67.74/34.89	The TRS R consists of the following rules:
67.74/34.89	
67.74/34.89	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.89	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.89	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.89	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.89	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.89	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.89	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.89	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.89	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.89	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.89	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.89	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.89	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.89	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.89	   new_error -> error([])
67.74/34.89	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.89	   new_primEqInt2 -> True
67.74/34.89	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.89	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.89	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.89	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.89	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.89	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.89	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.89	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.89	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.89	   new_primMinusNatS1 -> Zero
67.74/34.89	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.89	   new_primEqInt1 -> True
67.74/34.89	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.89	   new_primEqInt0(vuz3260) -> False
67.74/34.89	   new_primEqInt(vuz3250) -> False
67.74/34.89	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.89	
67.74/34.89	The set Q consists of the following terms:
67.74/34.89	
67.74/34.89	   new_rem(Neg(x0), Neg(Zero))
67.74/34.89	   new_primEqInt1
67.74/34.89	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.89	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.89	   new_primMinusNatS1
67.74/34.89	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.89	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.89	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.89	   new_primMinusNatS2(Zero, Zero)
67.74/34.89	   new_error
67.74/34.89	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.89	   new_rem(Pos(x0), Pos(Zero))
67.74/34.89	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.89	   new_primEqInt0(x0)
67.74/34.89	   new_esEs(Pos(Zero))
67.74/34.89	   new_esEs(Pos(Succ(x0)))
67.74/34.89	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.89	   new_primModNatS02(x0, x1)
67.74/34.89	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.89	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.89	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.89	   new_primModNatS1(Zero, x0)
67.74/34.89	   new_primEqInt(x0)
67.74/34.89	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.89	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.89	   new_rem(Pos(x0), Neg(Zero))
67.74/34.89	   new_rem(Neg(x0), Pos(Zero))
67.74/34.89	   new_primMinusNatS0(x0)
67.74/34.89	   new_primEqInt2
67.74/34.89	   new_esEs(Neg(Zero))
67.74/34.89	   new_esEs(Neg(Succ(x0)))
67.74/34.89	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.89	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.89	
67.74/34.89	We have to consider all minimal (P,Q,R)-chains.
67.74/34.89	----------------------------------------
67.74/34.89	
67.74/34.89	(318) TransformationProof (EQUIVALENT)
67.74/34.89	By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Succ(Succ(x2)), Succ(Zero)), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]:
67.74/34.89	
67.74/34.89	   (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Succ(x2), Zero), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Succ(x2), Zero), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))))
67.74/34.90	
67.74/34.90	
67.74/34.90	----------------------------------------
67.74/34.90	
67.74/34.90	(319)
67.74/34.90	Obligation:
67.74/34.90	Q DP problem:
67.74/34.90	The TRS P consists of the following rules:
67.74/34.90	
67.74/34.90	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.90	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0))))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero)))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0))))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Zero, Zero), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero)))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Succ(x2), Zero), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.74/34.90	
67.74/34.90	The TRS R consists of the following rules:
67.74/34.90	
67.74/34.90	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.90	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.90	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.90	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.90	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.90	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.90	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.90	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.90	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.90	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.90	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.90	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.90	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.90	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.90	   new_error -> error([])
67.74/34.90	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.90	   new_primEqInt2 -> True
67.74/34.90	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.90	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.90	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.90	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.90	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.90	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.90	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.90	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.90	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.90	   new_primMinusNatS1 -> Zero
67.74/34.90	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.90	   new_primEqInt1 -> True
67.74/34.90	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.90	   new_primEqInt0(vuz3260) -> False
67.74/34.90	   new_primEqInt(vuz3250) -> False
67.74/34.90	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.90	
67.74/34.90	The set Q consists of the following terms:
67.74/34.90	
67.74/34.90	   new_rem(Neg(x0), Neg(Zero))
67.74/34.90	   new_primEqInt1
67.74/34.90	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.90	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.90	   new_primMinusNatS1
67.74/34.90	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.90	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.90	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.90	   new_primMinusNatS2(Zero, Zero)
67.74/34.90	   new_error
67.74/34.90	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.90	   new_rem(Pos(x0), Pos(Zero))
67.74/34.90	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.90	   new_primEqInt0(x0)
67.74/34.90	   new_esEs(Pos(Zero))
67.74/34.90	   new_esEs(Pos(Succ(x0)))
67.74/34.90	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.90	   new_primModNatS02(x0, x1)
67.74/34.90	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.90	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.90	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.90	   new_primModNatS1(Zero, x0)
67.74/34.90	   new_primEqInt(x0)
67.74/34.90	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.90	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.90	   new_rem(Pos(x0), Neg(Zero))
67.74/34.90	   new_rem(Neg(x0), Pos(Zero))
67.74/34.90	   new_primMinusNatS0(x0)
67.74/34.90	   new_primEqInt2
67.74/34.90	   new_esEs(Neg(Zero))
67.74/34.90	   new_esEs(Neg(Succ(x0)))
67.74/34.90	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.90	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.90	
67.74/34.90	We have to consider all minimal (P,Q,R)-chains.
67.74/34.90	----------------------------------------
67.74/34.90	
67.74/34.90	(320) TransformationProof (EQUIVALENT)
67.74/34.90	By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Zero, Zero), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]:
67.74/34.90	
67.74/34.90	   (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Zero, Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Zero, Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))))
67.74/34.90	
67.74/34.90	
67.74/34.90	----------------------------------------
67.74/34.90	
67.74/34.90	(321)
67.74/34.90	Obligation:
67.74/34.90	Q DP problem:
67.74/34.90	The TRS P consists of the following rules:
67.74/34.90	
67.74/34.90	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.90	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0))))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero)))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0))))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Succ(x2), Zero), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Zero, Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero)))))
67.74/34.90	
67.74/34.90	The TRS R consists of the following rules:
67.74/34.90	
67.74/34.90	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.90	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.90	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.90	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.90	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.90	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.90	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.90	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.90	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.90	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.90	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.90	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.90	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.90	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.90	   new_error -> error([])
67.74/34.90	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.90	   new_primEqInt2 -> True
67.74/34.90	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.90	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.90	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.90	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.90	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.90	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.90	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.90	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.90	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.90	   new_primMinusNatS1 -> Zero
67.74/34.90	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.90	   new_primEqInt1 -> True
67.74/34.90	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.90	   new_primEqInt0(vuz3260) -> False
67.74/34.90	   new_primEqInt(vuz3250) -> False
67.74/34.90	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.90	
67.74/34.90	The set Q consists of the following terms:
67.74/34.90	
67.74/34.90	   new_rem(Neg(x0), Neg(Zero))
67.74/34.90	   new_primEqInt1
67.74/34.90	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.90	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.90	   new_primMinusNatS1
67.74/34.90	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.90	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.90	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.90	   new_primMinusNatS2(Zero, Zero)
67.74/34.90	   new_error
67.74/34.90	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.90	   new_rem(Pos(x0), Pos(Zero))
67.74/34.90	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.90	   new_primEqInt0(x0)
67.74/34.90	   new_esEs(Pos(Zero))
67.74/34.90	   new_esEs(Pos(Succ(x0)))
67.74/34.90	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.90	   new_primModNatS02(x0, x1)
67.74/34.90	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.90	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.90	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.90	   new_primModNatS1(Zero, x0)
67.74/34.90	   new_primEqInt(x0)
67.74/34.90	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.90	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.90	   new_rem(Pos(x0), Neg(Zero))
67.74/34.90	   new_rem(Neg(x0), Pos(Zero))
67.74/34.90	   new_primMinusNatS0(x0)
67.74/34.90	   new_primEqInt2
67.74/34.90	   new_esEs(Neg(Zero))
67.74/34.90	   new_esEs(Neg(Succ(x0)))
67.74/34.90	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.90	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.90	
67.74/34.90	We have to consider all minimal (P,Q,R)-chains.
67.74/34.90	----------------------------------------
67.74/34.90	
67.74/34.90	(322) TransformationProof (EQUIVALENT)
67.74/34.90	By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Succ(x2), Zero), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]:
67.74/34.90	
67.74/34.90	   (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))))
67.74/34.90	
67.74/34.90	
67.74/34.90	----------------------------------------
67.74/34.90	
67.74/34.90	(323)
67.74/34.90	Obligation:
67.74/34.90	Q DP problem:
67.74/34.90	The TRS P consists of the following rules:
67.74/34.90	
67.74/34.90	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.90	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0))))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero)))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0))))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Zero, Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero)))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.74/34.90	
67.74/34.90	The TRS R consists of the following rules:
67.74/34.90	
67.74/34.90	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.90	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.90	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.90	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.90	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.90	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.90	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.90	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.90	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.90	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.90	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.90	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.90	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.90	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.90	   new_error -> error([])
67.74/34.90	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.90	   new_primEqInt2 -> True
67.74/34.90	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.90	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.90	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.90	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.90	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.90	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.90	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.90	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.90	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.90	   new_primMinusNatS1 -> Zero
67.74/34.90	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.90	   new_primEqInt1 -> True
67.74/34.90	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.90	   new_primEqInt0(vuz3260) -> False
67.74/34.90	   new_primEqInt(vuz3250) -> False
67.74/34.90	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.90	
67.74/34.90	The set Q consists of the following terms:
67.74/34.90	
67.74/34.90	   new_rem(Neg(x0), Neg(Zero))
67.74/34.90	   new_primEqInt1
67.74/34.90	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.90	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.90	   new_primMinusNatS1
67.74/34.90	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.90	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.90	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.90	   new_primMinusNatS2(Zero, Zero)
67.74/34.90	   new_error
67.74/34.90	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.90	   new_rem(Pos(x0), Pos(Zero))
67.74/34.90	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.90	   new_primEqInt0(x0)
67.74/34.90	   new_esEs(Pos(Zero))
67.74/34.90	   new_esEs(Pos(Succ(x0)))
67.74/34.90	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.90	   new_primModNatS02(x0, x1)
67.74/34.90	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.90	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.90	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.90	   new_primModNatS1(Zero, x0)
67.74/34.90	   new_primEqInt(x0)
67.74/34.90	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.90	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.90	   new_rem(Pos(x0), Neg(Zero))
67.74/34.90	   new_rem(Neg(x0), Pos(Zero))
67.74/34.90	   new_primMinusNatS0(x0)
67.74/34.90	   new_primEqInt2
67.74/34.90	   new_esEs(Neg(Zero))
67.74/34.90	   new_esEs(Neg(Succ(x0)))
67.74/34.90	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.90	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.90	
67.74/34.90	We have to consider all minimal (P,Q,R)-chains.
67.74/34.90	----------------------------------------
67.74/34.90	
67.74/34.90	(324) TransformationProof (EQUIVALENT)
67.74/34.90	By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Zero, Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) at position [0,0,0] we obtained the following new rules [LPAR04]:
67.74/34.90	
67.74/34.90	   (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Pos(Zero)), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Pos(Zero)), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))))
67.74/34.90	
67.74/34.90	
67.74/34.90	----------------------------------------
67.74/34.90	
67.74/34.90	(325)
67.74/34.90	Obligation:
67.74/34.90	Q DP problem:
67.74/34.90	The TRS P consists of the following rules:
67.74/34.90	
67.74/34.90	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.90	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0))))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero)))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0))))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Pos(Zero)), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero)))))
67.74/34.90	
67.74/34.90	The TRS R consists of the following rules:
67.74/34.90	
67.74/34.90	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.90	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.90	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.90	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.90	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.90	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.90	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.90	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.90	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.90	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.90	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.90	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.90	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.90	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.90	   new_error -> error([])
67.74/34.90	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.90	   new_primEqInt2 -> True
67.74/34.90	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.90	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.90	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.90	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.90	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.90	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.90	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.90	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.90	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.90	   new_primMinusNatS1 -> Zero
67.74/34.90	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.90	   new_primEqInt1 -> True
67.74/34.90	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.90	   new_primEqInt0(vuz3260) -> False
67.74/34.90	   new_primEqInt(vuz3250) -> False
67.74/34.90	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.90	
67.74/34.90	The set Q consists of the following terms:
67.74/34.90	
67.74/34.90	   new_rem(Neg(x0), Neg(Zero))
67.74/34.90	   new_primEqInt1
67.74/34.90	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.90	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.90	   new_primMinusNatS1
67.74/34.90	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.90	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.90	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.90	   new_primMinusNatS2(Zero, Zero)
67.74/34.90	   new_error
67.74/34.90	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.90	   new_rem(Pos(x0), Pos(Zero))
67.74/34.90	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.90	   new_primEqInt0(x0)
67.74/34.90	   new_esEs(Pos(Zero))
67.74/34.90	   new_esEs(Pos(Succ(x0)))
67.74/34.90	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.90	   new_primModNatS02(x0, x1)
67.74/34.90	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.90	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.90	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.90	   new_primModNatS1(Zero, x0)
67.74/34.90	   new_primEqInt(x0)
67.74/34.90	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.90	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.90	   new_rem(Pos(x0), Neg(Zero))
67.74/34.90	   new_rem(Neg(x0), Pos(Zero))
67.74/34.90	   new_primMinusNatS0(x0)
67.74/34.90	   new_primEqInt2
67.74/34.90	   new_esEs(Neg(Zero))
67.74/34.90	   new_esEs(Neg(Succ(x0)))
67.74/34.90	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.90	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.90	
67.74/34.90	We have to consider all minimal (P,Q,R)-chains.
67.74/34.90	----------------------------------------
67.74/34.90	
67.74/34.90	(326) DependencyGraphProof (EQUIVALENT)
67.74/34.90	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
67.74/34.90	----------------------------------------
67.74/34.90	
67.74/34.90	(327)
67.74/34.90	Obligation:
67.74/34.90	Q DP problem:
67.74/34.90	The TRS P consists of the following rules:
67.74/34.90	
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.90	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.90	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0))))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero)))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0))))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.74/34.90	
67.74/34.90	The TRS R consists of the following rules:
67.74/34.90	
67.74/34.90	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.90	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.90	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.90	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.90	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.90	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.90	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.90	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.90	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.90	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.90	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.90	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.90	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.90	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.90	   new_error -> error([])
67.74/34.90	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.90	   new_primEqInt2 -> True
67.74/34.90	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.90	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.90	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.90	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.90	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.90	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.90	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.90	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.90	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.90	   new_primMinusNatS1 -> Zero
67.74/34.90	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.90	   new_primEqInt1 -> True
67.74/34.90	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.90	   new_primEqInt0(vuz3260) -> False
67.74/34.90	   new_primEqInt(vuz3250) -> False
67.74/34.90	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.90	
67.74/34.90	The set Q consists of the following terms:
67.74/34.90	
67.74/34.90	   new_rem(Neg(x0), Neg(Zero))
67.74/34.90	   new_primEqInt1
67.74/34.90	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.90	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.90	   new_primMinusNatS1
67.74/34.90	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.90	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.90	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.90	   new_primMinusNatS2(Zero, Zero)
67.74/34.90	   new_error
67.74/34.90	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.90	   new_rem(Pos(x0), Pos(Zero))
67.74/34.90	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.90	   new_primEqInt0(x0)
67.74/34.90	   new_esEs(Pos(Zero))
67.74/34.90	   new_esEs(Pos(Succ(x0)))
67.74/34.90	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.90	   new_primModNatS02(x0, x1)
67.74/34.90	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.90	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.90	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.90	   new_primModNatS1(Zero, x0)
67.74/34.90	   new_primEqInt(x0)
67.74/34.90	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.90	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.90	   new_rem(Pos(x0), Neg(Zero))
67.74/34.90	   new_rem(Neg(x0), Pos(Zero))
67.74/34.90	   new_primMinusNatS0(x0)
67.74/34.90	   new_primEqInt2
67.74/34.90	   new_esEs(Neg(Zero))
67.74/34.90	   new_esEs(Neg(Succ(x0)))
67.74/34.90	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.90	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.90	
67.74/34.90	We have to consider all minimal (P,Q,R)-chains.
67.74/34.90	----------------------------------------
67.74/34.90	
67.74/34.90	(328) TransformationProof (EQUIVALENT)
67.74/34.90	By narrowing [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) at position [0] we obtained the following new rules [LPAR04]:
67.74/34.90	
67.74/34.90	   (new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Pos(Succ(Zero))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))),new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Pos(Succ(Zero))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))))
67.74/34.90	   (new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, Zero, x0, Zero))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0)))))),new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, Zero, x0, Zero))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0)))))))
67.74/34.90	
67.74/34.90	
67.74/34.90	----------------------------------------
67.74/34.90	
67.74/34.90	(329)
67.74/34.90	Obligation:
67.74/34.90	Q DP problem:
67.74/34.90	The TRS P consists of the following rules:
67.74/34.90	
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.90	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.90	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0))))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero)))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0))))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Pos(Succ(Zero))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero)))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, Zero, x0, Zero))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0))))))
67.74/34.90	
67.74/34.90	The TRS R consists of the following rules:
67.74/34.90	
67.74/34.90	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.90	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.90	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.90	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.90	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.90	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.90	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.90	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.90	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.90	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.90	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.90	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.90	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.90	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.90	   new_error -> error([])
67.74/34.90	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.90	   new_primEqInt2 -> True
67.74/34.90	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.90	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.90	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.90	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.90	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.90	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.90	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.90	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.90	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.90	   new_primMinusNatS1 -> Zero
67.74/34.90	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.90	   new_primEqInt1 -> True
67.74/34.90	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.90	   new_primEqInt0(vuz3260) -> False
67.74/34.90	   new_primEqInt(vuz3250) -> False
67.74/34.90	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.90	
67.74/34.90	The set Q consists of the following terms:
67.74/34.90	
67.74/34.90	   new_rem(Neg(x0), Neg(Zero))
67.74/34.90	   new_primEqInt1
67.74/34.90	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.90	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.90	   new_primMinusNatS1
67.74/34.90	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.90	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.90	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.90	   new_primMinusNatS2(Zero, Zero)
67.74/34.90	   new_error
67.74/34.90	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.90	   new_rem(Pos(x0), Pos(Zero))
67.74/34.90	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.90	   new_primEqInt0(x0)
67.74/34.90	   new_esEs(Pos(Zero))
67.74/34.90	   new_esEs(Pos(Succ(x0)))
67.74/34.90	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.90	   new_primModNatS02(x0, x1)
67.74/34.90	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.90	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.90	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.90	   new_primModNatS1(Zero, x0)
67.74/34.90	   new_primEqInt(x0)
67.74/34.90	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.90	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.90	   new_rem(Pos(x0), Neg(Zero))
67.74/34.90	   new_rem(Neg(x0), Pos(Zero))
67.74/34.90	   new_primMinusNatS0(x0)
67.74/34.90	   new_primEqInt2
67.74/34.90	   new_esEs(Neg(Zero))
67.74/34.90	   new_esEs(Neg(Succ(x0)))
67.74/34.90	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.90	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.90	
67.74/34.90	We have to consider all minimal (P,Q,R)-chains.
67.74/34.90	----------------------------------------
67.74/34.90	
67.74/34.90	(330) TransformationProof (EQUIVALENT)
67.74/34.90	By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Pos(Succ(Zero))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) at position [0] we obtained the following new rules [LPAR04]:
67.74/34.90	
67.74/34.90	   (new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_primEqInt(Zero), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))),new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_primEqInt(Zero), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))))
67.74/34.90	
67.74/34.90	
67.74/34.90	----------------------------------------
67.74/34.90	
67.74/34.90	(331)
67.74/34.90	Obligation:
67.74/34.90	Q DP problem:
67.74/34.90	The TRS P consists of the following rules:
67.74/34.90	
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.90	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.90	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0))))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero)))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0))))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, Zero, x0, Zero))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0))))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_primEqInt(Zero), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero)))))
67.74/34.90	
67.74/34.90	The TRS R consists of the following rules:
67.74/34.90	
67.74/34.90	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.90	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.90	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.90	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.90	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.90	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.90	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.90	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.90	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.90	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.90	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.90	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.90	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.90	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.90	   new_error -> error([])
67.74/34.90	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.90	   new_primEqInt2 -> True
67.74/34.90	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.90	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.90	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.90	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.90	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.90	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.90	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.90	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.90	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.90	   new_primMinusNatS1 -> Zero
67.74/34.90	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.90	   new_primEqInt1 -> True
67.74/34.90	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.90	   new_primEqInt0(vuz3260) -> False
67.74/34.90	   new_primEqInt(vuz3250) -> False
67.74/34.90	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.90	
67.74/34.90	The set Q consists of the following terms:
67.74/34.90	
67.74/34.90	   new_rem(Neg(x0), Neg(Zero))
67.74/34.90	   new_primEqInt1
67.74/34.90	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.90	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.90	   new_primMinusNatS1
67.74/34.90	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.90	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.90	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.90	   new_primMinusNatS2(Zero, Zero)
67.74/34.90	   new_error
67.74/34.90	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.90	   new_rem(Pos(x0), Pos(Zero))
67.74/34.90	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.90	   new_primEqInt0(x0)
67.74/34.90	   new_esEs(Pos(Zero))
67.74/34.90	   new_esEs(Pos(Succ(x0)))
67.74/34.90	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.90	   new_primModNatS02(x0, x1)
67.74/34.90	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.90	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.90	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.90	   new_primModNatS1(Zero, x0)
67.74/34.90	   new_primEqInt(x0)
67.74/34.90	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.90	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.90	   new_rem(Pos(x0), Neg(Zero))
67.74/34.90	   new_rem(Neg(x0), Pos(Zero))
67.74/34.90	   new_primMinusNatS0(x0)
67.74/34.90	   new_primEqInt2
67.74/34.90	   new_esEs(Neg(Zero))
67.74/34.90	   new_esEs(Neg(Succ(x0)))
67.74/34.90	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.90	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.90	
67.74/34.90	We have to consider all minimal (P,Q,R)-chains.
67.74/34.90	----------------------------------------
67.74/34.90	
67.74/34.90	(332) TransformationProof (EQUIVALENT)
67.74/34.90	By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_primEqInt(Zero), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) at position [0] we obtained the following new rules [LPAR04]:
67.74/34.90	
67.74/34.90	   (new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))),new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))))
67.74/34.90	
67.74/34.90	
67.74/34.90	----------------------------------------
67.74/34.90	
67.74/34.90	(333)
67.74/34.90	Obligation:
67.74/34.90	Q DP problem:
67.74/34.90	The TRS P consists of the following rules:
67.74/34.90	
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.90	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.90	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0))))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero)))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0))))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, Zero, x0, Zero))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0))))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero)))))
67.74/34.90	
67.74/34.90	The TRS R consists of the following rules:
67.74/34.90	
67.74/34.90	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.90	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.90	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.90	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.90	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.90	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.90	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.90	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.90	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.90	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.90	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.90	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.90	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.90	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.90	   new_error -> error([])
67.74/34.90	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.90	   new_primEqInt2 -> True
67.74/34.90	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.90	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.90	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.90	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.90	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.90	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.90	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.90	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.90	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.90	   new_primMinusNatS1 -> Zero
67.74/34.90	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.90	   new_primEqInt1 -> True
67.74/34.90	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.90	   new_primEqInt0(vuz3260) -> False
67.74/34.90	   new_primEqInt(vuz3250) -> False
67.74/34.90	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.90	
67.74/34.90	The set Q consists of the following terms:
67.74/34.90	
67.74/34.90	   new_rem(Neg(x0), Neg(Zero))
67.74/34.90	   new_primEqInt1
67.74/34.90	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.90	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.90	   new_primMinusNatS1
67.74/34.90	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.90	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.90	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.90	   new_primMinusNatS2(Zero, Zero)
67.74/34.90	   new_error
67.74/34.90	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.90	   new_rem(Pos(x0), Pos(Zero))
67.74/34.90	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.90	   new_primEqInt0(x0)
67.74/34.90	   new_esEs(Pos(Zero))
67.74/34.90	   new_esEs(Pos(Succ(x0)))
67.74/34.90	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.90	   new_primModNatS02(x0, x1)
67.74/34.90	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.90	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.90	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.90	   new_primModNatS1(Zero, x0)
67.74/34.90	   new_primEqInt(x0)
67.74/34.90	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.90	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.90	   new_rem(Pos(x0), Neg(Zero))
67.74/34.90	   new_rem(Neg(x0), Pos(Zero))
67.74/34.90	   new_primMinusNatS0(x0)
67.74/34.90	   new_primEqInt2
67.74/34.90	   new_esEs(Neg(Zero))
67.74/34.90	   new_esEs(Neg(Succ(x0)))
67.74/34.90	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.90	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.90	
67.74/34.90	We have to consider all minimal (P,Q,R)-chains.
67.74/34.90	----------------------------------------
67.74/34.90	
67.74/34.90	(334) TransformationProof (EQUIVALENT)
67.74/34.90	By narrowing [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) at position [0] we obtained the following new rules [LPAR04]:
67.74/34.90	
67.74/34.90	   (new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS0(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0)))))),new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS0(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0)))))))
67.74/34.90	   (new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS1, Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Zero))))),new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS1, Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Zero))))))
67.74/34.90	
67.74/34.90	
67.74/34.90	----------------------------------------
67.74/34.90	
67.74/34.90	(335)
67.74/34.90	Obligation:
67.74/34.90	Q DP problem:
67.74/34.90	The TRS P consists of the following rules:
67.74/34.90	
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.90	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.90	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0))))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero)))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0))))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, Zero, x0, Zero))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0))))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero)))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS0(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0))))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS1, Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Zero)))))
67.74/34.90	
67.74/34.90	The TRS R consists of the following rules:
67.74/34.90	
67.74/34.90	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.90	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.90	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.90	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.90	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.90	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.90	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.90	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.90	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.90	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.90	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.90	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.90	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.90	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.90	   new_error -> error([])
67.74/34.90	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.90	   new_primEqInt2 -> True
67.74/34.90	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.90	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.90	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.90	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.90	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.90	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.90	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.90	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.90	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.90	   new_primMinusNatS1 -> Zero
67.74/34.90	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.90	   new_primEqInt1 -> True
67.74/34.90	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.90	   new_primEqInt0(vuz3260) -> False
67.74/34.90	   new_primEqInt(vuz3250) -> False
67.74/34.90	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.90	
67.74/34.90	The set Q consists of the following terms:
67.74/34.90	
67.74/34.90	   new_rem(Neg(x0), Neg(Zero))
67.74/34.90	   new_primEqInt1
67.74/34.90	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.90	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.90	   new_primMinusNatS1
67.74/34.90	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.90	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.90	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.90	   new_primMinusNatS2(Zero, Zero)
67.74/34.90	   new_error
67.74/34.90	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.90	   new_rem(Pos(x0), Pos(Zero))
67.74/34.90	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.90	   new_primEqInt0(x0)
67.74/34.90	   new_esEs(Pos(Zero))
67.74/34.90	   new_esEs(Pos(Succ(x0)))
67.74/34.90	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.90	   new_primModNatS02(x0, x1)
67.74/34.90	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.90	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.90	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.90	   new_primModNatS1(Zero, x0)
67.74/34.90	   new_primEqInt(x0)
67.74/34.90	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.90	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.90	   new_rem(Pos(x0), Neg(Zero))
67.74/34.90	   new_rem(Neg(x0), Pos(Zero))
67.74/34.90	   new_primMinusNatS0(x0)
67.74/34.90	   new_primEqInt2
67.74/34.90	   new_esEs(Neg(Zero))
67.74/34.90	   new_esEs(Neg(Succ(x0)))
67.74/34.90	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.90	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.90	
67.74/34.90	We have to consider all minimal (P,Q,R)-chains.
67.74/34.90	----------------------------------------
67.74/34.90	
67.74/34.90	(336) TransformationProof (EQUIVALENT)
67.74/34.90	By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS0(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0)))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]:
67.74/34.90	
67.74/34.90	   (new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0)))))),new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0)))))))
67.74/34.90	
67.74/34.90	
67.74/34.90	----------------------------------------
67.74/34.90	
67.74/34.90	(337)
67.74/34.90	Obligation:
67.74/34.90	Q DP problem:
67.74/34.90	The TRS P consists of the following rules:
67.74/34.90	
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.90	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.90	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0))))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero)))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0))))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, Zero, x0, Zero))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0))))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero)))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS1, Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Zero)))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0))))))
67.74/34.90	
67.74/34.90	The TRS R consists of the following rules:
67.74/34.90	
67.74/34.90	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.90	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.90	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.90	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.90	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.90	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.90	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.90	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.90	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.90	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.90	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.90	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.90	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.90	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.90	   new_error -> error([])
67.74/34.90	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.90	   new_primEqInt2 -> True
67.74/34.90	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.90	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.90	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.90	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.90	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.90	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.90	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.90	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.90	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.90	   new_primMinusNatS1 -> Zero
67.74/34.90	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.90	   new_primEqInt1 -> True
67.74/34.90	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.90	   new_primEqInt0(vuz3260) -> False
67.74/34.90	   new_primEqInt(vuz3250) -> False
67.74/34.90	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.90	
67.74/34.90	The set Q consists of the following terms:
67.74/34.90	
67.74/34.90	   new_rem(Neg(x0), Neg(Zero))
67.74/34.90	   new_primEqInt1
67.74/34.90	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.90	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.90	   new_primMinusNatS1
67.74/34.90	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.90	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.90	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.90	   new_primMinusNatS2(Zero, Zero)
67.74/34.90	   new_error
67.74/34.90	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.90	   new_rem(Pos(x0), Pos(Zero))
67.74/34.90	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.90	   new_primEqInt0(x0)
67.74/34.90	   new_esEs(Pos(Zero))
67.74/34.90	   new_esEs(Pos(Succ(x0)))
67.74/34.90	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.90	   new_primModNatS02(x0, x1)
67.74/34.90	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.90	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.90	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.90	   new_primModNatS1(Zero, x0)
67.74/34.90	   new_primEqInt(x0)
67.74/34.90	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.90	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.90	   new_rem(Pos(x0), Neg(Zero))
67.74/34.90	   new_rem(Neg(x0), Pos(Zero))
67.74/34.90	   new_primMinusNatS0(x0)
67.74/34.90	   new_primEqInt2
67.74/34.90	   new_esEs(Neg(Zero))
67.74/34.90	   new_esEs(Neg(Succ(x0)))
67.74/34.90	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.90	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.90	
67.74/34.90	We have to consider all minimal (P,Q,R)-chains.
67.74/34.90	----------------------------------------
67.74/34.90	
67.74/34.90	(338) TransformationProof (EQUIVALENT)
67.74/34.90	By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS1, Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Zero))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]:
67.74/34.90	
67.74/34.90	   (new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Zero, Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Zero))))),new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Zero, Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Zero))))))
67.74/34.90	
67.74/34.90	
67.74/34.90	----------------------------------------
67.74/34.90	
67.74/34.90	(339)
67.74/34.90	Obligation:
67.74/34.90	Q DP problem:
67.74/34.90	The TRS P consists of the following rules:
67.74/34.90	
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.90	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.90	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0))))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero)))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0))))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, Zero, x0, Zero))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0))))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero)))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0))))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Zero, Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Zero)))))
67.74/34.90	
67.74/34.90	The TRS R consists of the following rules:
67.74/34.90	
67.74/34.90	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.90	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.90	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.90	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.90	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.90	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.90	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.90	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.90	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.90	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.90	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.90	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.90	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.90	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.90	   new_error -> error([])
67.74/34.90	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.90	   new_primEqInt2 -> True
67.74/34.90	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.90	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.90	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.90	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.90	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.90	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.90	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.90	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.90	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.90	   new_primMinusNatS1 -> Zero
67.74/34.90	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.90	   new_primEqInt1 -> True
67.74/34.90	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.90	   new_primEqInt0(vuz3260) -> False
67.74/34.90	   new_primEqInt(vuz3250) -> False
67.74/34.90	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.90	
67.74/34.90	The set Q consists of the following terms:
67.74/34.90	
67.74/34.90	   new_rem(Neg(x0), Neg(Zero))
67.74/34.90	   new_primEqInt1
67.74/34.90	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.90	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.90	   new_primMinusNatS1
67.74/34.90	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.90	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.90	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.90	   new_primMinusNatS2(Zero, Zero)
67.74/34.90	   new_error
67.74/34.90	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.90	   new_rem(Pos(x0), Pos(Zero))
67.74/34.90	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.90	   new_primEqInt0(x0)
67.74/34.90	   new_esEs(Pos(Zero))
67.74/34.90	   new_esEs(Pos(Succ(x0)))
67.74/34.90	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.90	   new_primModNatS02(x0, x1)
67.74/34.90	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.90	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.90	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.90	   new_primModNatS1(Zero, x0)
67.74/34.90	   new_primEqInt(x0)
67.74/34.90	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.90	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.90	   new_rem(Pos(x0), Neg(Zero))
67.74/34.90	   new_rem(Neg(x0), Pos(Zero))
67.74/34.90	   new_primMinusNatS0(x0)
67.74/34.90	   new_primEqInt2
67.74/34.90	   new_esEs(Neg(Zero))
67.74/34.90	   new_esEs(Neg(Succ(x0)))
67.74/34.90	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.90	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.90	
67.74/34.90	We have to consider all minimal (P,Q,R)-chains.
67.74/34.90	----------------------------------------
67.74/34.90	
67.74/34.90	(340) TransformationProof (EQUIVALENT)
67.74/34.90	By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Zero, Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Zero))))) at position [0,0,0] we obtained the following new rules [LPAR04]:
67.74/34.90	
67.74/34.90	   (new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Pos(Zero)), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Zero))))),new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Pos(Zero)), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Zero))))))
67.74/34.90	
67.74/34.90	
67.74/34.90	----------------------------------------
67.74/34.90	
67.74/34.90	(341)
67.74/34.90	Obligation:
67.74/34.90	Q DP problem:
67.74/34.90	The TRS P consists of the following rules:
67.74/34.90	
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.90	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.90	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0))))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero)))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0))))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, Zero, x0, Zero))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0))))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero)))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0))))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Pos(Zero)), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Zero)))))
67.74/34.90	
67.74/34.90	The TRS R consists of the following rules:
67.74/34.90	
67.74/34.90	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.90	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.90	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.90	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.90	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.90	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.90	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.90	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.90	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.90	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.90	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.90	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.90	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.90	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.90	   new_error -> error([])
67.74/34.90	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.90	   new_primEqInt2 -> True
67.74/34.90	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.90	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.90	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.90	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.90	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.90	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.90	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.90	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.90	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.90	   new_primMinusNatS1 -> Zero
67.74/34.90	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.90	   new_primEqInt1 -> True
67.74/34.90	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.90	   new_primEqInt0(vuz3260) -> False
67.74/34.90	   new_primEqInt(vuz3250) -> False
67.74/34.90	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.90	
67.74/34.90	The set Q consists of the following terms:
67.74/34.90	
67.74/34.90	   new_rem(Neg(x0), Neg(Zero))
67.74/34.90	   new_primEqInt1
67.74/34.90	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.90	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.90	   new_primMinusNatS1
67.74/34.90	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.90	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.90	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.90	   new_primMinusNatS2(Zero, Zero)
67.74/34.90	   new_error
67.74/34.90	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.90	   new_rem(Pos(x0), Pos(Zero))
67.74/34.90	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.90	   new_primEqInt0(x0)
67.74/34.90	   new_esEs(Pos(Zero))
67.74/34.90	   new_esEs(Pos(Succ(x0)))
67.74/34.90	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.90	   new_primModNatS02(x0, x1)
67.74/34.90	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.90	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.90	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.90	   new_primModNatS1(Zero, x0)
67.74/34.90	   new_primEqInt(x0)
67.74/34.90	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.90	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.90	   new_rem(Pos(x0), Neg(Zero))
67.74/34.90	   new_rem(Neg(x0), Pos(Zero))
67.74/34.90	   new_primMinusNatS0(x0)
67.74/34.90	   new_primEqInt2
67.74/34.90	   new_esEs(Neg(Zero))
67.74/34.90	   new_esEs(Neg(Succ(x0)))
67.74/34.90	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.90	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.90	
67.74/34.90	We have to consider all minimal (P,Q,R)-chains.
67.74/34.90	----------------------------------------
67.74/34.90	
67.74/34.90	(342) DependencyGraphProof (EQUIVALENT)
67.74/34.90	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
67.74/34.90	----------------------------------------
67.74/34.90	
67.74/34.90	(343)
67.74/34.90	Obligation:
67.74/34.90	Q DP problem:
67.74/34.90	The TRS P consists of the following rules:
67.74/34.90	
67.74/34.90	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.90	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0))))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero)))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0))))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, Zero, x0, Zero))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0))))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero)))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0))))))
67.74/34.90	
67.74/34.90	The TRS R consists of the following rules:
67.74/34.90	
67.74/34.90	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.90	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.90	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.90	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.90	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.90	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.90	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.90	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.90	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.90	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.90	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.90	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.90	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.90	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.90	   new_error -> error([])
67.74/34.90	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.90	   new_primEqInt2 -> True
67.74/34.90	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.90	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.90	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.90	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.90	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.90	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.90	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.90	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.90	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.90	   new_primMinusNatS1 -> Zero
67.74/34.90	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.90	   new_primEqInt1 -> True
67.74/34.90	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.90	   new_primEqInt0(vuz3260) -> False
67.74/34.90	   new_primEqInt(vuz3250) -> False
67.74/34.90	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.90	
67.74/34.90	The set Q consists of the following terms:
67.74/34.90	
67.74/34.90	   new_rem(Neg(x0), Neg(Zero))
67.74/34.90	   new_primEqInt1
67.74/34.90	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.90	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.90	   new_primMinusNatS1
67.74/34.90	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.90	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.90	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.90	   new_primMinusNatS2(Zero, Zero)
67.74/34.90	   new_error
67.74/34.90	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.90	   new_rem(Pos(x0), Pos(Zero))
67.74/34.90	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.90	   new_primEqInt0(x0)
67.74/34.90	   new_esEs(Pos(Zero))
67.74/34.90	   new_esEs(Pos(Succ(x0)))
67.74/34.90	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.90	   new_primModNatS02(x0, x1)
67.74/34.90	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.90	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.90	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.90	   new_primModNatS1(Zero, x0)
67.74/34.90	   new_primEqInt(x0)
67.74/34.90	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.90	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.90	   new_rem(Pos(x0), Neg(Zero))
67.74/34.90	   new_rem(Neg(x0), Pos(Zero))
67.74/34.90	   new_primMinusNatS0(x0)
67.74/34.90	   new_primEqInt2
67.74/34.90	   new_esEs(Neg(Zero))
67.74/34.90	   new_esEs(Neg(Succ(x0)))
67.74/34.90	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.90	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.90	
67.74/34.90	We have to consider all minimal (P,Q,R)-chains.
67.74/34.90	----------------------------------------
67.74/34.90	
67.74/34.90	(344) TransformationProof (EQUIVALENT)
67.74/34.90	By narrowing [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Neg(Succ(Succ(Succ(x3)))), Pos(Succ(Succ(Succ(x2))))) at position [0] we obtained the following new rules [LPAR04]:
67.74/34.90	
67.74/34.90	   (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))))
67.74/34.90	   (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Pos(Succ(Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Pos(Succ(Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))))
67.74/34.90	   (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS02(Succ(Zero), Succ(Zero)))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS02(Succ(Zero), Succ(Zero)))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))))
67.74/34.90	   (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS02(Succ(Succ(x2)), Succ(Zero)))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS02(Succ(Succ(x2)), Succ(Zero)))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))))
67.74/34.90	
67.74/34.90	
67.74/34.90	----------------------------------------
67.74/34.90	
67.74/34.90	(345)
67.74/34.90	Obligation:
67.74/34.90	Q DP problem:
67.74/34.90	The TRS P consists of the following rules:
67.74/34.90	
67.74/34.90	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.90	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0))))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero)))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0))))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, Zero, x0, Zero))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0))))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero)))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0))))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Pos(Succ(Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS02(Succ(Zero), Succ(Zero)))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero)))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS02(Succ(Succ(x2)), Succ(Zero)))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.74/34.90	
67.74/34.90	The TRS R consists of the following rules:
67.74/34.90	
67.74/34.90	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.90	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.90	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.90	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.90	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.90	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.90	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.90	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.90	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.90	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.90	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.90	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.90	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.90	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.90	   new_error -> error([])
67.74/34.90	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.90	   new_primEqInt2 -> True
67.74/34.90	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.90	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.90	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.90	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.90	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.90	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.90	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.90	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.90	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.90	   new_primMinusNatS1 -> Zero
67.74/34.90	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.90	   new_primEqInt1 -> True
67.74/34.90	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.90	   new_primEqInt0(vuz3260) -> False
67.74/34.90	   new_primEqInt(vuz3250) -> False
67.74/34.90	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.90	
67.74/34.90	The set Q consists of the following terms:
67.74/34.90	
67.74/34.90	   new_rem(Neg(x0), Neg(Zero))
67.74/34.90	   new_primEqInt1
67.74/34.90	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.90	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.90	   new_primMinusNatS1
67.74/34.90	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.90	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.90	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.90	   new_primMinusNatS2(Zero, Zero)
67.74/34.90	   new_error
67.74/34.90	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.90	   new_rem(Pos(x0), Pos(Zero))
67.74/34.90	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.90	   new_primEqInt0(x0)
67.74/34.90	   new_esEs(Pos(Zero))
67.74/34.90	   new_esEs(Pos(Succ(x0)))
67.74/34.90	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.90	   new_primModNatS02(x0, x1)
67.74/34.90	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.90	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.90	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.90	   new_primModNatS1(Zero, x0)
67.74/34.90	   new_primEqInt(x0)
67.74/34.90	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.90	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.90	   new_rem(Pos(x0), Neg(Zero))
67.74/34.90	   new_rem(Neg(x0), Pos(Zero))
67.74/34.90	   new_primMinusNatS0(x0)
67.74/34.90	   new_primEqInt2
67.74/34.90	   new_esEs(Neg(Zero))
67.74/34.90	   new_esEs(Neg(Succ(x0)))
67.74/34.90	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.90	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.90	
67.74/34.90	We have to consider all minimal (P,Q,R)-chains.
67.74/34.90	----------------------------------------
67.74/34.90	
67.74/34.90	(346) TransformationProof (EQUIVALENT)
67.74/34.90	By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Pos(Succ(Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) at position [0] we obtained the following new rules [LPAR04]:
67.74/34.90	
67.74/34.90	   (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_primEqInt(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_primEqInt(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))))
67.74/34.90	
67.74/34.90	
67.74/34.90	----------------------------------------
67.74/34.90	
67.74/34.90	(347)
67.74/34.90	Obligation:
67.74/34.90	Q DP problem:
67.74/34.90	The TRS P consists of the following rules:
67.74/34.90	
67.74/34.90	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.90	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0))))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero)))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0))))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, Zero, x0, Zero))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0))))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero)))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0))))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS02(Succ(Zero), Succ(Zero)))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero)))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS02(Succ(Succ(x2)), Succ(Zero)))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_primEqInt(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.74/34.90	
67.74/34.90	The TRS R consists of the following rules:
67.74/34.90	
67.74/34.90	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.90	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.90	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.90	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.90	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.90	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.90	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.90	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.90	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.90	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.90	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.90	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.90	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.90	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.90	   new_error -> error([])
67.74/34.90	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.90	   new_primEqInt2 -> True
67.74/34.90	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.90	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.90	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.90	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.90	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.90	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.90	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.90	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.90	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.90	   new_primMinusNatS1 -> Zero
67.74/34.90	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.90	   new_primEqInt1 -> True
67.74/34.90	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.90	   new_primEqInt0(vuz3260) -> False
67.74/34.90	   new_primEqInt(vuz3250) -> False
67.74/34.90	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.90	
67.74/34.90	The set Q consists of the following terms:
67.74/34.90	
67.74/34.90	   new_rem(Neg(x0), Neg(Zero))
67.74/34.90	   new_primEqInt1
67.74/34.90	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.90	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.90	   new_primMinusNatS1
67.74/34.90	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.90	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.90	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.90	   new_primMinusNatS2(Zero, Zero)
67.74/34.90	   new_error
67.74/34.90	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.90	   new_rem(Pos(x0), Pos(Zero))
67.74/34.90	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.90	   new_primEqInt0(x0)
67.74/34.90	   new_esEs(Pos(Zero))
67.74/34.90	   new_esEs(Pos(Succ(x0)))
67.74/34.90	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.90	   new_primModNatS02(x0, x1)
67.74/34.90	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.90	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.90	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.90	   new_primModNatS1(Zero, x0)
67.74/34.90	   new_primEqInt(x0)
67.74/34.90	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.90	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.90	   new_rem(Pos(x0), Neg(Zero))
67.74/34.90	   new_rem(Neg(x0), Pos(Zero))
67.74/34.90	   new_primMinusNatS0(x0)
67.74/34.90	   new_primEqInt2
67.74/34.90	   new_esEs(Neg(Zero))
67.74/34.90	   new_esEs(Neg(Succ(x0)))
67.74/34.90	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.90	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.90	
67.74/34.90	We have to consider all minimal (P,Q,R)-chains.
67.74/34.90	----------------------------------------
67.74/34.90	
67.74/34.90	(348) TransformationProof (EQUIVALENT)
67.74/34.90	By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS02(Succ(Zero), Succ(Zero)))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) at position [0,0,0] we obtained the following new rules [LPAR04]:
67.74/34.90	
67.74/34.90	   (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Succ(Succ(Zero)), Succ(Succ(Zero))), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Succ(Succ(Zero)), Succ(Succ(Zero))), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))))
67.74/34.90	
67.74/34.90	
67.74/34.90	----------------------------------------
67.74/34.90	
67.74/34.90	(349)
67.74/34.90	Obligation:
67.74/34.90	Q DP problem:
67.74/34.90	The TRS P consists of the following rules:
67.74/34.90	
67.74/34.90	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.90	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0))))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero)))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0))))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, Zero, x0, Zero))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0))))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero)))))
67.74/34.90	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0))))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS02(Succ(Succ(x2)), Succ(Zero)))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_primEqInt(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.74/34.90	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Succ(Succ(Zero)), Succ(Succ(Zero))), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero)))))
67.74/34.90	
67.74/34.90	The TRS R consists of the following rules:
67.74/34.90	
67.74/34.90	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.90	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.90	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.90	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.90	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.90	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.90	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.90	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.90	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.90	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.90	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.90	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.90	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.90	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.90	   new_error -> error([])
67.74/34.90	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.90	   new_primEqInt2 -> True
67.74/34.90	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.90	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.90	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.90	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.90	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.90	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.90	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.90	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.91	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.91	   new_primMinusNatS1 -> Zero
67.74/34.91	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.91	   new_primEqInt1 -> True
67.74/34.91	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.91	   new_primEqInt0(vuz3260) -> False
67.74/34.91	   new_primEqInt(vuz3250) -> False
67.74/34.91	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.91	
67.74/34.91	The set Q consists of the following terms:
67.74/34.91	
67.74/34.91	   new_rem(Neg(x0), Neg(Zero))
67.74/34.91	   new_primEqInt1
67.74/34.91	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.91	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.91	   new_primMinusNatS1
67.74/34.91	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.91	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.91	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.91	   new_primMinusNatS2(Zero, Zero)
67.74/34.91	   new_error
67.74/34.91	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.91	   new_rem(Pos(x0), Pos(Zero))
67.74/34.91	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.91	   new_primEqInt0(x0)
67.74/34.91	   new_esEs(Pos(Zero))
67.74/34.91	   new_esEs(Pos(Succ(x0)))
67.74/34.91	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.91	   new_primModNatS02(x0, x1)
67.74/34.91	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.91	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.91	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.91	   new_primModNatS1(Zero, x0)
67.74/34.91	   new_primEqInt(x0)
67.74/34.91	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.91	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.91	   new_rem(Pos(x0), Neg(Zero))
67.74/34.91	   new_rem(Neg(x0), Pos(Zero))
67.74/34.91	   new_primMinusNatS0(x0)
67.74/34.91	   new_primEqInt2
67.74/34.91	   new_esEs(Neg(Zero))
67.74/34.91	   new_esEs(Neg(Succ(x0)))
67.74/34.91	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.91	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.91	
67.74/34.91	We have to consider all minimal (P,Q,R)-chains.
67.74/34.91	----------------------------------------
67.74/34.91	
67.74/34.91	(350) TransformationProof (EQUIVALENT)
67.74/34.91	By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS02(Succ(Succ(x2)), Succ(Zero)))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) at position [0,0,0] we obtained the following new rules [LPAR04]:
67.74/34.91	
67.74/34.91	   (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Succ(Succ(Succ(x2))), Succ(Succ(Zero))), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Succ(Succ(Succ(x2))), Succ(Succ(Zero))), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))))
67.74/34.91	
67.74/34.91	
67.74/34.91	----------------------------------------
67.74/34.91	
67.74/34.91	(351)
67.74/34.91	Obligation:
67.74/34.91	Q DP problem:
67.74/34.91	The TRS P consists of the following rules:
67.74/34.91	
67.74/34.91	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.91	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.91	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.91	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.74/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.74/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.74/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0))))))
67.74/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero)))))
67.74/34.91	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0))))))
67.74/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.74/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.74/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.74/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, Zero, x0, Zero))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0))))))
67.74/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero)))))
67.74/34.91	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0))))))
67.74/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.74/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_primEqInt(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.74/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Succ(Succ(Zero)), Succ(Succ(Zero))), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero)))))
67.74/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Succ(Succ(Succ(x2))), Succ(Succ(Zero))), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.74/34.91	
67.74/34.91	The TRS R consists of the following rules:
67.74/34.91	
67.74/34.91	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.91	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.91	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.91	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.91	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.91	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.91	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.91	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.91	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.91	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.91	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.91	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.91	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.91	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.91	   new_error -> error([])
67.74/34.91	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.91	   new_primEqInt2 -> True
67.74/34.91	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.91	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.91	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.91	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.91	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.91	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.91	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.91	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.91	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.91	   new_primMinusNatS1 -> Zero
67.74/34.91	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.91	   new_primEqInt1 -> True
67.74/34.91	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.91	   new_primEqInt0(vuz3260) -> False
67.74/34.91	   new_primEqInt(vuz3250) -> False
67.74/34.91	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.91	
67.74/34.91	The set Q consists of the following terms:
67.74/34.91	
67.74/34.91	   new_rem(Neg(x0), Neg(Zero))
67.74/34.91	   new_primEqInt1
67.74/34.91	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.91	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.91	   new_primMinusNatS1
67.74/34.91	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.91	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.91	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.91	   new_primMinusNatS2(Zero, Zero)
67.74/34.91	   new_error
67.74/34.91	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.91	   new_rem(Pos(x0), Pos(Zero))
67.74/34.91	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.91	   new_primEqInt0(x0)
67.74/34.91	   new_esEs(Pos(Zero))
67.74/34.91	   new_esEs(Pos(Succ(x0)))
67.74/34.91	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.91	   new_primModNatS02(x0, x1)
67.74/34.91	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.91	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.91	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.91	   new_primModNatS1(Zero, x0)
67.74/34.91	   new_primEqInt(x0)
67.74/34.91	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.91	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.91	   new_rem(Pos(x0), Neg(Zero))
67.74/34.91	   new_rem(Neg(x0), Pos(Zero))
67.74/34.91	   new_primMinusNatS0(x0)
67.74/34.91	   new_primEqInt2
67.74/34.91	   new_esEs(Neg(Zero))
67.74/34.91	   new_esEs(Neg(Succ(x0)))
67.74/34.91	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.91	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.91	
67.74/34.91	We have to consider all minimal (P,Q,R)-chains.
67.74/34.91	----------------------------------------
67.74/34.91	
67.74/34.91	(352) TransformationProof (EQUIVALENT)
67.74/34.91	By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_primEqInt(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) at position [0] we obtained the following new rules [LPAR04]:
67.74/34.91	
67.74/34.91	   (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))))
67.74/34.91	
67.74/34.91	
67.74/34.91	----------------------------------------
67.74/34.91	
67.74/34.91	(353)
67.74/34.91	Obligation:
67.74/34.91	Q DP problem:
67.74/34.91	The TRS P consists of the following rules:
67.74/34.91	
67.74/34.91	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.91	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.91	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.91	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.74/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.74/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.74/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0))))))
67.74/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero)))))
67.74/34.91	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0))))))
67.74/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.74/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.74/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.74/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, Zero, x0, Zero))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0))))))
67.74/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero)))))
67.74/34.91	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0))))))
67.74/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.74/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Succ(Succ(Zero)), Succ(Succ(Zero))), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero)))))
67.74/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Succ(Succ(Succ(x2))), Succ(Succ(Zero))), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.74/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.74/34.91	
67.74/34.91	The TRS R consists of the following rules:
67.74/34.91	
67.74/34.91	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.91	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.91	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.91	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.91	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.91	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.91	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.91	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.91	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.91	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.91	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.91	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.91	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.91	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.91	   new_error -> error([])
67.74/34.91	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.91	   new_primEqInt2 -> True
67.74/34.91	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.91	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.91	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.91	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.91	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.91	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.91	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.91	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.91	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.91	   new_primMinusNatS1 -> Zero
67.74/34.91	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.91	   new_primEqInt1 -> True
67.74/34.91	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.91	   new_primEqInt0(vuz3260) -> False
67.74/34.91	   new_primEqInt(vuz3250) -> False
67.74/34.91	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.91	
67.74/34.91	The set Q consists of the following terms:
67.74/34.91	
67.74/34.91	   new_rem(Neg(x0), Neg(Zero))
67.74/34.91	   new_primEqInt1
67.74/34.91	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.91	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.91	   new_primMinusNatS1
67.74/34.91	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.91	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.91	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.91	   new_primMinusNatS2(Zero, Zero)
67.74/34.91	   new_error
67.74/34.91	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.91	   new_rem(Pos(x0), Pos(Zero))
67.74/34.91	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.91	   new_primEqInt0(x0)
67.74/34.91	   new_esEs(Pos(Zero))
67.74/34.91	   new_esEs(Pos(Succ(x0)))
67.74/34.91	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.91	   new_primModNatS02(x0, x1)
67.74/34.91	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.91	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.91	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.91	   new_primModNatS1(Zero, x0)
67.74/34.91	   new_primEqInt(x0)
67.74/34.91	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.91	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.91	   new_rem(Pos(x0), Neg(Zero))
67.74/34.91	   new_rem(Neg(x0), Pos(Zero))
67.74/34.91	   new_primMinusNatS0(x0)
67.74/34.91	   new_primEqInt2
67.74/34.91	   new_esEs(Neg(Zero))
67.74/34.91	   new_esEs(Neg(Succ(x0)))
67.74/34.91	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.91	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.91	
67.74/34.91	We have to consider all minimal (P,Q,R)-chains.
67.74/34.91	----------------------------------------
67.74/34.91	
67.74/34.91	(354) TransformationProof (EQUIVALENT)
67.74/34.91	By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Succ(Succ(Zero)), Succ(Succ(Zero))), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]:
67.74/34.91	
67.74/34.91	   (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Succ(Zero), Succ(Zero)), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Succ(Zero), Succ(Zero)), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))))
67.74/34.91	
67.74/34.91	
67.74/34.91	----------------------------------------
67.74/34.91	
67.74/34.91	(355)
67.74/34.91	Obligation:
67.74/34.91	Q DP problem:
67.74/34.91	The TRS P consists of the following rules:
67.74/34.91	
67.74/34.91	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.91	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.91	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.91	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.74/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.74/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.74/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0))))))
67.74/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero)))))
67.74/34.91	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0))))))
67.74/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.74/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.74/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.74/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, Zero, x0, Zero))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0))))))
67.74/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero)))))
67.74/34.91	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0))))))
67.74/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.74/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Succ(Succ(Succ(x2))), Succ(Succ(Zero))), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.74/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.74/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Succ(Zero), Succ(Zero)), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero)))))
67.74/34.91	
67.74/34.91	The TRS R consists of the following rules:
67.74/34.91	
67.74/34.91	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.91	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.91	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.91	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.91	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.91	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.91	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.91	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.91	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.91	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.91	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.91	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.91	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.91	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.91	   new_error -> error([])
67.74/34.91	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.91	   new_primEqInt2 -> True
67.74/34.91	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.91	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.91	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.91	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.91	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.91	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.91	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.91	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.91	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.91	   new_primMinusNatS1 -> Zero
67.74/34.91	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.91	   new_primEqInt1 -> True
67.74/34.91	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.91	   new_primEqInt0(vuz3260) -> False
67.74/34.91	   new_primEqInt(vuz3250) -> False
67.74/34.91	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.91	
67.74/34.91	The set Q consists of the following terms:
67.74/34.91	
67.74/34.91	   new_rem(Neg(x0), Neg(Zero))
67.74/34.91	   new_primEqInt1
67.74/34.91	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.91	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.91	   new_primMinusNatS1
67.74/34.91	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.91	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.91	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.91	   new_primMinusNatS2(Zero, Zero)
67.74/34.91	   new_error
67.74/34.91	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.91	   new_rem(Pos(x0), Pos(Zero))
67.74/34.91	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.91	   new_primEqInt0(x0)
67.74/34.91	   new_esEs(Pos(Zero))
67.74/34.91	   new_esEs(Pos(Succ(x0)))
67.74/34.91	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.91	   new_primModNatS02(x0, x1)
67.74/34.91	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.91	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.91	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.91	   new_primModNatS1(Zero, x0)
67.74/34.91	   new_primEqInt(x0)
67.74/34.91	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.91	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.91	   new_rem(Pos(x0), Neg(Zero))
67.74/34.91	   new_rem(Neg(x0), Pos(Zero))
67.74/34.91	   new_primMinusNatS0(x0)
67.74/34.91	   new_primEqInt2
67.74/34.91	   new_esEs(Neg(Zero))
67.74/34.91	   new_esEs(Neg(Succ(x0)))
67.74/34.91	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.91	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.91	
67.74/34.91	We have to consider all minimal (P,Q,R)-chains.
67.74/34.91	----------------------------------------
67.74/34.91	
67.74/34.91	(356) TransformationProof (EQUIVALENT)
67.74/34.91	By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Succ(Succ(Succ(x2))), Succ(Succ(Zero))), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]:
67.74/34.91	
67.74/34.91	   (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Succ(Succ(x2)), Succ(Zero)), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Succ(Succ(x2)), Succ(Zero)), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))))
67.74/34.91	
67.74/34.91	
67.74/34.91	----------------------------------------
67.74/34.91	
67.74/34.91	(357)
67.74/34.91	Obligation:
67.74/34.91	Q DP problem:
67.74/34.91	The TRS P consists of the following rules:
67.74/34.91	
67.74/34.91	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.74/34.91	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.74/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.74/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.74/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.74/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.74/34.91	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.74/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.74/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.74/34.91	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.74/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.74/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.74/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.74/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0))))))
67.74/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero)))))
67.74/34.91	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0))))))
67.74/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.74/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.74/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.74/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, Zero, x0, Zero))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0))))))
67.74/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero)))))
67.74/34.91	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0))))))
67.74/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.74/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.74/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Succ(Zero), Succ(Zero)), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero)))))
67.74/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Succ(Succ(x2)), Succ(Zero)), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.74/34.91	
67.74/34.91	The TRS R consists of the following rules:
67.74/34.91	
67.74/34.91	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.74/34.91	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.74/34.91	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.74/34.91	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.74/34.91	   new_primMinusNatS2(Zero, Zero) -> Zero
67.74/34.91	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.74/34.91	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.74/34.91	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.74/34.91	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.74/34.91	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.74/34.91	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.91	   new_primModNatS1(Zero, vuz54200) -> Zero
67.74/34.91	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.91	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.74/34.91	   new_error -> error([])
67.74/34.91	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.74/34.91	   new_primEqInt2 -> True
67.74/34.91	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.74/34.91	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.91	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.74/34.91	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.74/34.91	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.74/34.91	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.74/34.91	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.74/34.91	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.74/34.91	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.74/34.91	   new_primMinusNatS1 -> Zero
67.74/34.91	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.74/34.91	   new_primEqInt1 -> True
67.74/34.91	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.74/34.91	   new_primEqInt0(vuz3260) -> False
67.74/34.91	   new_primEqInt(vuz3250) -> False
67.74/34.91	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.74/34.91	
67.74/34.91	The set Q consists of the following terms:
67.74/34.91	
67.74/34.91	   new_rem(Neg(x0), Neg(Zero))
67.74/34.91	   new_primEqInt1
67.74/34.91	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.74/34.91	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.74/34.91	   new_primMinusNatS1
67.74/34.91	   new_rem(Neg(x0), Neg(Succ(x1)))
67.74/34.91	   new_primMinusNatS2(Succ(x0), Zero)
67.74/34.91	   new_primModNatS1(Succ(Zero), Succ(x0))
67.74/34.91	   new_primMinusNatS2(Zero, Zero)
67.74/34.91	   new_error
67.74/34.91	   new_primModNatS1(Succ(Zero), Zero)
67.74/34.91	   new_rem(Pos(x0), Pos(Zero))
67.74/34.91	   new_primModNatS01(x0, x1, Zero, Zero)
67.74/34.91	   new_primEqInt0(x0)
67.74/34.91	   new_esEs(Pos(Zero))
67.74/34.91	   new_esEs(Pos(Succ(x0)))
67.74/34.91	   new_rem(Pos(x0), Pos(Succ(x1)))
67.74/34.91	   new_primModNatS02(x0, x1)
67.74/34.91	   new_primMinusNatS2(Zero, Succ(x0))
67.74/34.91	   new_rem(Pos(x0), Neg(Succ(x1)))
67.74/34.91	   new_rem(Neg(x0), Pos(Succ(x1)))
67.74/34.91	   new_primModNatS1(Zero, x0)
67.74/34.91	   new_primEqInt(x0)
67.74/34.91	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.74/34.91	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.74/34.91	   new_rem(Pos(x0), Neg(Zero))
67.74/34.91	   new_rem(Neg(x0), Pos(Zero))
67.74/34.91	   new_primMinusNatS0(x0)
67.74/34.91	   new_primEqInt2
67.74/34.91	   new_esEs(Neg(Zero))
67.74/34.91	   new_esEs(Neg(Succ(x0)))
67.74/34.91	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.74/34.91	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.74/34.91	
67.74/34.91	We have to consider all minimal (P,Q,R)-chains.
67.74/34.91	----------------------------------------
67.74/34.91	
67.74/34.91	(358) TransformationProof (EQUIVALENT)
67.74/34.91	By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Succ(Zero), Succ(Zero)), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]:
67.74/34.91	
67.74/34.91	   (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Zero, Zero), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Zero, Zero), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))))
67.83/34.91	
67.83/34.91	
67.83/34.91	----------------------------------------
67.83/34.91	
67.83/34.91	(359)
67.83/34.91	Obligation:
67.83/34.91	Q DP problem:
67.83/34.91	The TRS P consists of the following rules:
67.83/34.91	
67.83/34.91	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.83/34.91	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0))))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0))))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, Zero, x0, Zero))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Succ(Succ(x2)), Succ(Zero)), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Zero, Zero), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.91	
67.83/34.91	The TRS R consists of the following rules:
67.83/34.91	
67.83/34.91	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.83/34.91	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.83/34.91	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.83/34.91	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.83/34.91	   new_primMinusNatS2(Zero, Zero) -> Zero
67.83/34.91	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.83/34.91	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.83/34.91	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.83/34.91	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.83/34.91	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.83/34.91	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.83/34.91	   new_primModNatS1(Zero, vuz54200) -> Zero
67.83/34.91	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.83/34.91	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.83/34.91	   new_error -> error([])
67.83/34.91	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.83/34.91	   new_primEqInt2 -> True
67.83/34.91	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.83/34.91	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.83/34.91	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.83/34.91	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.83/34.91	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.83/34.91	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.83/34.91	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.83/34.91	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.83/34.91	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.83/34.91	   new_primMinusNatS1 -> Zero
67.83/34.91	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.83/34.91	   new_primEqInt1 -> True
67.83/34.91	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.83/34.91	   new_primEqInt0(vuz3260) -> False
67.83/34.91	   new_primEqInt(vuz3250) -> False
67.83/34.91	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.83/34.91	
67.83/34.91	The set Q consists of the following terms:
67.83/34.91	
67.83/34.91	   new_rem(Neg(x0), Neg(Zero))
67.83/34.91	   new_primEqInt1
67.83/34.91	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.83/34.91	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.83/34.91	   new_primMinusNatS1
67.83/34.91	   new_rem(Neg(x0), Neg(Succ(x1)))
67.83/34.91	   new_primMinusNatS2(Succ(x0), Zero)
67.83/34.91	   new_primModNatS1(Succ(Zero), Succ(x0))
67.83/34.91	   new_primMinusNatS2(Zero, Zero)
67.83/34.91	   new_error
67.83/34.91	   new_primModNatS1(Succ(Zero), Zero)
67.83/34.91	   new_rem(Pos(x0), Pos(Zero))
67.83/34.91	   new_primModNatS01(x0, x1, Zero, Zero)
67.83/34.91	   new_primEqInt0(x0)
67.83/34.91	   new_esEs(Pos(Zero))
67.83/34.91	   new_esEs(Pos(Succ(x0)))
67.83/34.91	   new_rem(Pos(x0), Pos(Succ(x1)))
67.83/34.91	   new_primModNatS02(x0, x1)
67.83/34.91	   new_primMinusNatS2(Zero, Succ(x0))
67.83/34.91	   new_rem(Pos(x0), Neg(Succ(x1)))
67.83/34.91	   new_rem(Neg(x0), Pos(Succ(x1)))
67.83/34.91	   new_primModNatS1(Zero, x0)
67.83/34.91	   new_primEqInt(x0)
67.83/34.91	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.83/34.91	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.83/34.91	   new_rem(Pos(x0), Neg(Zero))
67.83/34.91	   new_rem(Neg(x0), Pos(Zero))
67.83/34.91	   new_primMinusNatS0(x0)
67.83/34.91	   new_primEqInt2
67.83/34.91	   new_esEs(Neg(Zero))
67.83/34.91	   new_esEs(Neg(Succ(x0)))
67.83/34.91	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.83/34.91	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.83/34.91	
67.83/34.91	We have to consider all minimal (P,Q,R)-chains.
67.83/34.91	----------------------------------------
67.83/34.91	
67.83/34.91	(360) TransformationProof (EQUIVALENT)
67.83/34.91	By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Succ(Succ(x2)), Succ(Zero)), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]:
67.83/34.91	
67.83/34.91	   (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Succ(x2), Zero), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Succ(x2), Zero), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))))
67.83/34.91	
67.83/34.91	
67.83/34.91	----------------------------------------
67.83/34.91	
67.83/34.91	(361)
67.83/34.91	Obligation:
67.83/34.91	Q DP problem:
67.83/34.91	The TRS P consists of the following rules:
67.83/34.91	
67.83/34.91	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.83/34.91	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0))))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0))))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, Zero, x0, Zero))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Zero, Zero), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Succ(x2), Zero), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.91	
67.83/34.91	The TRS R consists of the following rules:
67.83/34.91	
67.83/34.91	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.83/34.91	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.83/34.91	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.83/34.91	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.83/34.91	   new_primMinusNatS2(Zero, Zero) -> Zero
67.83/34.91	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.83/34.91	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.83/34.91	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.83/34.91	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.83/34.91	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.83/34.91	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.83/34.91	   new_primModNatS1(Zero, vuz54200) -> Zero
67.83/34.91	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.83/34.91	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.83/34.91	   new_error -> error([])
67.83/34.91	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.83/34.91	   new_primEqInt2 -> True
67.83/34.91	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.83/34.91	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.83/34.91	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.83/34.91	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.83/34.91	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.83/34.91	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.83/34.91	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.83/34.91	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.83/34.91	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.83/34.91	   new_primMinusNatS1 -> Zero
67.83/34.91	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.83/34.91	   new_primEqInt1 -> True
67.83/34.91	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.83/34.91	   new_primEqInt0(vuz3260) -> False
67.83/34.91	   new_primEqInt(vuz3250) -> False
67.83/34.91	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.83/34.91	
67.83/34.91	The set Q consists of the following terms:
67.83/34.91	
67.83/34.91	   new_rem(Neg(x0), Neg(Zero))
67.83/34.91	   new_primEqInt1
67.83/34.91	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.83/34.91	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.83/34.91	   new_primMinusNatS1
67.83/34.91	   new_rem(Neg(x0), Neg(Succ(x1)))
67.83/34.91	   new_primMinusNatS2(Succ(x0), Zero)
67.83/34.91	   new_primModNatS1(Succ(Zero), Succ(x0))
67.83/34.91	   new_primMinusNatS2(Zero, Zero)
67.83/34.91	   new_error
67.83/34.91	   new_primModNatS1(Succ(Zero), Zero)
67.83/34.91	   new_rem(Pos(x0), Pos(Zero))
67.83/34.91	   new_primModNatS01(x0, x1, Zero, Zero)
67.83/34.91	   new_primEqInt0(x0)
67.83/34.91	   new_esEs(Pos(Zero))
67.83/34.91	   new_esEs(Pos(Succ(x0)))
67.83/34.91	   new_rem(Pos(x0), Pos(Succ(x1)))
67.83/34.91	   new_primModNatS02(x0, x1)
67.83/34.91	   new_primMinusNatS2(Zero, Succ(x0))
67.83/34.91	   new_rem(Pos(x0), Neg(Succ(x1)))
67.83/34.91	   new_rem(Neg(x0), Pos(Succ(x1)))
67.83/34.91	   new_primModNatS1(Zero, x0)
67.83/34.91	   new_primEqInt(x0)
67.83/34.91	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.83/34.91	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.83/34.91	   new_rem(Pos(x0), Neg(Zero))
67.83/34.91	   new_rem(Neg(x0), Pos(Zero))
67.83/34.91	   new_primMinusNatS0(x0)
67.83/34.91	   new_primEqInt2
67.83/34.91	   new_esEs(Neg(Zero))
67.83/34.91	   new_esEs(Neg(Succ(x0)))
67.83/34.91	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.83/34.91	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.83/34.91	
67.83/34.91	We have to consider all minimal (P,Q,R)-chains.
67.83/34.91	----------------------------------------
67.83/34.91	
67.83/34.91	(362) TransformationProof (EQUIVALENT)
67.83/34.91	By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Zero, Zero), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]:
67.83/34.91	
67.83/34.91	   (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Zero, Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Zero, Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))))
67.83/34.91	
67.83/34.91	
67.83/34.91	----------------------------------------
67.83/34.91	
67.83/34.91	(363)
67.83/34.91	Obligation:
67.83/34.91	Q DP problem:
67.83/34.91	The TRS P consists of the following rules:
67.83/34.91	
67.83/34.91	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.83/34.91	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0))))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0))))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, Zero, x0, Zero))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Succ(x2), Zero), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Zero, Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.91	
67.83/34.91	The TRS R consists of the following rules:
67.83/34.91	
67.83/34.91	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.83/34.91	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.83/34.91	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.83/34.91	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.83/34.91	   new_primMinusNatS2(Zero, Zero) -> Zero
67.83/34.91	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.83/34.91	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.83/34.91	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.83/34.91	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.83/34.91	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.83/34.91	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.83/34.91	   new_primModNatS1(Zero, vuz54200) -> Zero
67.83/34.91	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.83/34.91	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.83/34.91	   new_error -> error([])
67.83/34.91	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.83/34.91	   new_primEqInt2 -> True
67.83/34.91	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.83/34.91	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.83/34.91	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.83/34.91	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.83/34.91	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.83/34.91	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.83/34.91	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.83/34.91	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.83/34.91	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.83/34.91	   new_primMinusNatS1 -> Zero
67.83/34.91	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.83/34.91	   new_primEqInt1 -> True
67.83/34.91	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.83/34.91	   new_primEqInt0(vuz3260) -> False
67.83/34.91	   new_primEqInt(vuz3250) -> False
67.83/34.91	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.83/34.91	
67.83/34.91	The set Q consists of the following terms:
67.83/34.91	
67.83/34.91	   new_rem(Neg(x0), Neg(Zero))
67.83/34.91	   new_primEqInt1
67.83/34.91	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.83/34.91	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.83/34.91	   new_primMinusNatS1
67.83/34.91	   new_rem(Neg(x0), Neg(Succ(x1)))
67.83/34.91	   new_primMinusNatS2(Succ(x0), Zero)
67.83/34.91	   new_primModNatS1(Succ(Zero), Succ(x0))
67.83/34.91	   new_primMinusNatS2(Zero, Zero)
67.83/34.91	   new_error
67.83/34.91	   new_primModNatS1(Succ(Zero), Zero)
67.83/34.91	   new_rem(Pos(x0), Pos(Zero))
67.83/34.91	   new_primModNatS01(x0, x1, Zero, Zero)
67.83/34.91	   new_primEqInt0(x0)
67.83/34.91	   new_esEs(Pos(Zero))
67.83/34.91	   new_esEs(Pos(Succ(x0)))
67.83/34.91	   new_rem(Pos(x0), Pos(Succ(x1)))
67.83/34.91	   new_primModNatS02(x0, x1)
67.83/34.91	   new_primMinusNatS2(Zero, Succ(x0))
67.83/34.91	   new_rem(Pos(x0), Neg(Succ(x1)))
67.83/34.91	   new_rem(Neg(x0), Pos(Succ(x1)))
67.83/34.91	   new_primModNatS1(Zero, x0)
67.83/34.91	   new_primEqInt(x0)
67.83/34.91	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.83/34.91	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.83/34.91	   new_rem(Pos(x0), Neg(Zero))
67.83/34.91	   new_rem(Neg(x0), Pos(Zero))
67.83/34.91	   new_primMinusNatS0(x0)
67.83/34.91	   new_primEqInt2
67.83/34.91	   new_esEs(Neg(Zero))
67.83/34.91	   new_esEs(Neg(Succ(x0)))
67.83/34.91	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.83/34.91	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.83/34.91	
67.83/34.91	We have to consider all minimal (P,Q,R)-chains.
67.83/34.91	----------------------------------------
67.83/34.91	
67.83/34.91	(364) TransformationProof (EQUIVALENT)
67.83/34.91	By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS2(Succ(x2), Zero), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]:
67.83/34.91	
67.83/34.91	   (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))))
67.83/34.91	
67.83/34.91	
67.83/34.91	----------------------------------------
67.83/34.91	
67.83/34.91	(365)
67.83/34.91	Obligation:
67.83/34.91	Q DP problem:
67.83/34.91	The TRS P consists of the following rules:
67.83/34.91	
67.83/34.91	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.83/34.91	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0))))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0))))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, Zero, x0, Zero))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Zero, Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.91	
67.83/34.91	The TRS R consists of the following rules:
67.83/34.91	
67.83/34.91	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.83/34.91	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.83/34.91	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.83/34.91	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.83/34.91	   new_primMinusNatS2(Zero, Zero) -> Zero
67.83/34.91	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.83/34.91	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.83/34.91	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.83/34.91	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.83/34.91	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.83/34.91	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.83/34.91	   new_primModNatS1(Zero, vuz54200) -> Zero
67.83/34.91	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.83/34.91	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.83/34.91	   new_error -> error([])
67.83/34.91	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.83/34.91	   new_primEqInt2 -> True
67.83/34.91	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.83/34.91	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.83/34.91	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.83/34.91	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.83/34.91	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.83/34.91	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.83/34.91	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.83/34.91	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.83/34.91	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.83/34.91	   new_primMinusNatS1 -> Zero
67.83/34.91	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.83/34.91	   new_primEqInt1 -> True
67.83/34.91	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.83/34.91	   new_primEqInt0(vuz3260) -> False
67.83/34.91	   new_primEqInt(vuz3250) -> False
67.83/34.91	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.83/34.91	
67.83/34.91	The set Q consists of the following terms:
67.83/34.91	
67.83/34.91	   new_rem(Neg(x0), Neg(Zero))
67.83/34.91	   new_primEqInt1
67.83/34.91	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.83/34.91	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.83/34.91	   new_primMinusNatS1
67.83/34.91	   new_rem(Neg(x0), Neg(Succ(x1)))
67.83/34.91	   new_primMinusNatS2(Succ(x0), Zero)
67.83/34.91	   new_primModNatS1(Succ(Zero), Succ(x0))
67.83/34.91	   new_primMinusNatS2(Zero, Zero)
67.83/34.91	   new_error
67.83/34.91	   new_primModNatS1(Succ(Zero), Zero)
67.83/34.91	   new_rem(Pos(x0), Pos(Zero))
67.83/34.91	   new_primModNatS01(x0, x1, Zero, Zero)
67.83/34.91	   new_primEqInt0(x0)
67.83/34.91	   new_esEs(Pos(Zero))
67.83/34.91	   new_esEs(Pos(Succ(x0)))
67.83/34.91	   new_rem(Pos(x0), Pos(Succ(x1)))
67.83/34.91	   new_primModNatS02(x0, x1)
67.83/34.91	   new_primMinusNatS2(Zero, Succ(x0))
67.83/34.91	   new_rem(Pos(x0), Neg(Succ(x1)))
67.83/34.91	   new_rem(Neg(x0), Pos(Succ(x1)))
67.83/34.91	   new_primModNatS1(Zero, x0)
67.83/34.91	   new_primEqInt(x0)
67.83/34.91	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.83/34.91	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.83/34.91	   new_rem(Pos(x0), Neg(Zero))
67.83/34.91	   new_rem(Neg(x0), Pos(Zero))
67.83/34.91	   new_primMinusNatS0(x0)
67.83/34.91	   new_primEqInt2
67.83/34.91	   new_esEs(Neg(Zero))
67.83/34.91	   new_esEs(Neg(Succ(x0)))
67.83/34.91	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.83/34.91	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.83/34.91	
67.83/34.91	We have to consider all minimal (P,Q,R)-chains.
67.83/34.91	----------------------------------------
67.83/34.91	
67.83/34.91	(366) TransformationProof (EQUIVALENT)
67.83/34.91	By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Zero, Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) at position [0,0,0] we obtained the following new rules [LPAR04]:
67.83/34.91	
67.83/34.91	   (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Pos(Zero)), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))),new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Pos(Zero)), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))))
67.83/34.91	
67.83/34.91	
67.83/34.91	----------------------------------------
67.83/34.91	
67.83/34.91	(367)
67.83/34.91	Obligation:
67.83/34.91	Q DP problem:
67.83/34.91	The TRS P consists of the following rules:
67.83/34.91	
67.83/34.91	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.83/34.91	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0))))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0))))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, Zero, x0, Zero))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Pos(Zero)), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.91	
67.83/34.91	The TRS R consists of the following rules:
67.83/34.91	
67.83/34.91	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.83/34.91	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.83/34.91	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.83/34.91	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.83/34.91	   new_primMinusNatS2(Zero, Zero) -> Zero
67.83/34.91	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.83/34.91	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.83/34.91	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.83/34.91	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.83/34.91	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.83/34.91	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.83/34.91	   new_primModNatS1(Zero, vuz54200) -> Zero
67.83/34.91	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.83/34.91	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.83/34.91	   new_error -> error([])
67.83/34.91	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.83/34.91	   new_primEqInt2 -> True
67.83/34.91	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.83/34.91	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.83/34.91	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.83/34.91	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.83/34.91	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.83/34.91	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.83/34.91	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.83/34.91	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.83/34.91	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.83/34.91	   new_primMinusNatS1 -> Zero
67.83/34.91	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.83/34.91	   new_primEqInt1 -> True
67.83/34.91	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.83/34.91	   new_primEqInt0(vuz3260) -> False
67.83/34.91	   new_primEqInt(vuz3250) -> False
67.83/34.91	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.83/34.91	
67.83/34.91	The set Q consists of the following terms:
67.83/34.91	
67.83/34.91	   new_rem(Neg(x0), Neg(Zero))
67.83/34.91	   new_primEqInt1
67.83/34.91	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.83/34.91	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.83/34.91	   new_primMinusNatS1
67.83/34.91	   new_rem(Neg(x0), Neg(Succ(x1)))
67.83/34.91	   new_primMinusNatS2(Succ(x0), Zero)
67.83/34.91	   new_primModNatS1(Succ(Zero), Succ(x0))
67.83/34.91	   new_primMinusNatS2(Zero, Zero)
67.83/34.91	   new_error
67.83/34.91	   new_primModNatS1(Succ(Zero), Zero)
67.83/34.91	   new_rem(Pos(x0), Pos(Zero))
67.83/34.91	   new_primModNatS01(x0, x1, Zero, Zero)
67.83/34.91	   new_primEqInt0(x0)
67.83/34.91	   new_esEs(Pos(Zero))
67.83/34.91	   new_esEs(Pos(Succ(x0)))
67.83/34.91	   new_rem(Pos(x0), Pos(Succ(x1)))
67.83/34.91	   new_primModNatS02(x0, x1)
67.83/34.91	   new_primMinusNatS2(Zero, Succ(x0))
67.83/34.91	   new_rem(Pos(x0), Neg(Succ(x1)))
67.83/34.91	   new_rem(Neg(x0), Pos(Succ(x1)))
67.83/34.91	   new_primModNatS1(Zero, x0)
67.83/34.91	   new_primEqInt(x0)
67.83/34.91	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.83/34.91	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.83/34.91	   new_rem(Pos(x0), Neg(Zero))
67.83/34.91	   new_rem(Neg(x0), Pos(Zero))
67.83/34.91	   new_primMinusNatS0(x0)
67.83/34.91	   new_primEqInt2
67.83/34.91	   new_esEs(Neg(Zero))
67.83/34.91	   new_esEs(Neg(Succ(x0)))
67.83/34.91	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.83/34.91	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.83/34.91	
67.83/34.91	We have to consider all minimal (P,Q,R)-chains.
67.83/34.91	----------------------------------------
67.83/34.91	
67.83/34.91	(368) DependencyGraphProof (EQUIVALENT)
67.83/34.91	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
67.83/34.91	----------------------------------------
67.83/34.91	
67.83/34.91	(369)
67.83/34.91	Obligation:
67.83/34.91	Q DP problem:
67.83/34.91	The TRS P consists of the following rules:
67.83/34.91	
67.83/34.91	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.83/34.91	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2)))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0))))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0))))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, Zero, x0, Zero))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.91	
67.83/34.91	The TRS R consists of the following rules:
67.83/34.91	
67.83/34.91	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.83/34.91	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.83/34.91	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.83/34.91	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.83/34.91	   new_primMinusNatS2(Zero, Zero) -> Zero
67.83/34.91	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.83/34.91	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.83/34.91	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.83/34.91	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.83/34.91	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.83/34.91	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.83/34.91	   new_primModNatS1(Zero, vuz54200) -> Zero
67.83/34.91	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.83/34.91	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.83/34.91	   new_error -> error([])
67.83/34.91	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.83/34.91	   new_primEqInt2 -> True
67.83/34.91	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.83/34.91	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.83/34.91	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.83/34.91	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.83/34.91	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.83/34.91	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.83/34.91	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.83/34.91	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.83/34.91	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.83/34.91	   new_primMinusNatS1 -> Zero
67.83/34.91	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.83/34.91	   new_primEqInt1 -> True
67.83/34.91	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.83/34.91	   new_primEqInt0(vuz3260) -> False
67.83/34.91	   new_primEqInt(vuz3250) -> False
67.83/34.91	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.83/34.91	
67.83/34.91	The set Q consists of the following terms:
67.83/34.91	
67.83/34.91	   new_rem(Neg(x0), Neg(Zero))
67.83/34.91	   new_primEqInt1
67.83/34.91	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.83/34.91	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.83/34.91	   new_primMinusNatS1
67.83/34.91	   new_rem(Neg(x0), Neg(Succ(x1)))
67.83/34.91	   new_primMinusNatS2(Succ(x0), Zero)
67.83/34.91	   new_primModNatS1(Succ(Zero), Succ(x0))
67.83/34.91	   new_primMinusNatS2(Zero, Zero)
67.83/34.91	   new_error
67.83/34.91	   new_primModNatS1(Succ(Zero), Zero)
67.83/34.91	   new_rem(Pos(x0), Pos(Zero))
67.83/34.91	   new_primModNatS01(x0, x1, Zero, Zero)
67.83/34.91	   new_primEqInt0(x0)
67.83/34.91	   new_esEs(Pos(Zero))
67.83/34.91	   new_esEs(Pos(Succ(x0)))
67.83/34.91	   new_rem(Pos(x0), Pos(Succ(x1)))
67.83/34.91	   new_primModNatS02(x0, x1)
67.83/34.91	   new_primMinusNatS2(Zero, Succ(x0))
67.83/34.91	   new_rem(Pos(x0), Neg(Succ(x1)))
67.83/34.91	   new_rem(Neg(x0), Pos(Succ(x1)))
67.83/34.91	   new_primModNatS1(Zero, x0)
67.83/34.91	   new_primEqInt(x0)
67.83/34.91	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.83/34.91	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.83/34.91	   new_rem(Pos(x0), Neg(Zero))
67.83/34.91	   new_rem(Neg(x0), Pos(Zero))
67.83/34.91	   new_primMinusNatS0(x0)
67.83/34.91	   new_primEqInt2
67.83/34.91	   new_esEs(Neg(Zero))
67.83/34.91	   new_esEs(Neg(Succ(x0)))
67.83/34.91	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.83/34.91	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.83/34.91	
67.83/34.91	We have to consider all minimal (P,Q,R)-chains.
67.83/34.91	----------------------------------------
67.83/34.91	
67.83/34.91	(370) TransformationProof (EQUIVALENT)
67.83/34.91	By narrowing [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Zero)))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x2))))) at position [0] we obtained the following new rules [LPAR04]:
67.83/34.91	
67.83/34.91	   (new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Pos(Succ(Zero))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))),new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Pos(Succ(Zero))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))))
67.83/34.91	   (new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0)))))),new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0)))))))
67.83/34.91	
67.83/34.91	
67.83/34.91	----------------------------------------
67.83/34.91	
67.83/34.91	(371)
67.83/34.91	Obligation:
67.83/34.91	Q DP problem:
67.83/34.91	The TRS P consists of the following rules:
67.83/34.91	
67.83/34.91	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.83/34.91	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0))))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0))))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, Zero, x0, Zero))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Pos(Succ(Zero))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.91	
67.83/34.91	The TRS R consists of the following rules:
67.83/34.91	
67.83/34.91	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.83/34.91	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.83/34.91	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.83/34.91	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.83/34.91	   new_primMinusNatS2(Zero, Zero) -> Zero
67.83/34.91	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.83/34.91	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.83/34.91	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.83/34.91	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.83/34.91	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.83/34.91	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.83/34.91	   new_primModNatS1(Zero, vuz54200) -> Zero
67.83/34.91	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.83/34.91	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.83/34.91	   new_error -> error([])
67.83/34.91	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.83/34.91	   new_primEqInt2 -> True
67.83/34.91	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.83/34.91	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.83/34.91	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.83/34.91	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.83/34.91	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.83/34.91	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.83/34.91	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.83/34.91	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.83/34.91	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.83/34.91	   new_primMinusNatS1 -> Zero
67.83/34.91	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.83/34.91	   new_primEqInt1 -> True
67.83/34.91	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.83/34.91	   new_primEqInt0(vuz3260) -> False
67.83/34.91	   new_primEqInt(vuz3250) -> False
67.83/34.91	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.83/34.91	
67.83/34.91	The set Q consists of the following terms:
67.83/34.91	
67.83/34.91	   new_rem(Neg(x0), Neg(Zero))
67.83/34.91	   new_primEqInt1
67.83/34.91	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.83/34.91	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.83/34.91	   new_primMinusNatS1
67.83/34.91	   new_rem(Neg(x0), Neg(Succ(x1)))
67.83/34.91	   new_primMinusNatS2(Succ(x0), Zero)
67.83/34.91	   new_primModNatS1(Succ(Zero), Succ(x0))
67.83/34.91	   new_primMinusNatS2(Zero, Zero)
67.83/34.91	   new_error
67.83/34.91	   new_primModNatS1(Succ(Zero), Zero)
67.83/34.91	   new_rem(Pos(x0), Pos(Zero))
67.83/34.91	   new_primModNatS01(x0, x1, Zero, Zero)
67.83/34.91	   new_primEqInt0(x0)
67.83/34.91	   new_esEs(Pos(Zero))
67.83/34.91	   new_esEs(Pos(Succ(x0)))
67.83/34.91	   new_rem(Pos(x0), Pos(Succ(x1)))
67.83/34.91	   new_primModNatS02(x0, x1)
67.83/34.91	   new_primMinusNatS2(Zero, Succ(x0))
67.83/34.91	   new_rem(Pos(x0), Neg(Succ(x1)))
67.83/34.91	   new_rem(Neg(x0), Pos(Succ(x1)))
67.83/34.91	   new_primModNatS1(Zero, x0)
67.83/34.91	   new_primEqInt(x0)
67.83/34.91	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.83/34.91	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.83/34.91	   new_rem(Pos(x0), Neg(Zero))
67.83/34.91	   new_rem(Neg(x0), Pos(Zero))
67.83/34.91	   new_primMinusNatS0(x0)
67.83/34.91	   new_primEqInt2
67.83/34.91	   new_esEs(Neg(Zero))
67.83/34.91	   new_esEs(Neg(Succ(x0)))
67.83/34.91	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.83/34.91	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.83/34.91	
67.83/34.91	We have to consider all minimal (P,Q,R)-chains.
67.83/34.91	----------------------------------------
67.83/34.91	
67.83/34.91	(372) TransformationProof (EQUIVALENT)
67.83/34.91	By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Pos(Succ(Zero))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) at position [0] we obtained the following new rules [LPAR04]:
67.83/34.91	
67.83/34.91	   (new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_primEqInt(Zero), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))),new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_primEqInt(Zero), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))))
67.83/34.91	
67.83/34.91	
67.83/34.91	----------------------------------------
67.83/34.91	
67.83/34.91	(373)
67.83/34.91	Obligation:
67.83/34.91	Q DP problem:
67.83/34.91	The TRS P consists of the following rules:
67.83/34.91	
67.83/34.91	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.83/34.91	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0))))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0))))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, Zero, x0, Zero))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_primEqInt(Zero), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.91	
67.83/34.91	The TRS R consists of the following rules:
67.83/34.91	
67.83/34.91	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.83/34.91	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.83/34.91	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.83/34.91	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.83/34.91	   new_primMinusNatS2(Zero, Zero) -> Zero
67.83/34.91	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.83/34.91	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.83/34.91	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.83/34.91	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.83/34.91	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.83/34.91	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.83/34.91	   new_primModNatS1(Zero, vuz54200) -> Zero
67.83/34.91	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.83/34.91	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.83/34.91	   new_error -> error([])
67.83/34.91	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.83/34.91	   new_primEqInt2 -> True
67.83/34.91	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.83/34.91	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.83/34.91	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.83/34.91	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.83/34.91	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.83/34.91	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.83/34.91	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.83/34.91	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.83/34.91	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.83/34.91	   new_primMinusNatS1 -> Zero
67.83/34.91	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.83/34.91	   new_primEqInt1 -> True
67.83/34.91	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.83/34.91	   new_primEqInt0(vuz3260) -> False
67.83/34.91	   new_primEqInt(vuz3250) -> False
67.83/34.91	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.83/34.91	
67.83/34.91	The set Q consists of the following terms:
67.83/34.91	
67.83/34.91	   new_rem(Neg(x0), Neg(Zero))
67.83/34.91	   new_primEqInt1
67.83/34.91	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.83/34.91	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.83/34.91	   new_primMinusNatS1
67.83/34.91	   new_rem(Neg(x0), Neg(Succ(x1)))
67.83/34.91	   new_primMinusNatS2(Succ(x0), Zero)
67.83/34.91	   new_primModNatS1(Succ(Zero), Succ(x0))
67.83/34.91	   new_primMinusNatS2(Zero, Zero)
67.83/34.91	   new_error
67.83/34.91	   new_primModNatS1(Succ(Zero), Zero)
67.83/34.91	   new_rem(Pos(x0), Pos(Zero))
67.83/34.91	   new_primModNatS01(x0, x1, Zero, Zero)
67.83/34.91	   new_primEqInt0(x0)
67.83/34.91	   new_esEs(Pos(Zero))
67.83/34.91	   new_esEs(Pos(Succ(x0)))
67.83/34.91	   new_rem(Pos(x0), Pos(Succ(x1)))
67.83/34.91	   new_primModNatS02(x0, x1)
67.83/34.91	   new_primMinusNatS2(Zero, Succ(x0))
67.83/34.91	   new_rem(Pos(x0), Neg(Succ(x1)))
67.83/34.91	   new_rem(Neg(x0), Pos(Succ(x1)))
67.83/34.91	   new_primModNatS1(Zero, x0)
67.83/34.91	   new_primEqInt(x0)
67.83/34.91	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.83/34.91	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.83/34.91	   new_rem(Pos(x0), Neg(Zero))
67.83/34.91	   new_rem(Neg(x0), Pos(Zero))
67.83/34.91	   new_primMinusNatS0(x0)
67.83/34.91	   new_primEqInt2
67.83/34.91	   new_esEs(Neg(Zero))
67.83/34.91	   new_esEs(Neg(Succ(x0)))
67.83/34.91	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.83/34.91	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.83/34.91	
67.83/34.91	We have to consider all minimal (P,Q,R)-chains.
67.83/34.91	----------------------------------------
67.83/34.91	
67.83/34.91	(374) TransformationProof (EQUIVALENT)
67.83/34.91	By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_primEqInt(Zero), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) at position [0] we obtained the following new rules [LPAR04]:
67.83/34.91	
67.83/34.91	   (new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))),new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))))
67.83/34.91	
67.83/34.91	
67.83/34.91	----------------------------------------
67.83/34.91	
67.83/34.91	(375)
67.83/34.91	Obligation:
67.83/34.91	Q DP problem:
67.83/34.91	The TRS P consists of the following rules:
67.83/34.91	
67.83/34.91	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.83/34.91	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0)))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0))))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0))))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, Zero, x0, Zero))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.91	
67.83/34.91	The TRS R consists of the following rules:
67.83/34.91	
67.83/34.91	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.83/34.91	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.83/34.91	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.83/34.91	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.83/34.91	   new_primMinusNatS2(Zero, Zero) -> Zero
67.83/34.91	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.83/34.91	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.83/34.91	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.83/34.91	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.83/34.91	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.83/34.91	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.83/34.91	   new_primModNatS1(Zero, vuz54200) -> Zero
67.83/34.91	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.83/34.91	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.83/34.91	   new_error -> error([])
67.83/34.91	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.83/34.91	   new_primEqInt2 -> True
67.83/34.91	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.83/34.91	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.83/34.91	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.83/34.91	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.83/34.91	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.83/34.91	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.83/34.91	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.83/34.91	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.83/34.91	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.83/34.91	   new_primMinusNatS1 -> Zero
67.83/34.91	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.83/34.91	   new_primEqInt1 -> True
67.83/34.91	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.83/34.91	   new_primEqInt0(vuz3260) -> False
67.83/34.91	   new_primEqInt(vuz3250) -> False
67.83/34.91	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.83/34.91	
67.83/34.91	The set Q consists of the following terms:
67.83/34.91	
67.83/34.91	   new_rem(Neg(x0), Neg(Zero))
67.83/34.91	   new_primEqInt1
67.83/34.91	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.83/34.91	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.83/34.91	   new_primMinusNatS1
67.83/34.91	   new_rem(Neg(x0), Neg(Succ(x1)))
67.83/34.91	   new_primMinusNatS2(Succ(x0), Zero)
67.83/34.91	   new_primModNatS1(Succ(Zero), Succ(x0))
67.83/34.91	   new_primMinusNatS2(Zero, Zero)
67.83/34.91	   new_error
67.83/34.91	   new_primModNatS1(Succ(Zero), Zero)
67.83/34.91	   new_rem(Pos(x0), Pos(Zero))
67.83/34.91	   new_primModNatS01(x0, x1, Zero, Zero)
67.83/34.91	   new_primEqInt0(x0)
67.83/34.91	   new_esEs(Pos(Zero))
67.83/34.91	   new_esEs(Pos(Succ(x0)))
67.83/34.91	   new_rem(Pos(x0), Pos(Succ(x1)))
67.83/34.91	   new_primModNatS02(x0, x1)
67.83/34.91	   new_primMinusNatS2(Zero, Succ(x0))
67.83/34.91	   new_rem(Pos(x0), Neg(Succ(x1)))
67.83/34.91	   new_rem(Neg(x0), Pos(Succ(x1)))
67.83/34.91	   new_primModNatS1(Zero, x0)
67.83/34.91	   new_primEqInt(x0)
67.83/34.91	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.83/34.91	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.83/34.91	   new_rem(Pos(x0), Neg(Zero))
67.83/34.91	   new_rem(Neg(x0), Pos(Zero))
67.83/34.91	   new_primMinusNatS0(x0)
67.83/34.91	   new_primEqInt2
67.83/34.91	   new_esEs(Neg(Zero))
67.83/34.91	   new_esEs(Neg(Succ(x0)))
67.83/34.91	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.83/34.91	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.83/34.91	
67.83/34.91	We have to consider all minimal (P,Q,R)-chains.
67.83/34.91	----------------------------------------
67.83/34.91	
67.83/34.91	(376) TransformationProof (EQUIVALENT)
67.83/34.91	By narrowing [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(x0))))) at position [0] we obtained the following new rules [LPAR04]:
67.83/34.91	
67.83/34.91	   (new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS0(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0)))))),new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS0(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0)))))))
67.83/34.91	   (new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS1, Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(Zero))))),new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS1, Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(Zero))))))
67.83/34.91	
67.83/34.91	
67.83/34.91	----------------------------------------
67.83/34.91	
67.83/34.91	(377)
67.83/34.91	Obligation:
67.83/34.91	Q DP problem:
67.83/34.91	The TRS P consists of the following rules:
67.83/34.91	
67.83/34.91	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.83/34.91	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0))))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0))))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, Zero, x0, Zero))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.91	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS0(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.91	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS1, Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.91	
67.83/34.91	The TRS R consists of the following rules:
67.83/34.91	
67.83/34.91	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.83/34.91	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.83/34.91	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.83/34.91	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.83/34.91	   new_primMinusNatS2(Zero, Zero) -> Zero
67.83/34.91	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.83/34.91	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.83/34.91	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.83/34.91	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.83/34.91	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.83/34.91	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.83/34.91	   new_primModNatS1(Zero, vuz54200) -> Zero
67.83/34.91	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.83/34.91	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.83/34.91	   new_error -> error([])
67.83/34.91	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.83/34.91	   new_primEqInt2 -> True
67.83/34.91	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.83/34.91	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.83/34.91	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.83/34.91	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.83/34.91	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.83/34.92	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.83/34.92	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.83/34.92	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.83/34.92	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.83/34.92	   new_primMinusNatS1 -> Zero
67.83/34.92	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.83/34.92	   new_primEqInt1 -> True
67.83/34.92	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.83/34.92	   new_primEqInt0(vuz3260) -> False
67.83/34.92	   new_primEqInt(vuz3250) -> False
67.83/34.92	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.83/34.92	
67.83/34.92	The set Q consists of the following terms:
67.83/34.92	
67.83/34.92	   new_rem(Neg(x0), Neg(Zero))
67.83/34.92	   new_primEqInt1
67.83/34.92	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.83/34.92	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.83/34.92	   new_primMinusNatS1
67.83/34.92	   new_rem(Neg(x0), Neg(Succ(x1)))
67.83/34.92	   new_primMinusNatS2(Succ(x0), Zero)
67.83/34.92	   new_primModNatS1(Succ(Zero), Succ(x0))
67.83/34.92	   new_primMinusNatS2(Zero, Zero)
67.83/34.92	   new_error
67.83/34.92	   new_primModNatS1(Succ(Zero), Zero)
67.83/34.92	   new_rem(Pos(x0), Pos(Zero))
67.83/34.92	   new_primModNatS01(x0, x1, Zero, Zero)
67.83/34.92	   new_primEqInt0(x0)
67.83/34.92	   new_esEs(Pos(Zero))
67.83/34.92	   new_esEs(Pos(Succ(x0)))
67.83/34.92	   new_rem(Pos(x0), Pos(Succ(x1)))
67.83/34.92	   new_primModNatS02(x0, x1)
67.83/34.92	   new_primMinusNatS2(Zero, Succ(x0))
67.83/34.92	   new_rem(Pos(x0), Neg(Succ(x1)))
67.83/34.92	   new_rem(Neg(x0), Pos(Succ(x1)))
67.83/34.92	   new_primModNatS1(Zero, x0)
67.83/34.92	   new_primEqInt(x0)
67.83/34.92	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.83/34.92	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.83/34.92	   new_rem(Pos(x0), Neg(Zero))
67.83/34.92	   new_rem(Neg(x0), Pos(Zero))
67.83/34.92	   new_primMinusNatS0(x0)
67.83/34.92	   new_primEqInt2
67.83/34.92	   new_esEs(Neg(Zero))
67.83/34.92	   new_esEs(Neg(Succ(x0)))
67.83/34.92	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.83/34.92	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.83/34.92	
67.83/34.92	We have to consider all minimal (P,Q,R)-chains.
67.83/34.92	----------------------------------------
67.83/34.92	
67.83/34.92	(378) TransformationProof (EQUIVALENT)
67.83/34.92	By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS0(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0)))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]:
67.83/34.92	
67.83/34.92	   (new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0)))))),new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0)))))))
67.83/34.92	
67.83/34.92	
67.83/34.92	----------------------------------------
67.83/34.92	
67.83/34.92	(379)
67.83/34.92	Obligation:
67.83/34.92	Q DP problem:
67.83/34.92	The TRS P consists of the following rules:
67.83/34.92	
67.83/34.92	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.83/34.92	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0))))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, Zero, x0, Zero))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS1, Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.92	
67.83/34.92	The TRS R consists of the following rules:
67.83/34.92	
67.83/34.92	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.83/34.92	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.83/34.92	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.83/34.92	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.83/34.92	   new_primMinusNatS2(Zero, Zero) -> Zero
67.83/34.92	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.83/34.92	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.83/34.92	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.83/34.92	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.83/34.92	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.83/34.92	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.83/34.92	   new_primModNatS1(Zero, vuz54200) -> Zero
67.83/34.92	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.83/34.92	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.83/34.92	   new_error -> error([])
67.83/34.92	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.83/34.92	   new_primEqInt2 -> True
67.83/34.92	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.83/34.92	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.83/34.92	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.83/34.92	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.83/34.92	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.83/34.92	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.83/34.92	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.83/34.92	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.83/34.92	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.83/34.92	   new_primMinusNatS1 -> Zero
67.83/34.92	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.83/34.92	   new_primEqInt1 -> True
67.83/34.92	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.83/34.92	   new_primEqInt0(vuz3260) -> False
67.83/34.92	   new_primEqInt(vuz3250) -> False
67.83/34.92	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.83/34.92	
67.83/34.92	The set Q consists of the following terms:
67.83/34.92	
67.83/34.92	   new_rem(Neg(x0), Neg(Zero))
67.83/34.92	   new_primEqInt1
67.83/34.92	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.83/34.92	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.83/34.92	   new_primMinusNatS1
67.83/34.92	   new_rem(Neg(x0), Neg(Succ(x1)))
67.83/34.92	   new_primMinusNatS2(Succ(x0), Zero)
67.83/34.92	   new_primModNatS1(Succ(Zero), Succ(x0))
67.83/34.92	   new_primMinusNatS2(Zero, Zero)
67.83/34.92	   new_error
67.83/34.92	   new_primModNatS1(Succ(Zero), Zero)
67.83/34.92	   new_rem(Pos(x0), Pos(Zero))
67.83/34.92	   new_primModNatS01(x0, x1, Zero, Zero)
67.83/34.92	   new_primEqInt0(x0)
67.83/34.92	   new_esEs(Pos(Zero))
67.83/34.92	   new_esEs(Pos(Succ(x0)))
67.83/34.92	   new_rem(Pos(x0), Pos(Succ(x1)))
67.83/34.92	   new_primModNatS02(x0, x1)
67.83/34.92	   new_primMinusNatS2(Zero, Succ(x0))
67.83/34.92	   new_rem(Pos(x0), Neg(Succ(x1)))
67.83/34.92	   new_rem(Neg(x0), Pos(Succ(x1)))
67.83/34.92	   new_primModNatS1(Zero, x0)
67.83/34.92	   new_primEqInt(x0)
67.83/34.92	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.83/34.92	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.83/34.92	   new_rem(Pos(x0), Neg(Zero))
67.83/34.92	   new_rem(Neg(x0), Pos(Zero))
67.83/34.92	   new_primMinusNatS0(x0)
67.83/34.92	   new_primEqInt2
67.83/34.92	   new_esEs(Neg(Zero))
67.83/34.92	   new_esEs(Neg(Succ(x0)))
67.83/34.92	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.83/34.92	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.83/34.92	
67.83/34.92	We have to consider all minimal (P,Q,R)-chains.
67.83/34.92	----------------------------------------
67.83/34.92	
67.83/34.92	(380) TransformationProof (EQUIVALENT)
67.83/34.92	By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(new_primMinusNatS1, Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(Zero))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]:
67.83/34.92	
67.83/34.92	   (new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Zero, Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(Zero))))),new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Zero, Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(Zero))))))
67.83/34.92	
67.83/34.92	
67.83/34.92	----------------------------------------
67.83/34.92	
67.83/34.92	(381)
67.83/34.92	Obligation:
67.83/34.92	Q DP problem:
67.83/34.92	The TRS P consists of the following rules:
67.83/34.92	
67.83/34.92	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.83/34.92	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0))))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, Zero, x0, Zero))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Zero, Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.92	
67.83/34.92	The TRS R consists of the following rules:
67.83/34.92	
67.83/34.92	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.83/34.92	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.83/34.92	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.83/34.92	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.83/34.92	   new_primMinusNatS2(Zero, Zero) -> Zero
67.83/34.92	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.83/34.92	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.83/34.92	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.83/34.92	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.83/34.92	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.83/34.92	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.83/34.92	   new_primModNatS1(Zero, vuz54200) -> Zero
67.83/34.92	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.83/34.92	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.83/34.92	   new_error -> error([])
67.83/34.92	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.83/34.92	   new_primEqInt2 -> True
67.83/34.92	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.83/34.92	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.83/34.92	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.83/34.92	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.83/34.92	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.83/34.92	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.83/34.92	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.83/34.92	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.83/34.92	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.83/34.92	   new_primMinusNatS1 -> Zero
67.83/34.92	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.83/34.92	   new_primEqInt1 -> True
67.83/34.92	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.83/34.92	   new_primEqInt0(vuz3260) -> False
67.83/34.92	   new_primEqInt(vuz3250) -> False
67.83/34.92	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.83/34.92	
67.83/34.92	The set Q consists of the following terms:
67.83/34.92	
67.83/34.92	   new_rem(Neg(x0), Neg(Zero))
67.83/34.92	   new_primEqInt1
67.83/34.92	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.83/34.92	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.83/34.92	   new_primMinusNatS1
67.83/34.92	   new_rem(Neg(x0), Neg(Succ(x1)))
67.83/34.92	   new_primMinusNatS2(Succ(x0), Zero)
67.83/34.92	   new_primModNatS1(Succ(Zero), Succ(x0))
67.83/34.92	   new_primMinusNatS2(Zero, Zero)
67.83/34.92	   new_error
67.83/34.92	   new_primModNatS1(Succ(Zero), Zero)
67.83/34.92	   new_rem(Pos(x0), Pos(Zero))
67.83/34.92	   new_primModNatS01(x0, x1, Zero, Zero)
67.83/34.92	   new_primEqInt0(x0)
67.83/34.92	   new_esEs(Pos(Zero))
67.83/34.92	   new_esEs(Pos(Succ(x0)))
67.83/34.92	   new_rem(Pos(x0), Pos(Succ(x1)))
67.83/34.92	   new_primModNatS02(x0, x1)
67.83/34.92	   new_primMinusNatS2(Zero, Succ(x0))
67.83/34.92	   new_rem(Pos(x0), Neg(Succ(x1)))
67.83/34.92	   new_rem(Neg(x0), Pos(Succ(x1)))
67.83/34.92	   new_primModNatS1(Zero, x0)
67.83/34.92	   new_primEqInt(x0)
67.83/34.92	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.83/34.92	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.83/34.92	   new_rem(Pos(x0), Neg(Zero))
67.83/34.92	   new_rem(Neg(x0), Pos(Zero))
67.83/34.92	   new_primMinusNatS0(x0)
67.83/34.92	   new_primEqInt2
67.83/34.92	   new_esEs(Neg(Zero))
67.83/34.92	   new_esEs(Neg(Succ(x0)))
67.83/34.92	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.83/34.92	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.83/34.92	
67.83/34.92	We have to consider all minimal (P,Q,R)-chains.
67.83/34.92	----------------------------------------
67.83/34.92	
67.83/34.92	(382) TransformationProof (EQUIVALENT)
67.83/34.92	By rewriting [LPAR04] the rule new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Zero, Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(Zero))))) at position [0,0,0] we obtained the following new rules [LPAR04]:
67.83/34.92	
67.83/34.92	   (new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Pos(Zero)), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(Zero))))),new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Pos(Zero)), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(Zero))))))
67.83/34.92	
67.83/34.92	
67.83/34.92	----------------------------------------
67.83/34.92	
67.83/34.92	(383)
67.83/34.92	Obligation:
67.83/34.92	Q DP problem:
67.83/34.92	The TRS P consists of the following rules:
67.83/34.92	
67.83/34.92	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.83/34.92	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0))))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, Zero, x0, Zero))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Pos(Zero)), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.92	
67.83/34.92	The TRS R consists of the following rules:
67.83/34.92	
67.83/34.92	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.83/34.92	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.83/34.92	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.83/34.92	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.83/34.92	   new_primMinusNatS2(Zero, Zero) -> Zero
67.83/34.92	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.83/34.92	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.83/34.92	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.83/34.92	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.83/34.92	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.83/34.92	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.83/34.92	   new_primModNatS1(Zero, vuz54200) -> Zero
67.83/34.92	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.83/34.92	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.83/34.92	   new_error -> error([])
67.83/34.92	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.83/34.92	   new_primEqInt2 -> True
67.83/34.92	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.83/34.92	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.83/34.92	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.83/34.92	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.83/34.92	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.83/34.92	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.83/34.92	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.83/34.92	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.83/34.92	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.83/34.92	   new_primMinusNatS1 -> Zero
67.83/34.92	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.83/34.92	   new_primEqInt1 -> True
67.83/34.92	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.83/34.92	   new_primEqInt0(vuz3260) -> False
67.83/34.92	   new_primEqInt(vuz3250) -> False
67.83/34.92	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.83/34.92	
67.83/34.92	The set Q consists of the following terms:
67.83/34.92	
67.83/34.92	   new_rem(Neg(x0), Neg(Zero))
67.83/34.92	   new_primEqInt1
67.83/34.92	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.83/34.92	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.83/34.92	   new_primMinusNatS1
67.83/34.92	   new_rem(Neg(x0), Neg(Succ(x1)))
67.83/34.92	   new_primMinusNatS2(Succ(x0), Zero)
67.83/34.92	   new_primModNatS1(Succ(Zero), Succ(x0))
67.83/34.92	   new_primMinusNatS2(Zero, Zero)
67.83/34.92	   new_error
67.83/34.92	   new_primModNatS1(Succ(Zero), Zero)
67.83/34.92	   new_rem(Pos(x0), Pos(Zero))
67.83/34.92	   new_primModNatS01(x0, x1, Zero, Zero)
67.83/34.92	   new_primEqInt0(x0)
67.83/34.92	   new_esEs(Pos(Zero))
67.83/34.92	   new_esEs(Pos(Succ(x0)))
67.83/34.92	   new_rem(Pos(x0), Pos(Succ(x1)))
67.83/34.92	   new_primModNatS02(x0, x1)
67.83/34.92	   new_primMinusNatS2(Zero, Succ(x0))
67.83/34.92	   new_rem(Pos(x0), Neg(Succ(x1)))
67.83/34.92	   new_rem(Neg(x0), Pos(Succ(x1)))
67.83/34.92	   new_primModNatS1(Zero, x0)
67.83/34.92	   new_primEqInt(x0)
67.83/34.92	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.83/34.92	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.83/34.92	   new_rem(Pos(x0), Neg(Zero))
67.83/34.92	   new_rem(Neg(x0), Pos(Zero))
67.83/34.92	   new_primMinusNatS0(x0)
67.83/34.92	   new_primEqInt2
67.83/34.92	   new_esEs(Neg(Zero))
67.83/34.92	   new_esEs(Neg(Succ(x0)))
67.83/34.92	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.83/34.92	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.83/34.92	
67.83/34.92	We have to consider all minimal (P,Q,R)-chains.
67.83/34.92	----------------------------------------
67.83/34.92	
67.83/34.92	(384) DependencyGraphProof (EQUIVALENT)
67.83/34.92	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
67.83/34.92	----------------------------------------
67.83/34.92	
67.83/34.92	(385)
67.83/34.92	Obligation:
67.83/34.92	Q DP problem:
67.83/34.92	The TRS P consists of the following rules:
67.83/34.92	
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.83/34.92	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.83/34.92	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2)))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0))))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, Zero, x0, Zero))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.92	
67.83/34.92	The TRS R consists of the following rules:
67.83/34.92	
67.83/34.92	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.83/34.92	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.83/34.92	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.83/34.92	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.83/34.92	   new_primMinusNatS2(Zero, Zero) -> Zero
67.83/34.92	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.83/34.92	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.83/34.92	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.83/34.92	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.83/34.92	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.83/34.92	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.83/34.92	   new_primModNatS1(Zero, vuz54200) -> Zero
67.83/34.92	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.83/34.92	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.83/34.92	   new_error -> error([])
67.83/34.92	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.83/34.92	   new_primEqInt2 -> True
67.83/34.92	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.83/34.92	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.83/34.92	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.83/34.92	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.83/34.92	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.83/34.92	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.83/34.92	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.83/34.92	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.83/34.92	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.83/34.92	   new_primMinusNatS1 -> Zero
67.83/34.92	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.83/34.92	   new_primEqInt1 -> True
67.83/34.92	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.83/34.92	   new_primEqInt0(vuz3260) -> False
67.83/34.92	   new_primEqInt(vuz3250) -> False
67.83/34.92	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.83/34.92	
67.83/34.92	The set Q consists of the following terms:
67.83/34.92	
67.83/34.92	   new_rem(Neg(x0), Neg(Zero))
67.83/34.92	   new_primEqInt1
67.83/34.92	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.83/34.92	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.83/34.92	   new_primMinusNatS1
67.83/34.92	   new_rem(Neg(x0), Neg(Succ(x1)))
67.83/34.92	   new_primMinusNatS2(Succ(x0), Zero)
67.83/34.92	   new_primModNatS1(Succ(Zero), Succ(x0))
67.83/34.92	   new_primMinusNatS2(Zero, Zero)
67.83/34.92	   new_error
67.83/34.92	   new_primModNatS1(Succ(Zero), Zero)
67.83/34.92	   new_rem(Pos(x0), Pos(Zero))
67.83/34.92	   new_primModNatS01(x0, x1, Zero, Zero)
67.83/34.92	   new_primEqInt0(x0)
67.83/34.92	   new_esEs(Pos(Zero))
67.83/34.92	   new_esEs(Pos(Succ(x0)))
67.83/34.92	   new_rem(Pos(x0), Pos(Succ(x1)))
67.83/34.92	   new_primModNatS02(x0, x1)
67.83/34.92	   new_primMinusNatS2(Zero, Succ(x0))
67.83/34.92	   new_rem(Pos(x0), Neg(Succ(x1)))
67.83/34.92	   new_rem(Neg(x0), Pos(Succ(x1)))
67.83/34.92	   new_primModNatS1(Zero, x0)
67.83/34.92	   new_primEqInt(x0)
67.83/34.92	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.83/34.92	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.83/34.92	   new_rem(Pos(x0), Neg(Zero))
67.83/34.92	   new_rem(Neg(x0), Pos(Zero))
67.83/34.92	   new_primMinusNatS0(x0)
67.83/34.92	   new_primEqInt2
67.83/34.92	   new_esEs(Neg(Zero))
67.83/34.92	   new_esEs(Neg(Succ(x0)))
67.83/34.92	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.83/34.92	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.83/34.92	
67.83/34.92	We have to consider all minimal (P,Q,R)-chains.
67.83/34.92	----------------------------------------
67.83/34.92	
67.83/34.92	(386) TransformationProof (EQUIVALENT)
67.83/34.92	By narrowing [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x2), Succ(x3), x2, x3))), Pos(Succ(Succ(Succ(x3)))), Neg(Succ(Succ(Succ(x2))))) at position [0] we obtained the following new rules [LPAR04]:
67.83/34.92	
67.83/34.92	   (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Pos(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Pos(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))))
67.83/34.92	   (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Neg(Succ(Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Neg(Succ(Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))))
67.83/34.92	   (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS02(Succ(Zero), Succ(Zero)))), Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS02(Succ(Zero), Succ(Zero)))), Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))))
67.83/34.92	   (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS02(Succ(Succ(x2)), Succ(Zero)))), Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS02(Succ(Succ(x2)), Succ(Zero)))), Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))))
67.83/34.92	
67.83/34.92	
67.83/34.92	----------------------------------------
67.83/34.92	
67.83/34.92	(387)
67.83/34.92	Obligation:
67.83/34.92	Q DP problem:
67.83/34.92	The TRS P consists of the following rules:
67.83/34.92	
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.83/34.92	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.83/34.92	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0))))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, Zero, x0, Zero))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Pos(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Neg(Succ(Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS02(Succ(Zero), Succ(Zero)))), Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS02(Succ(Succ(x2)), Succ(Zero)))), Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	
67.83/34.92	The TRS R consists of the following rules:
67.83/34.92	
67.83/34.92	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.83/34.92	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.83/34.92	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.83/34.92	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.83/34.92	   new_primMinusNatS2(Zero, Zero) -> Zero
67.83/34.92	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.83/34.92	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.83/34.92	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.83/34.92	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.83/34.92	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.83/34.92	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.83/34.92	   new_primModNatS1(Zero, vuz54200) -> Zero
67.83/34.92	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.83/34.92	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.83/34.92	   new_error -> error([])
67.83/34.92	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.83/34.92	   new_primEqInt2 -> True
67.83/34.92	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.83/34.92	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.83/34.92	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.83/34.92	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.83/34.92	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.83/34.92	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.83/34.92	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.83/34.92	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.83/34.92	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.83/34.92	   new_primMinusNatS1 -> Zero
67.83/34.92	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.83/34.92	   new_primEqInt1 -> True
67.83/34.92	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.83/34.92	   new_primEqInt0(vuz3260) -> False
67.83/34.92	   new_primEqInt(vuz3250) -> False
67.83/34.92	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.83/34.92	
67.83/34.92	The set Q consists of the following terms:
67.83/34.92	
67.83/34.92	   new_rem(Neg(x0), Neg(Zero))
67.83/34.92	   new_primEqInt1
67.83/34.92	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.83/34.92	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.83/34.92	   new_primMinusNatS1
67.83/34.92	   new_rem(Neg(x0), Neg(Succ(x1)))
67.83/34.92	   new_primMinusNatS2(Succ(x0), Zero)
67.83/34.92	   new_primModNatS1(Succ(Zero), Succ(x0))
67.83/34.92	   new_primMinusNatS2(Zero, Zero)
67.83/34.92	   new_error
67.83/34.92	   new_primModNatS1(Succ(Zero), Zero)
67.83/34.92	   new_rem(Pos(x0), Pos(Zero))
67.83/34.92	   new_primModNatS01(x0, x1, Zero, Zero)
67.83/34.92	   new_primEqInt0(x0)
67.83/34.92	   new_esEs(Pos(Zero))
67.83/34.92	   new_esEs(Pos(Succ(x0)))
67.83/34.92	   new_rem(Pos(x0), Pos(Succ(x1)))
67.83/34.92	   new_primModNatS02(x0, x1)
67.83/34.92	   new_primMinusNatS2(Zero, Succ(x0))
67.83/34.92	   new_rem(Pos(x0), Neg(Succ(x1)))
67.83/34.92	   new_rem(Neg(x0), Pos(Succ(x1)))
67.83/34.92	   new_primModNatS1(Zero, x0)
67.83/34.92	   new_primEqInt(x0)
67.83/34.92	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.83/34.92	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.83/34.92	   new_rem(Pos(x0), Neg(Zero))
67.83/34.92	   new_rem(Neg(x0), Pos(Zero))
67.83/34.92	   new_primMinusNatS0(x0)
67.83/34.92	   new_primEqInt2
67.83/34.92	   new_esEs(Neg(Zero))
67.83/34.92	   new_esEs(Neg(Succ(x0)))
67.83/34.92	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.83/34.92	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.83/34.92	
67.83/34.92	We have to consider all minimal (P,Q,R)-chains.
67.83/34.92	----------------------------------------
67.83/34.92	
67.83/34.92	(388) TransformationProof (EQUIVALENT)
67.83/34.92	By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Neg(Succ(Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) at position [0] we obtained the following new rules [LPAR04]:
67.83/34.92	
67.83/34.92	   (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_primEqInt0(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_primEqInt0(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))))
67.83/34.92	
67.83/34.92	
67.83/34.92	----------------------------------------
67.83/34.92	
67.83/34.92	(389)
67.83/34.92	Obligation:
67.83/34.92	Q DP problem:
67.83/34.92	The TRS P consists of the following rules:
67.83/34.92	
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.83/34.92	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.83/34.92	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0))))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, Zero, x0, Zero))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Pos(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS02(Succ(Zero), Succ(Zero)))), Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS02(Succ(Succ(x2)), Succ(Zero)))), Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_primEqInt0(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.92	
67.83/34.92	The TRS R consists of the following rules:
67.83/34.92	
67.83/34.92	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.83/34.92	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.83/34.92	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.83/34.92	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.83/34.92	   new_primMinusNatS2(Zero, Zero) -> Zero
67.83/34.92	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.83/34.92	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.83/34.92	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.83/34.92	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.83/34.92	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.83/34.92	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.83/34.92	   new_primModNatS1(Zero, vuz54200) -> Zero
67.83/34.92	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.83/34.92	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.83/34.92	   new_error -> error([])
67.83/34.92	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.83/34.92	   new_primEqInt2 -> True
67.83/34.92	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.83/34.92	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.83/34.92	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.83/34.92	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.83/34.92	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.83/34.92	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.83/34.92	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.83/34.92	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.83/34.92	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.83/34.92	   new_primMinusNatS1 -> Zero
67.83/34.92	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.83/34.92	   new_primEqInt1 -> True
67.83/34.92	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.83/34.92	   new_primEqInt0(vuz3260) -> False
67.83/34.92	   new_primEqInt(vuz3250) -> False
67.83/34.92	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.83/34.92	
67.83/34.92	The set Q consists of the following terms:
67.83/34.92	
67.83/34.92	   new_rem(Neg(x0), Neg(Zero))
67.83/34.92	   new_primEqInt1
67.83/34.92	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.83/34.92	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.83/34.92	   new_primMinusNatS1
67.83/34.92	   new_rem(Neg(x0), Neg(Succ(x1)))
67.83/34.92	   new_primMinusNatS2(Succ(x0), Zero)
67.83/34.92	   new_primModNatS1(Succ(Zero), Succ(x0))
67.83/34.92	   new_primMinusNatS2(Zero, Zero)
67.83/34.92	   new_error
67.83/34.92	   new_primModNatS1(Succ(Zero), Zero)
67.83/34.92	   new_rem(Pos(x0), Pos(Zero))
67.83/34.92	   new_primModNatS01(x0, x1, Zero, Zero)
67.83/34.92	   new_primEqInt0(x0)
67.83/34.92	   new_esEs(Pos(Zero))
67.83/34.92	   new_esEs(Pos(Succ(x0)))
67.83/34.92	   new_rem(Pos(x0), Pos(Succ(x1)))
67.83/34.92	   new_primModNatS02(x0, x1)
67.83/34.92	   new_primMinusNatS2(Zero, Succ(x0))
67.83/34.92	   new_rem(Pos(x0), Neg(Succ(x1)))
67.83/34.92	   new_rem(Neg(x0), Pos(Succ(x1)))
67.83/34.92	   new_primModNatS1(Zero, x0)
67.83/34.92	   new_primEqInt(x0)
67.83/34.92	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.83/34.92	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.83/34.92	   new_rem(Pos(x0), Neg(Zero))
67.83/34.92	   new_rem(Neg(x0), Pos(Zero))
67.83/34.92	   new_primMinusNatS0(x0)
67.83/34.92	   new_primEqInt2
67.83/34.92	   new_esEs(Neg(Zero))
67.83/34.92	   new_esEs(Neg(Succ(x0)))
67.83/34.92	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.83/34.92	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.83/34.92	
67.83/34.92	We have to consider all minimal (P,Q,R)-chains.
67.83/34.92	----------------------------------------
67.83/34.92	
67.83/34.92	(390) TransformationProof (EQUIVALENT)
67.83/34.92	By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS02(Succ(Zero), Succ(Zero)))), Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) at position [0,0,0] we obtained the following new rules [LPAR04]:
67.83/34.92	
67.83/34.92	   (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Succ(Succ(Zero)), Succ(Succ(Zero))), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Succ(Succ(Zero)), Succ(Succ(Zero))), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))))
67.83/34.92	
67.83/34.92	
67.83/34.92	----------------------------------------
67.83/34.92	
67.83/34.92	(391)
67.83/34.92	Obligation:
67.83/34.92	Q DP problem:
67.83/34.92	The TRS P consists of the following rules:
67.83/34.92	
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.83/34.92	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.83/34.92	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0))))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, Zero, x0, Zero))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Pos(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS02(Succ(Succ(x2)), Succ(Zero)))), Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_primEqInt0(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Succ(Succ(Zero)), Succ(Succ(Zero))), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.92	
67.83/34.92	The TRS R consists of the following rules:
67.83/34.92	
67.83/34.92	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.83/34.92	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.83/34.92	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.83/34.92	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.83/34.92	   new_primMinusNatS2(Zero, Zero) -> Zero
67.83/34.92	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.83/34.92	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.83/34.92	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.83/34.92	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.83/34.92	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.83/34.92	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.83/34.92	   new_primModNatS1(Zero, vuz54200) -> Zero
67.83/34.92	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.83/34.92	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.83/34.92	   new_error -> error([])
67.83/34.92	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.83/34.92	   new_primEqInt2 -> True
67.83/34.92	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.83/34.92	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.83/34.92	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.83/34.92	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.83/34.92	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.83/34.92	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.83/34.92	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.83/34.92	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.83/34.92	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.83/34.92	   new_primMinusNatS1 -> Zero
67.83/34.92	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.83/34.92	   new_primEqInt1 -> True
67.83/34.92	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.83/34.92	   new_primEqInt0(vuz3260) -> False
67.83/34.92	   new_primEqInt(vuz3250) -> False
67.83/34.92	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.83/34.92	
67.83/34.92	The set Q consists of the following terms:
67.83/34.92	
67.83/34.92	   new_rem(Neg(x0), Neg(Zero))
67.83/34.92	   new_primEqInt1
67.83/34.92	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.83/34.92	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.83/34.92	   new_primMinusNatS1
67.83/34.92	   new_rem(Neg(x0), Neg(Succ(x1)))
67.83/34.92	   new_primMinusNatS2(Succ(x0), Zero)
67.83/34.92	   new_primModNatS1(Succ(Zero), Succ(x0))
67.83/34.92	   new_primMinusNatS2(Zero, Zero)
67.83/34.92	   new_error
67.83/34.92	   new_primModNatS1(Succ(Zero), Zero)
67.83/34.92	   new_rem(Pos(x0), Pos(Zero))
67.83/34.92	   new_primModNatS01(x0, x1, Zero, Zero)
67.83/34.92	   new_primEqInt0(x0)
67.83/34.92	   new_esEs(Pos(Zero))
67.83/34.92	   new_esEs(Pos(Succ(x0)))
67.83/34.92	   new_rem(Pos(x0), Pos(Succ(x1)))
67.83/34.92	   new_primModNatS02(x0, x1)
67.83/34.92	   new_primMinusNatS2(Zero, Succ(x0))
67.83/34.92	   new_rem(Pos(x0), Neg(Succ(x1)))
67.83/34.92	   new_rem(Neg(x0), Pos(Succ(x1)))
67.83/34.92	   new_primModNatS1(Zero, x0)
67.83/34.92	   new_primEqInt(x0)
67.83/34.92	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.83/34.92	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.83/34.92	   new_rem(Pos(x0), Neg(Zero))
67.83/34.92	   new_rem(Neg(x0), Pos(Zero))
67.83/34.92	   new_primMinusNatS0(x0)
67.83/34.92	   new_primEqInt2
67.83/34.92	   new_esEs(Neg(Zero))
67.83/34.92	   new_esEs(Neg(Succ(x0)))
67.83/34.92	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.83/34.92	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.83/34.92	
67.83/34.92	We have to consider all minimal (P,Q,R)-chains.
67.83/34.92	----------------------------------------
67.83/34.92	
67.83/34.92	(392) TransformationProof (EQUIVALENT)
67.83/34.92	By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS02(Succ(Succ(x2)), Succ(Zero)))), Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) at position [0,0,0] we obtained the following new rules [LPAR04]:
67.83/34.92	
67.83/34.92	   (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Succ(Succ(Succ(x2))), Succ(Succ(Zero))), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Succ(Succ(Succ(x2))), Succ(Succ(Zero))), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))))
67.83/34.92	
67.83/34.92	
67.83/34.92	----------------------------------------
67.83/34.92	
67.83/34.92	(393)
67.83/34.92	Obligation:
67.83/34.92	Q DP problem:
67.83/34.92	The TRS P consists of the following rules:
67.83/34.92	
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.83/34.92	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.83/34.92	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0))))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, Zero, x0, Zero))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Pos(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_primEqInt0(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Succ(Succ(Zero)), Succ(Succ(Zero))), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Succ(Succ(Succ(x2))), Succ(Succ(Zero))), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	
67.83/34.92	The TRS R consists of the following rules:
67.83/34.92	
67.83/34.92	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.83/34.92	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.83/34.92	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.83/34.92	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.83/34.92	   new_primMinusNatS2(Zero, Zero) -> Zero
67.83/34.92	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.83/34.92	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.83/34.92	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.83/34.92	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.83/34.92	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.83/34.92	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.83/34.92	   new_primModNatS1(Zero, vuz54200) -> Zero
67.83/34.92	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.83/34.92	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.83/34.92	   new_error -> error([])
67.83/34.92	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.83/34.92	   new_primEqInt2 -> True
67.83/34.92	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.83/34.92	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.83/34.92	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.83/34.92	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.83/34.92	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.83/34.92	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.83/34.92	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.83/34.92	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.83/34.92	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.83/34.92	   new_primMinusNatS1 -> Zero
67.83/34.92	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.83/34.92	   new_primEqInt1 -> True
67.83/34.92	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.83/34.92	   new_primEqInt0(vuz3260) -> False
67.83/34.92	   new_primEqInt(vuz3250) -> False
67.83/34.92	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.83/34.92	
67.83/34.92	The set Q consists of the following terms:
67.83/34.92	
67.83/34.92	   new_rem(Neg(x0), Neg(Zero))
67.83/34.92	   new_primEqInt1
67.83/34.92	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.83/34.92	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.83/34.92	   new_primMinusNatS1
67.83/34.92	   new_rem(Neg(x0), Neg(Succ(x1)))
67.83/34.92	   new_primMinusNatS2(Succ(x0), Zero)
67.83/34.92	   new_primModNatS1(Succ(Zero), Succ(x0))
67.83/34.92	   new_primMinusNatS2(Zero, Zero)
67.83/34.92	   new_error
67.83/34.92	   new_primModNatS1(Succ(Zero), Zero)
67.83/34.92	   new_rem(Pos(x0), Pos(Zero))
67.83/34.92	   new_primModNatS01(x0, x1, Zero, Zero)
67.83/34.92	   new_primEqInt0(x0)
67.83/34.92	   new_esEs(Pos(Zero))
67.83/34.92	   new_esEs(Pos(Succ(x0)))
67.83/34.92	   new_rem(Pos(x0), Pos(Succ(x1)))
67.83/34.92	   new_primModNatS02(x0, x1)
67.83/34.92	   new_primMinusNatS2(Zero, Succ(x0))
67.83/34.92	   new_rem(Pos(x0), Neg(Succ(x1)))
67.83/34.92	   new_rem(Neg(x0), Pos(Succ(x1)))
67.83/34.92	   new_primModNatS1(Zero, x0)
67.83/34.92	   new_primEqInt(x0)
67.83/34.92	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.83/34.92	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.83/34.92	   new_rem(Pos(x0), Neg(Zero))
67.83/34.92	   new_rem(Neg(x0), Pos(Zero))
67.83/34.92	   new_primMinusNatS0(x0)
67.83/34.92	   new_primEqInt2
67.83/34.92	   new_esEs(Neg(Zero))
67.83/34.92	   new_esEs(Neg(Succ(x0)))
67.83/34.92	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.83/34.92	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.83/34.92	
67.83/34.92	We have to consider all minimal (P,Q,R)-chains.
67.83/34.92	----------------------------------------
67.83/34.92	
67.83/34.92	(394) TransformationProof (EQUIVALENT)
67.83/34.92	By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_primEqInt0(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) at position [0] we obtained the following new rules [LPAR04]:
67.83/34.92	
67.83/34.92	   (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))))
67.83/34.92	
67.83/34.92	
67.83/34.92	----------------------------------------
67.83/34.92	
67.83/34.92	(395)
67.83/34.92	Obligation:
67.83/34.92	Q DP problem:
67.83/34.92	The TRS P consists of the following rules:
67.83/34.92	
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.83/34.92	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.83/34.92	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0))))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, Zero, x0, Zero))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Pos(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Succ(Succ(Zero)), Succ(Succ(Zero))), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Succ(Succ(Succ(x2))), Succ(Succ(Zero))), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.92	
67.83/34.92	The TRS R consists of the following rules:
67.83/34.92	
67.83/34.92	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.83/34.92	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.83/34.92	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.83/34.92	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.83/34.92	   new_primMinusNatS2(Zero, Zero) -> Zero
67.83/34.92	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.83/34.92	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.83/34.92	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.83/34.92	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.83/34.92	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.83/34.92	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.83/34.92	   new_primModNatS1(Zero, vuz54200) -> Zero
67.83/34.92	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.83/34.92	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.83/34.92	   new_error -> error([])
67.83/34.92	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.83/34.92	   new_primEqInt2 -> True
67.83/34.92	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.83/34.92	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.83/34.92	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.83/34.92	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.83/34.92	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.83/34.92	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.83/34.92	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.83/34.92	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.83/34.92	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.83/34.92	   new_primMinusNatS1 -> Zero
67.83/34.92	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.83/34.92	   new_primEqInt1 -> True
67.83/34.92	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.83/34.92	   new_primEqInt0(vuz3260) -> False
67.83/34.92	   new_primEqInt(vuz3250) -> False
67.83/34.92	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.83/34.92	
67.83/34.92	The set Q consists of the following terms:
67.83/34.92	
67.83/34.92	   new_rem(Neg(x0), Neg(Zero))
67.83/34.92	   new_primEqInt1
67.83/34.92	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.83/34.92	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.83/34.92	   new_primMinusNatS1
67.83/34.92	   new_rem(Neg(x0), Neg(Succ(x1)))
67.83/34.92	   new_primMinusNatS2(Succ(x0), Zero)
67.83/34.92	   new_primModNatS1(Succ(Zero), Succ(x0))
67.83/34.92	   new_primMinusNatS2(Zero, Zero)
67.83/34.92	   new_error
67.83/34.92	   new_primModNatS1(Succ(Zero), Zero)
67.83/34.92	   new_rem(Pos(x0), Pos(Zero))
67.83/34.92	   new_primModNatS01(x0, x1, Zero, Zero)
67.83/34.92	   new_primEqInt0(x0)
67.83/34.92	   new_esEs(Pos(Zero))
67.83/34.92	   new_esEs(Pos(Succ(x0)))
67.83/34.92	   new_rem(Pos(x0), Pos(Succ(x1)))
67.83/34.92	   new_primModNatS02(x0, x1)
67.83/34.92	   new_primMinusNatS2(Zero, Succ(x0))
67.83/34.92	   new_rem(Pos(x0), Neg(Succ(x1)))
67.83/34.92	   new_rem(Neg(x0), Pos(Succ(x1)))
67.83/34.92	   new_primModNatS1(Zero, x0)
67.83/34.92	   new_primEqInt(x0)
67.83/34.92	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.83/34.92	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.83/34.92	   new_rem(Pos(x0), Neg(Zero))
67.83/34.92	   new_rem(Neg(x0), Pos(Zero))
67.83/34.92	   new_primMinusNatS0(x0)
67.83/34.92	   new_primEqInt2
67.83/34.92	   new_esEs(Neg(Zero))
67.83/34.92	   new_esEs(Neg(Succ(x0)))
67.83/34.92	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.83/34.92	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.83/34.92	
67.83/34.92	We have to consider all minimal (P,Q,R)-chains.
67.83/34.92	----------------------------------------
67.83/34.92	
67.83/34.92	(396) TransformationProof (EQUIVALENT)
67.83/34.92	By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Succ(Succ(Zero)), Succ(Succ(Zero))), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]:
67.83/34.92	
67.83/34.92	   (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Succ(Zero), Succ(Zero)), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Succ(Zero), Succ(Zero)), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))))
67.83/34.92	
67.83/34.92	
67.83/34.92	----------------------------------------
67.83/34.92	
67.83/34.92	(397)
67.83/34.92	Obligation:
67.83/34.92	Q DP problem:
67.83/34.92	The TRS P consists of the following rules:
67.83/34.92	
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.83/34.92	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.83/34.92	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0))))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, Zero, x0, Zero))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Pos(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Succ(Succ(Succ(x2))), Succ(Succ(Zero))), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Succ(Zero), Succ(Zero)), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.92	
67.83/34.92	The TRS R consists of the following rules:
67.83/34.92	
67.83/34.92	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.83/34.92	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.83/34.92	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.83/34.92	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.83/34.92	   new_primMinusNatS2(Zero, Zero) -> Zero
67.83/34.92	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.83/34.92	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.83/34.92	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.83/34.92	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.83/34.92	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.83/34.92	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.83/34.92	   new_primModNatS1(Zero, vuz54200) -> Zero
67.83/34.92	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.83/34.92	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.83/34.92	   new_error -> error([])
67.83/34.92	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.83/34.92	   new_primEqInt2 -> True
67.83/34.92	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.83/34.92	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.83/34.92	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.83/34.92	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.83/34.92	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.83/34.92	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.83/34.92	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.83/34.92	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.83/34.92	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.83/34.92	   new_primMinusNatS1 -> Zero
67.83/34.92	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.83/34.92	   new_primEqInt1 -> True
67.83/34.92	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.83/34.92	   new_primEqInt0(vuz3260) -> False
67.83/34.92	   new_primEqInt(vuz3250) -> False
67.83/34.92	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.83/34.92	
67.83/34.92	The set Q consists of the following terms:
67.83/34.92	
67.83/34.92	   new_rem(Neg(x0), Neg(Zero))
67.83/34.92	   new_primEqInt1
67.83/34.92	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.83/34.92	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.83/34.92	   new_primMinusNatS1
67.83/34.92	   new_rem(Neg(x0), Neg(Succ(x1)))
67.83/34.92	   new_primMinusNatS2(Succ(x0), Zero)
67.83/34.92	   new_primModNatS1(Succ(Zero), Succ(x0))
67.83/34.92	   new_primMinusNatS2(Zero, Zero)
67.83/34.92	   new_error
67.83/34.92	   new_primModNatS1(Succ(Zero), Zero)
67.83/34.92	   new_rem(Pos(x0), Pos(Zero))
67.83/34.92	   new_primModNatS01(x0, x1, Zero, Zero)
67.83/34.92	   new_primEqInt0(x0)
67.83/34.92	   new_esEs(Pos(Zero))
67.83/34.92	   new_esEs(Pos(Succ(x0)))
67.83/34.92	   new_rem(Pos(x0), Pos(Succ(x1)))
67.83/34.92	   new_primModNatS02(x0, x1)
67.83/34.92	   new_primMinusNatS2(Zero, Succ(x0))
67.83/34.92	   new_rem(Pos(x0), Neg(Succ(x1)))
67.83/34.92	   new_rem(Neg(x0), Pos(Succ(x1)))
67.83/34.92	   new_primModNatS1(Zero, x0)
67.83/34.92	   new_primEqInt(x0)
67.83/34.92	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.83/34.92	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.83/34.92	   new_rem(Pos(x0), Neg(Zero))
67.83/34.92	   new_rem(Neg(x0), Pos(Zero))
67.83/34.92	   new_primMinusNatS0(x0)
67.83/34.92	   new_primEqInt2
67.83/34.92	   new_esEs(Neg(Zero))
67.83/34.92	   new_esEs(Neg(Succ(x0)))
67.83/34.92	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.83/34.92	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.83/34.92	
67.83/34.92	We have to consider all minimal (P,Q,R)-chains.
67.83/34.92	----------------------------------------
67.83/34.92	
67.83/34.92	(398) TransformationProof (EQUIVALENT)
67.83/34.92	By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Succ(Succ(Succ(x2))), Succ(Succ(Zero))), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]:
67.83/34.92	
67.83/34.92	   (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Succ(Succ(x2)), Succ(Zero)), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Succ(Succ(x2)), Succ(Zero)), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))))
67.83/34.92	
67.83/34.92	
67.83/34.92	----------------------------------------
67.83/34.92	
67.83/34.92	(399)
67.83/34.92	Obligation:
67.83/34.92	Q DP problem:
67.83/34.92	The TRS P consists of the following rules:
67.83/34.92	
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.83/34.92	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.83/34.92	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0))))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, Zero, x0, Zero))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Pos(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Succ(Zero), Succ(Zero)), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Succ(Succ(x2)), Succ(Zero)), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	
67.83/34.92	The TRS R consists of the following rules:
67.83/34.92	
67.83/34.92	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.83/34.92	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.83/34.92	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.83/34.92	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.83/34.92	   new_primMinusNatS2(Zero, Zero) -> Zero
67.83/34.92	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.83/34.92	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.83/34.92	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.83/34.92	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.83/34.92	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.83/34.92	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.83/34.92	   new_primModNatS1(Zero, vuz54200) -> Zero
67.83/34.92	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.83/34.92	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.83/34.92	   new_error -> error([])
67.83/34.92	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.83/34.92	   new_primEqInt2 -> True
67.83/34.92	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.83/34.92	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.83/34.92	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.83/34.92	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.83/34.92	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.83/34.92	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.83/34.92	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.83/34.92	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.83/34.92	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.83/34.92	   new_primMinusNatS1 -> Zero
67.83/34.92	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.83/34.92	   new_primEqInt1 -> True
67.83/34.92	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.83/34.92	   new_primEqInt0(vuz3260) -> False
67.83/34.92	   new_primEqInt(vuz3250) -> False
67.83/34.92	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.83/34.92	
67.83/34.92	The set Q consists of the following terms:
67.83/34.92	
67.83/34.92	   new_rem(Neg(x0), Neg(Zero))
67.83/34.92	   new_primEqInt1
67.83/34.92	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.83/34.92	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.83/34.92	   new_primMinusNatS1
67.83/34.92	   new_rem(Neg(x0), Neg(Succ(x1)))
67.83/34.92	   new_primMinusNatS2(Succ(x0), Zero)
67.83/34.92	   new_primModNatS1(Succ(Zero), Succ(x0))
67.83/34.92	   new_primMinusNatS2(Zero, Zero)
67.83/34.92	   new_error
67.83/34.92	   new_primModNatS1(Succ(Zero), Zero)
67.83/34.92	   new_rem(Pos(x0), Pos(Zero))
67.83/34.92	   new_primModNatS01(x0, x1, Zero, Zero)
67.83/34.92	   new_primEqInt0(x0)
67.83/34.92	   new_esEs(Pos(Zero))
67.83/34.92	   new_esEs(Pos(Succ(x0)))
67.83/34.92	   new_rem(Pos(x0), Pos(Succ(x1)))
67.83/34.92	   new_primModNatS02(x0, x1)
67.83/34.92	   new_primMinusNatS2(Zero, Succ(x0))
67.83/34.92	   new_rem(Pos(x0), Neg(Succ(x1)))
67.83/34.92	   new_rem(Neg(x0), Pos(Succ(x1)))
67.83/34.92	   new_primModNatS1(Zero, x0)
67.83/34.92	   new_primEqInt(x0)
67.83/34.92	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.83/34.92	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.83/34.92	   new_rem(Pos(x0), Neg(Zero))
67.83/34.92	   new_rem(Neg(x0), Pos(Zero))
67.83/34.92	   new_primMinusNatS0(x0)
67.83/34.92	   new_primEqInt2
67.83/34.92	   new_esEs(Neg(Zero))
67.83/34.92	   new_esEs(Neg(Succ(x0)))
67.83/34.92	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.83/34.92	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.83/34.92	
67.83/34.92	We have to consider all minimal (P,Q,R)-chains.
67.83/34.92	----------------------------------------
67.83/34.92	
67.83/34.92	(400) TransformationProof (EQUIVALENT)
67.83/34.92	By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Succ(Zero), Succ(Zero)), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]:
67.83/34.92	
67.83/34.92	   (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Zero, Zero), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Zero, Zero), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))))
67.83/34.92	
67.83/34.92	
67.83/34.92	----------------------------------------
67.83/34.92	
67.83/34.92	(401)
67.83/34.92	Obligation:
67.83/34.92	Q DP problem:
67.83/34.92	The TRS P consists of the following rules:
67.83/34.92	
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.83/34.92	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.83/34.92	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0))))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, Zero, x0, Zero))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Pos(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Succ(Succ(x2)), Succ(Zero)), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Zero, Zero), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.92	
67.83/34.92	The TRS R consists of the following rules:
67.83/34.92	
67.83/34.92	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.83/34.92	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.83/34.92	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.83/34.92	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.83/34.92	   new_primMinusNatS2(Zero, Zero) -> Zero
67.83/34.92	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.83/34.92	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.83/34.92	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.83/34.92	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.83/34.92	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.83/34.92	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.83/34.92	   new_primModNatS1(Zero, vuz54200) -> Zero
67.83/34.92	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.83/34.92	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.83/34.92	   new_error -> error([])
67.83/34.92	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.83/34.92	   new_primEqInt2 -> True
67.83/34.92	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.83/34.92	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.83/34.92	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.83/34.92	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.83/34.92	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.83/34.92	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.83/34.92	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.83/34.92	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.83/34.92	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.83/34.92	   new_primMinusNatS1 -> Zero
67.83/34.92	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.83/34.92	   new_primEqInt1 -> True
67.83/34.92	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.83/34.92	   new_primEqInt0(vuz3260) -> False
67.83/34.92	   new_primEqInt(vuz3250) -> False
67.83/34.92	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.83/34.92	
67.83/34.92	The set Q consists of the following terms:
67.83/34.92	
67.83/34.92	   new_rem(Neg(x0), Neg(Zero))
67.83/34.92	   new_primEqInt1
67.83/34.92	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.83/34.92	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.83/34.92	   new_primMinusNatS1
67.83/34.92	   new_rem(Neg(x0), Neg(Succ(x1)))
67.83/34.92	   new_primMinusNatS2(Succ(x0), Zero)
67.83/34.92	   new_primModNatS1(Succ(Zero), Succ(x0))
67.83/34.92	   new_primMinusNatS2(Zero, Zero)
67.83/34.92	   new_error
67.83/34.92	   new_primModNatS1(Succ(Zero), Zero)
67.83/34.92	   new_rem(Pos(x0), Pos(Zero))
67.83/34.92	   new_primModNatS01(x0, x1, Zero, Zero)
67.83/34.92	   new_primEqInt0(x0)
67.83/34.92	   new_esEs(Pos(Zero))
67.83/34.92	   new_esEs(Pos(Succ(x0)))
67.83/34.92	   new_rem(Pos(x0), Pos(Succ(x1)))
67.83/34.92	   new_primModNatS02(x0, x1)
67.83/34.92	   new_primMinusNatS2(Zero, Succ(x0))
67.83/34.92	   new_rem(Pos(x0), Neg(Succ(x1)))
67.83/34.92	   new_rem(Neg(x0), Pos(Succ(x1)))
67.83/34.92	   new_primModNatS1(Zero, x0)
67.83/34.92	   new_primEqInt(x0)
67.83/34.92	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.83/34.92	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.83/34.92	   new_rem(Pos(x0), Neg(Zero))
67.83/34.92	   new_rem(Neg(x0), Pos(Zero))
67.83/34.92	   new_primMinusNatS0(x0)
67.83/34.92	   new_primEqInt2
67.83/34.92	   new_esEs(Neg(Zero))
67.83/34.92	   new_esEs(Neg(Succ(x0)))
67.83/34.92	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.83/34.92	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.83/34.92	
67.83/34.92	We have to consider all minimal (P,Q,R)-chains.
67.83/34.92	----------------------------------------
67.83/34.92	
67.83/34.92	(402) TransformationProof (EQUIVALENT)
67.83/34.92	By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Succ(Succ(x2)), Succ(Zero)), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]:
67.83/34.92	
67.83/34.92	   (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Succ(x2), Zero), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Succ(x2), Zero), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))))
67.83/34.92	
67.83/34.92	
67.83/34.92	----------------------------------------
67.83/34.92	
67.83/34.92	(403)
67.83/34.92	Obligation:
67.83/34.92	Q DP problem:
67.83/34.92	The TRS P consists of the following rules:
67.83/34.92	
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.83/34.92	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.83/34.92	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0))))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, Zero, x0, Zero))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Pos(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Zero, Zero), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Succ(x2), Zero), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	
67.83/34.92	The TRS R consists of the following rules:
67.83/34.92	
67.83/34.92	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.83/34.92	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.83/34.92	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.83/34.92	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.83/34.92	   new_primMinusNatS2(Zero, Zero) -> Zero
67.83/34.92	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.83/34.92	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.83/34.92	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.83/34.92	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.83/34.92	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.83/34.92	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.83/34.92	   new_primModNatS1(Zero, vuz54200) -> Zero
67.83/34.92	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.83/34.92	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.83/34.92	   new_error -> error([])
67.83/34.92	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.83/34.92	   new_primEqInt2 -> True
67.83/34.92	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.83/34.92	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.83/34.92	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.83/34.92	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.83/34.92	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.83/34.92	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.83/34.92	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.83/34.92	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.83/34.92	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.83/34.92	   new_primMinusNatS1 -> Zero
67.83/34.92	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.83/34.92	   new_primEqInt1 -> True
67.83/34.92	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.83/34.92	   new_primEqInt0(vuz3260) -> False
67.83/34.92	   new_primEqInt(vuz3250) -> False
67.83/34.92	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.83/34.92	
67.83/34.92	The set Q consists of the following terms:
67.83/34.92	
67.83/34.92	   new_rem(Neg(x0), Neg(Zero))
67.83/34.92	   new_primEqInt1
67.83/34.92	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.83/34.92	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.83/34.92	   new_primMinusNatS1
67.83/34.92	   new_rem(Neg(x0), Neg(Succ(x1)))
67.83/34.92	   new_primMinusNatS2(Succ(x0), Zero)
67.83/34.92	   new_primModNatS1(Succ(Zero), Succ(x0))
67.83/34.92	   new_primMinusNatS2(Zero, Zero)
67.83/34.92	   new_error
67.83/34.92	   new_primModNatS1(Succ(Zero), Zero)
67.83/34.92	   new_rem(Pos(x0), Pos(Zero))
67.83/34.92	   new_primModNatS01(x0, x1, Zero, Zero)
67.83/34.92	   new_primEqInt0(x0)
67.83/34.92	   new_esEs(Pos(Zero))
67.83/34.92	   new_esEs(Pos(Succ(x0)))
67.83/34.92	   new_rem(Pos(x0), Pos(Succ(x1)))
67.83/34.92	   new_primModNatS02(x0, x1)
67.83/34.92	   new_primMinusNatS2(Zero, Succ(x0))
67.83/34.92	   new_rem(Pos(x0), Neg(Succ(x1)))
67.83/34.92	   new_rem(Neg(x0), Pos(Succ(x1)))
67.83/34.92	   new_primModNatS1(Zero, x0)
67.83/34.92	   new_primEqInt(x0)
67.83/34.92	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.83/34.92	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.83/34.92	   new_rem(Pos(x0), Neg(Zero))
67.83/34.92	   new_rem(Neg(x0), Pos(Zero))
67.83/34.92	   new_primMinusNatS0(x0)
67.83/34.92	   new_primEqInt2
67.83/34.92	   new_esEs(Neg(Zero))
67.83/34.92	   new_esEs(Neg(Succ(x0)))
67.83/34.92	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.83/34.92	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.83/34.92	
67.83/34.92	We have to consider all minimal (P,Q,R)-chains.
67.83/34.92	----------------------------------------
67.83/34.92	
67.83/34.92	(404) TransformationProof (EQUIVALENT)
67.83/34.92	By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Zero, Zero), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]:
67.83/34.92	
67.83/34.92	   (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Zero, Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Zero, Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))))
67.83/34.92	
67.83/34.92	
67.83/34.92	----------------------------------------
67.83/34.92	
67.83/34.92	(405)
67.83/34.92	Obligation:
67.83/34.92	Q DP problem:
67.83/34.92	The TRS P consists of the following rules:
67.83/34.92	
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.83/34.92	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.83/34.92	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0))))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, Zero, x0, Zero))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Pos(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Succ(x2), Zero), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Zero, Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.92	
67.83/34.92	The TRS R consists of the following rules:
67.83/34.92	
67.83/34.92	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.83/34.92	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.83/34.92	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.83/34.92	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.83/34.92	   new_primMinusNatS2(Zero, Zero) -> Zero
67.83/34.92	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.83/34.92	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.83/34.92	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.83/34.92	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.83/34.92	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.83/34.92	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.83/34.92	   new_primModNatS1(Zero, vuz54200) -> Zero
67.83/34.92	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.83/34.92	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.83/34.92	   new_error -> error([])
67.83/34.92	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.83/34.92	   new_primEqInt2 -> True
67.83/34.92	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.83/34.92	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.83/34.92	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.83/34.92	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.83/34.92	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.83/34.92	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.83/34.92	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.83/34.92	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.83/34.92	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.83/34.92	   new_primMinusNatS1 -> Zero
67.83/34.92	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.83/34.92	   new_primEqInt1 -> True
67.83/34.92	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.83/34.92	   new_primEqInt0(vuz3260) -> False
67.83/34.92	   new_primEqInt(vuz3250) -> False
67.83/34.92	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.83/34.92	
67.83/34.92	The set Q consists of the following terms:
67.83/34.92	
67.83/34.92	   new_rem(Neg(x0), Neg(Zero))
67.83/34.92	   new_primEqInt1
67.83/34.92	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.83/34.92	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.83/34.92	   new_primMinusNatS1
67.83/34.92	   new_rem(Neg(x0), Neg(Succ(x1)))
67.83/34.92	   new_primMinusNatS2(Succ(x0), Zero)
67.83/34.92	   new_primModNatS1(Succ(Zero), Succ(x0))
67.83/34.92	   new_primMinusNatS2(Zero, Zero)
67.83/34.92	   new_error
67.83/34.92	   new_primModNatS1(Succ(Zero), Zero)
67.83/34.92	   new_rem(Pos(x0), Pos(Zero))
67.83/34.92	   new_primModNatS01(x0, x1, Zero, Zero)
67.83/34.92	   new_primEqInt0(x0)
67.83/34.92	   new_esEs(Pos(Zero))
67.83/34.92	   new_esEs(Pos(Succ(x0)))
67.83/34.92	   new_rem(Pos(x0), Pos(Succ(x1)))
67.83/34.92	   new_primModNatS02(x0, x1)
67.83/34.92	   new_primMinusNatS2(Zero, Succ(x0))
67.83/34.92	   new_rem(Pos(x0), Neg(Succ(x1)))
67.83/34.92	   new_rem(Neg(x0), Pos(Succ(x1)))
67.83/34.92	   new_primModNatS1(Zero, x0)
67.83/34.92	   new_primEqInt(x0)
67.83/34.92	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.83/34.92	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.83/34.92	   new_rem(Pos(x0), Neg(Zero))
67.83/34.92	   new_rem(Neg(x0), Pos(Zero))
67.83/34.92	   new_primMinusNatS0(x0)
67.83/34.92	   new_primEqInt2
67.83/34.92	   new_esEs(Neg(Zero))
67.83/34.92	   new_esEs(Neg(Succ(x0)))
67.83/34.92	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.83/34.92	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.83/34.92	
67.83/34.92	We have to consider all minimal (P,Q,R)-chains.
67.83/34.92	----------------------------------------
67.83/34.92	
67.83/34.92	(406) TransformationProof (EQUIVALENT)
67.83/34.92	By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS2(Succ(x2), Zero), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]:
67.83/34.92	
67.83/34.92	   (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))))
67.83/34.92	
67.83/34.92	
67.83/34.92	----------------------------------------
67.83/34.92	
67.83/34.92	(407)
67.83/34.92	Obligation:
67.83/34.92	Q DP problem:
67.83/34.92	The TRS P consists of the following rules:
67.83/34.92	
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.83/34.92	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.83/34.92	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0))))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, Zero, x0, Zero))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Pos(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Zero, Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.92	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.92	
67.83/34.92	The TRS R consists of the following rules:
67.83/34.92	
67.83/34.92	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.83/34.93	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.83/34.93	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.83/34.93	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.83/34.93	   new_primMinusNatS2(Zero, Zero) -> Zero
67.83/34.93	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.83/34.93	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.83/34.93	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.83/34.93	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.83/34.93	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.83/34.93	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.83/34.93	   new_primModNatS1(Zero, vuz54200) -> Zero
67.83/34.93	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.83/34.93	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.83/34.93	   new_error -> error([])
67.83/34.93	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.83/34.93	   new_primEqInt2 -> True
67.83/34.93	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.83/34.93	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.83/34.93	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.83/34.93	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.83/34.93	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.83/34.93	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.83/34.93	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.83/34.93	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.83/34.93	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.83/34.93	   new_primMinusNatS1 -> Zero
67.83/34.93	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.83/34.93	   new_primEqInt1 -> True
67.83/34.93	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.83/34.93	   new_primEqInt0(vuz3260) -> False
67.83/34.93	   new_primEqInt(vuz3250) -> False
67.83/34.93	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.83/34.93	
67.83/34.93	The set Q consists of the following terms:
67.83/34.93	
67.83/34.93	   new_rem(Neg(x0), Neg(Zero))
67.83/34.93	   new_primEqInt1
67.83/34.93	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.83/34.93	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.83/34.93	   new_primMinusNatS1
67.83/34.93	   new_rem(Neg(x0), Neg(Succ(x1)))
67.83/34.93	   new_primMinusNatS2(Succ(x0), Zero)
67.83/34.93	   new_primModNatS1(Succ(Zero), Succ(x0))
67.83/34.93	   new_primMinusNatS2(Zero, Zero)
67.83/34.93	   new_error
67.83/34.93	   new_primModNatS1(Succ(Zero), Zero)
67.83/34.93	   new_rem(Pos(x0), Pos(Zero))
67.83/34.93	   new_primModNatS01(x0, x1, Zero, Zero)
67.83/34.93	   new_primEqInt0(x0)
67.83/34.93	   new_esEs(Pos(Zero))
67.83/34.93	   new_esEs(Pos(Succ(x0)))
67.83/34.93	   new_rem(Pos(x0), Pos(Succ(x1)))
67.83/34.93	   new_primModNatS02(x0, x1)
67.83/34.93	   new_primMinusNatS2(Zero, Succ(x0))
67.83/34.93	   new_rem(Pos(x0), Neg(Succ(x1)))
67.83/34.93	   new_rem(Neg(x0), Pos(Succ(x1)))
67.83/34.93	   new_primModNatS1(Zero, x0)
67.83/34.93	   new_primEqInt(x0)
67.83/34.93	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.83/34.93	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.83/34.93	   new_rem(Pos(x0), Neg(Zero))
67.83/34.93	   new_rem(Neg(x0), Pos(Zero))
67.83/34.93	   new_primMinusNatS0(x0)
67.83/34.93	   new_primEqInt2
67.83/34.93	   new_esEs(Neg(Zero))
67.83/34.93	   new_esEs(Neg(Succ(x0)))
67.83/34.93	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.83/34.93	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.83/34.93	
67.83/34.93	We have to consider all minimal (P,Q,R)-chains.
67.83/34.93	----------------------------------------
67.83/34.93	
67.83/34.93	(408) TransformationProof (EQUIVALENT)
67.83/34.93	By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Zero, Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) at position [0,0,0] we obtained the following new rules [LPAR04]:
67.83/34.93	
67.83/34.93	   (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Neg(Zero)), Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))),new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Neg(Zero)), Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))))
67.83/34.93	
67.83/34.93	
67.83/34.93	----------------------------------------
67.83/34.93	
67.83/34.93	(409)
67.83/34.93	Obligation:
67.83/34.93	Q DP problem:
67.83/34.93	The TRS P consists of the following rules:
67.83/34.93	
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.83/34.93	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.83/34.93	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0))))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0))))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, Zero, x0, Zero))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Pos(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Neg(Zero)), Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.93	
67.83/34.93	The TRS R consists of the following rules:
67.83/34.93	
67.83/34.93	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.83/34.93	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.83/34.93	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.83/34.93	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.83/34.93	   new_primMinusNatS2(Zero, Zero) -> Zero
67.83/34.93	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.83/34.93	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.83/34.93	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.83/34.93	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.83/34.93	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.83/34.93	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.83/34.93	   new_primModNatS1(Zero, vuz54200) -> Zero
67.83/34.93	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.83/34.93	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.83/34.93	   new_error -> error([])
67.83/34.93	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.83/34.93	   new_primEqInt2 -> True
67.83/34.93	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.83/34.93	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.83/34.93	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.83/34.93	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.83/34.93	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.83/34.93	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.83/34.93	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.83/34.93	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.83/34.93	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.83/34.93	   new_primMinusNatS1 -> Zero
67.83/34.93	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.83/34.93	   new_primEqInt1 -> True
67.83/34.93	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.83/34.93	   new_primEqInt0(vuz3260) -> False
67.83/34.93	   new_primEqInt(vuz3250) -> False
67.83/34.93	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.83/34.93	
67.83/34.93	The set Q consists of the following terms:
67.83/34.93	
67.83/34.93	   new_rem(Neg(x0), Neg(Zero))
67.83/34.93	   new_primEqInt1
67.83/34.93	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.83/34.93	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.83/34.93	   new_primMinusNatS1
67.83/34.93	   new_rem(Neg(x0), Neg(Succ(x1)))
67.83/34.93	   new_primMinusNatS2(Succ(x0), Zero)
67.83/34.93	   new_primModNatS1(Succ(Zero), Succ(x0))
67.83/34.93	   new_primMinusNatS2(Zero, Zero)
67.83/34.93	   new_error
67.83/34.93	   new_primModNatS1(Succ(Zero), Zero)
67.83/34.93	   new_rem(Pos(x0), Pos(Zero))
67.83/34.93	   new_primModNatS01(x0, x1, Zero, Zero)
67.83/34.93	   new_primEqInt0(x0)
67.83/34.93	   new_esEs(Pos(Zero))
67.83/34.93	   new_esEs(Pos(Succ(x0)))
67.83/34.93	   new_rem(Pos(x0), Pos(Succ(x1)))
67.83/34.93	   new_primModNatS02(x0, x1)
67.83/34.93	   new_primMinusNatS2(Zero, Succ(x0))
67.83/34.93	   new_rem(Pos(x0), Neg(Succ(x1)))
67.83/34.93	   new_rem(Neg(x0), Pos(Succ(x1)))
67.83/34.93	   new_primModNatS1(Zero, x0)
67.83/34.93	   new_primEqInt(x0)
67.83/34.93	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.83/34.93	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.83/34.93	   new_rem(Pos(x0), Neg(Zero))
67.83/34.93	   new_rem(Neg(x0), Pos(Zero))
67.83/34.93	   new_primMinusNatS0(x0)
67.83/34.93	   new_primEqInt2
67.83/34.93	   new_esEs(Neg(Zero))
67.83/34.93	   new_esEs(Neg(Succ(x0)))
67.83/34.93	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.83/34.93	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.83/34.93	
67.83/34.93	We have to consider all minimal (P,Q,R)-chains.
67.83/34.93	----------------------------------------
67.83/34.93	
67.83/34.93	(410) DependencyGraphProof (EQUIVALENT)
67.83/34.93	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
67.83/34.93	----------------------------------------
67.83/34.93	
67.83/34.93	(411)
67.83/34.93	Obligation:
67.83/34.93	Q DP problem:
67.83/34.93	The TRS P consists of the following rules:
67.83/34.93	
67.83/34.93	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.83/34.93	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2)))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0))))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0))))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, Zero, x0, Zero))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Pos(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.93	
67.83/34.93	The TRS R consists of the following rules:
67.83/34.93	
67.83/34.93	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.83/34.93	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.83/34.93	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.83/34.93	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.83/34.93	   new_primMinusNatS2(Zero, Zero) -> Zero
67.83/34.93	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.83/34.93	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.83/34.93	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.83/34.93	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.83/34.93	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.83/34.93	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.83/34.93	   new_primModNatS1(Zero, vuz54200) -> Zero
67.83/34.93	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.83/34.93	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.83/34.93	   new_error -> error([])
67.83/34.93	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.83/34.93	   new_primEqInt2 -> True
67.83/34.93	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.83/34.93	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.83/34.93	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.83/34.93	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.83/34.93	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.83/34.93	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.83/34.93	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.83/34.93	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.83/34.93	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.83/34.93	   new_primMinusNatS1 -> Zero
67.83/34.93	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.83/34.93	   new_primEqInt1 -> True
67.83/34.93	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.83/34.93	   new_primEqInt0(vuz3260) -> False
67.83/34.93	   new_primEqInt(vuz3250) -> False
67.83/34.93	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.83/34.93	
67.83/34.93	The set Q consists of the following terms:
67.83/34.93	
67.83/34.93	   new_rem(Neg(x0), Neg(Zero))
67.83/34.93	   new_primEqInt1
67.83/34.93	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.83/34.93	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.83/34.93	   new_primMinusNatS1
67.83/34.93	   new_rem(Neg(x0), Neg(Succ(x1)))
67.83/34.93	   new_primMinusNatS2(Succ(x0), Zero)
67.83/34.93	   new_primModNatS1(Succ(Zero), Succ(x0))
67.83/34.93	   new_primMinusNatS2(Zero, Zero)
67.83/34.93	   new_error
67.83/34.93	   new_primModNatS1(Succ(Zero), Zero)
67.83/34.93	   new_rem(Pos(x0), Pos(Zero))
67.83/34.93	   new_primModNatS01(x0, x1, Zero, Zero)
67.83/34.93	   new_primEqInt0(x0)
67.83/34.93	   new_esEs(Pos(Zero))
67.83/34.93	   new_esEs(Pos(Succ(x0)))
67.83/34.93	   new_rem(Pos(x0), Pos(Succ(x1)))
67.83/34.93	   new_primModNatS02(x0, x1)
67.83/34.93	   new_primMinusNatS2(Zero, Succ(x0))
67.83/34.93	   new_rem(Pos(x0), Neg(Succ(x1)))
67.83/34.93	   new_rem(Neg(x0), Pos(Succ(x1)))
67.83/34.93	   new_primModNatS1(Zero, x0)
67.83/34.93	   new_primEqInt(x0)
67.83/34.93	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.83/34.93	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.83/34.93	   new_rem(Pos(x0), Neg(Zero))
67.83/34.93	   new_rem(Neg(x0), Pos(Zero))
67.83/34.93	   new_primMinusNatS0(x0)
67.83/34.93	   new_primEqInt2
67.83/34.93	   new_esEs(Neg(Zero))
67.83/34.93	   new_esEs(Neg(Succ(x0)))
67.83/34.93	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.83/34.93	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.83/34.93	
67.83/34.93	We have to consider all minimal (P,Q,R)-chains.
67.83/34.93	----------------------------------------
67.83/34.93	
67.83/34.93	(412) TransformationProof (EQUIVALENT)
67.83/34.93	By narrowing [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Zero)))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x2))))) at position [0] we obtained the following new rules [LPAR04]:
67.83/34.93	
67.83/34.93	   (new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Neg(Succ(Zero))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))),new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Neg(Succ(Zero))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))))
67.83/34.93	   (new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, Zero, x0, Zero))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0)))))),new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, Zero, x0, Zero))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0)))))))
67.83/34.93	
67.83/34.93	
67.83/34.93	----------------------------------------
67.83/34.93	
67.83/34.93	(413)
67.83/34.93	Obligation:
67.83/34.93	Q DP problem:
67.83/34.93	The TRS P consists of the following rules:
67.83/34.93	
67.83/34.93	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.83/34.93	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0))))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0))))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, Zero, x0, Zero))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Pos(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Neg(Succ(Zero))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, Zero, x0, Zero))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0))))))
67.83/34.93	
67.83/34.93	The TRS R consists of the following rules:
67.83/34.93	
67.83/34.93	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.83/34.93	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.83/34.93	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.83/34.93	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.83/34.93	   new_primMinusNatS2(Zero, Zero) -> Zero
67.83/34.93	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.83/34.93	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.83/34.93	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.83/34.93	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.83/34.93	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.83/34.93	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.83/34.93	   new_primModNatS1(Zero, vuz54200) -> Zero
67.83/34.93	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.83/34.93	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.83/34.93	   new_error -> error([])
67.83/34.93	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.83/34.93	   new_primEqInt2 -> True
67.83/34.93	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.83/34.93	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.83/34.93	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.83/34.93	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.83/34.93	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.83/34.93	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.83/34.93	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.83/34.93	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.83/34.93	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.83/34.93	   new_primMinusNatS1 -> Zero
67.83/34.93	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.83/34.93	   new_primEqInt1 -> True
67.83/34.93	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.83/34.93	   new_primEqInt0(vuz3260) -> False
67.83/34.93	   new_primEqInt(vuz3250) -> False
67.83/34.93	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.83/34.93	
67.83/34.93	The set Q consists of the following terms:
67.83/34.93	
67.83/34.93	   new_rem(Neg(x0), Neg(Zero))
67.83/34.93	   new_primEqInt1
67.83/34.93	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.83/34.93	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.83/34.93	   new_primMinusNatS1
67.83/34.93	   new_rem(Neg(x0), Neg(Succ(x1)))
67.83/34.93	   new_primMinusNatS2(Succ(x0), Zero)
67.83/34.93	   new_primModNatS1(Succ(Zero), Succ(x0))
67.83/34.93	   new_primMinusNatS2(Zero, Zero)
67.83/34.93	   new_error
67.83/34.93	   new_primModNatS1(Succ(Zero), Zero)
67.83/34.93	   new_rem(Pos(x0), Pos(Zero))
67.83/34.93	   new_primModNatS01(x0, x1, Zero, Zero)
67.83/34.93	   new_primEqInt0(x0)
67.83/34.93	   new_esEs(Pos(Zero))
67.83/34.93	   new_esEs(Pos(Succ(x0)))
67.83/34.93	   new_rem(Pos(x0), Pos(Succ(x1)))
67.83/34.93	   new_primModNatS02(x0, x1)
67.83/34.93	   new_primMinusNatS2(Zero, Succ(x0))
67.83/34.93	   new_rem(Pos(x0), Neg(Succ(x1)))
67.83/34.93	   new_rem(Neg(x0), Pos(Succ(x1)))
67.83/34.93	   new_primModNatS1(Zero, x0)
67.83/34.93	   new_primEqInt(x0)
67.83/34.93	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.83/34.93	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.83/34.93	   new_rem(Pos(x0), Neg(Zero))
67.83/34.93	   new_rem(Neg(x0), Pos(Zero))
67.83/34.93	   new_primMinusNatS0(x0)
67.83/34.93	   new_primEqInt2
67.83/34.93	   new_esEs(Neg(Zero))
67.83/34.93	   new_esEs(Neg(Succ(x0)))
67.83/34.93	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.83/34.93	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.83/34.93	
67.83/34.93	We have to consider all minimal (P,Q,R)-chains.
67.83/34.93	----------------------------------------
67.83/34.93	
67.83/34.93	(414) TransformationProof (EQUIVALENT)
67.83/34.93	By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Neg(Succ(Zero))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) at position [0] we obtained the following new rules [LPAR04]:
67.83/34.93	
67.83/34.93	   (new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_primEqInt0(Zero), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))),new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_primEqInt0(Zero), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))))
67.83/34.93	
67.83/34.93	
67.83/34.93	----------------------------------------
67.83/34.93	
67.83/34.93	(415)
67.83/34.93	Obligation:
67.83/34.93	Q DP problem:
67.83/34.93	The TRS P consists of the following rules:
67.83/34.93	
67.83/34.93	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.83/34.93	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0))))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0))))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, Zero, x0, Zero))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Pos(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, Zero, x0, Zero))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0))))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_primEqInt0(Zero), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.93	
67.83/34.93	The TRS R consists of the following rules:
67.83/34.93	
67.83/34.93	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.83/34.93	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.83/34.93	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.83/34.93	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.83/34.93	   new_primMinusNatS2(Zero, Zero) -> Zero
67.83/34.93	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.83/34.93	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.83/34.93	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.83/34.93	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.83/34.93	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.83/34.93	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.83/34.93	   new_primModNatS1(Zero, vuz54200) -> Zero
67.83/34.93	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.83/34.93	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.83/34.93	   new_error -> error([])
67.83/34.93	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.83/34.93	   new_primEqInt2 -> True
67.83/34.93	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.83/34.93	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.83/34.93	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.83/34.93	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.83/34.93	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.83/34.93	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.83/34.93	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.83/34.93	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.83/34.93	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.83/34.93	   new_primMinusNatS1 -> Zero
67.83/34.93	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.83/34.93	   new_primEqInt1 -> True
67.83/34.93	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.83/34.93	   new_primEqInt0(vuz3260) -> False
67.83/34.93	   new_primEqInt(vuz3250) -> False
67.83/34.93	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.83/34.93	
67.83/34.93	The set Q consists of the following terms:
67.83/34.93	
67.83/34.93	   new_rem(Neg(x0), Neg(Zero))
67.83/34.93	   new_primEqInt1
67.83/34.93	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.83/34.93	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.83/34.93	   new_primMinusNatS1
67.83/34.93	   new_rem(Neg(x0), Neg(Succ(x1)))
67.83/34.93	   new_primMinusNatS2(Succ(x0), Zero)
67.83/34.93	   new_primModNatS1(Succ(Zero), Succ(x0))
67.83/34.93	   new_primMinusNatS2(Zero, Zero)
67.83/34.93	   new_error
67.83/34.93	   new_primModNatS1(Succ(Zero), Zero)
67.83/34.93	   new_rem(Pos(x0), Pos(Zero))
67.83/34.93	   new_primModNatS01(x0, x1, Zero, Zero)
67.83/34.93	   new_primEqInt0(x0)
67.83/34.93	   new_esEs(Pos(Zero))
67.83/34.93	   new_esEs(Pos(Succ(x0)))
67.83/34.93	   new_rem(Pos(x0), Pos(Succ(x1)))
67.83/34.93	   new_primModNatS02(x0, x1)
67.83/34.93	   new_primMinusNatS2(Zero, Succ(x0))
67.83/34.93	   new_rem(Pos(x0), Neg(Succ(x1)))
67.83/34.93	   new_rem(Neg(x0), Pos(Succ(x1)))
67.83/34.93	   new_primModNatS1(Zero, x0)
67.83/34.93	   new_primEqInt(x0)
67.83/34.93	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.83/34.93	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.83/34.93	   new_rem(Pos(x0), Neg(Zero))
67.83/34.93	   new_rem(Neg(x0), Pos(Zero))
67.83/34.93	   new_primMinusNatS0(x0)
67.83/34.93	   new_primEqInt2
67.83/34.93	   new_esEs(Neg(Zero))
67.83/34.93	   new_esEs(Neg(Succ(x0)))
67.83/34.93	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.83/34.93	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.83/34.93	
67.83/34.93	We have to consider all minimal (P,Q,R)-chains.
67.83/34.93	----------------------------------------
67.83/34.93	
67.83/34.93	(416) TransformationProof (EQUIVALENT)
67.83/34.93	By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_primEqInt0(Zero), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) at position [0] we obtained the following new rules [LPAR04]:
67.83/34.93	
67.83/34.93	   (new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))),new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))))
67.83/34.93	
67.83/34.93	
67.83/34.93	----------------------------------------
67.83/34.93	
67.83/34.93	(417)
67.83/34.93	Obligation:
67.83/34.93	Q DP problem:
67.83/34.93	The TRS P consists of the following rules:
67.83/34.93	
67.83/34.93	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.83/34.93	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0)))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0))))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0))))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, Zero, x0, Zero))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Pos(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, Zero, x0, Zero))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0))))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.93	
67.83/34.93	The TRS R consists of the following rules:
67.83/34.93	
67.83/34.93	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.83/34.93	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.83/34.93	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.83/34.93	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.83/34.93	   new_primMinusNatS2(Zero, Zero) -> Zero
67.83/34.93	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.83/34.93	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.83/34.93	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.83/34.93	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.83/34.93	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.83/34.93	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.83/34.93	   new_primModNatS1(Zero, vuz54200) -> Zero
67.83/34.93	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.83/34.93	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.83/34.93	   new_error -> error([])
67.83/34.93	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.83/34.93	   new_primEqInt2 -> True
67.83/34.93	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.83/34.93	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.83/34.93	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.83/34.93	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.83/34.93	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.83/34.93	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.83/34.93	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.83/34.93	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.83/34.93	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.83/34.93	   new_primMinusNatS1 -> Zero
67.83/34.93	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.83/34.93	   new_primEqInt1 -> True
67.83/34.93	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.83/34.93	   new_primEqInt0(vuz3260) -> False
67.83/34.93	   new_primEqInt(vuz3250) -> False
67.83/34.93	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.83/34.93	
67.83/34.93	The set Q consists of the following terms:
67.83/34.93	
67.83/34.93	   new_rem(Neg(x0), Neg(Zero))
67.83/34.93	   new_primEqInt1
67.83/34.93	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.83/34.93	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.83/34.93	   new_primMinusNatS1
67.83/34.93	   new_rem(Neg(x0), Neg(Succ(x1)))
67.83/34.93	   new_primMinusNatS2(Succ(x0), Zero)
67.83/34.93	   new_primModNatS1(Succ(Zero), Succ(x0))
67.83/34.93	   new_primMinusNatS2(Zero, Zero)
67.83/34.93	   new_error
67.83/34.93	   new_primModNatS1(Succ(Zero), Zero)
67.83/34.93	   new_rem(Pos(x0), Pos(Zero))
67.83/34.93	   new_primModNatS01(x0, x1, Zero, Zero)
67.83/34.93	   new_primEqInt0(x0)
67.83/34.93	   new_esEs(Pos(Zero))
67.83/34.93	   new_esEs(Pos(Succ(x0)))
67.83/34.93	   new_rem(Pos(x0), Pos(Succ(x1)))
67.83/34.93	   new_primModNatS02(x0, x1)
67.83/34.93	   new_primMinusNatS2(Zero, Succ(x0))
67.83/34.93	   new_rem(Pos(x0), Neg(Succ(x1)))
67.83/34.93	   new_rem(Neg(x0), Pos(Succ(x1)))
67.83/34.93	   new_primModNatS1(Zero, x0)
67.83/34.93	   new_primEqInt(x0)
67.83/34.93	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.83/34.93	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.83/34.93	   new_rem(Pos(x0), Neg(Zero))
67.83/34.93	   new_rem(Neg(x0), Pos(Zero))
67.83/34.93	   new_primMinusNatS0(x0)
67.83/34.93	   new_primEqInt2
67.83/34.93	   new_esEs(Neg(Zero))
67.83/34.93	   new_esEs(Neg(Succ(x0)))
67.83/34.93	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.83/34.93	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.83/34.93	
67.83/34.93	We have to consider all minimal (P,Q,R)-chains.
67.83/34.93	----------------------------------------
67.83/34.93	
67.83/34.93	(418) TransformationProof (EQUIVALENT)
67.83/34.93	By narrowing [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(x0))))) at position [0] we obtained the following new rules [LPAR04]:
67.83/34.93	
67.83/34.93	   (new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS0(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0)))))),new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS0(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0)))))))
67.83/34.93	   (new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS1, Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(Zero))))),new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS1, Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(Zero))))))
67.83/34.93	
67.83/34.93	
67.83/34.93	----------------------------------------
67.83/34.93	
67.83/34.93	(419)
67.83/34.93	Obligation:
67.83/34.93	Q DP problem:
67.83/34.93	The TRS P consists of the following rules:
67.83/34.93	
67.83/34.93	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.83/34.93	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0))))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0))))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, Zero, x0, Zero))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Pos(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, Zero, x0, Zero))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0))))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS0(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0))))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS1, Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.93	
67.83/34.93	The TRS R consists of the following rules:
67.83/34.93	
67.83/34.93	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.83/34.93	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.83/34.93	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.83/34.93	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.83/34.93	   new_primMinusNatS2(Zero, Zero) -> Zero
67.83/34.93	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.83/34.93	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.83/34.93	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.83/34.93	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.83/34.93	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.83/34.93	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.83/34.93	   new_primModNatS1(Zero, vuz54200) -> Zero
67.83/34.93	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.83/34.93	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.83/34.93	   new_error -> error([])
67.83/34.93	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.83/34.93	   new_primEqInt2 -> True
67.83/34.93	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.83/34.93	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.83/34.93	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.83/34.93	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.83/34.93	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.83/34.93	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.83/34.93	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.83/34.93	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.83/34.93	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.83/34.93	   new_primMinusNatS1 -> Zero
67.83/34.93	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.83/34.93	   new_primEqInt1 -> True
67.83/34.93	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.83/34.93	   new_primEqInt0(vuz3260) -> False
67.83/34.93	   new_primEqInt(vuz3250) -> False
67.83/34.93	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.83/34.93	
67.83/34.93	The set Q consists of the following terms:
67.83/34.93	
67.83/34.93	   new_rem(Neg(x0), Neg(Zero))
67.83/34.93	   new_primEqInt1
67.83/34.93	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.83/34.93	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.83/34.93	   new_primMinusNatS1
67.83/34.93	   new_rem(Neg(x0), Neg(Succ(x1)))
67.83/34.93	   new_primMinusNatS2(Succ(x0), Zero)
67.83/34.93	   new_primModNatS1(Succ(Zero), Succ(x0))
67.83/34.93	   new_primMinusNatS2(Zero, Zero)
67.83/34.93	   new_error
67.83/34.93	   new_primModNatS1(Succ(Zero), Zero)
67.83/34.93	   new_rem(Pos(x0), Pos(Zero))
67.83/34.93	   new_primModNatS01(x0, x1, Zero, Zero)
67.83/34.93	   new_primEqInt0(x0)
67.83/34.93	   new_esEs(Pos(Zero))
67.83/34.93	   new_esEs(Pos(Succ(x0)))
67.83/34.93	   new_rem(Pos(x0), Pos(Succ(x1)))
67.83/34.93	   new_primModNatS02(x0, x1)
67.83/34.93	   new_primMinusNatS2(Zero, Succ(x0))
67.83/34.93	   new_rem(Pos(x0), Neg(Succ(x1)))
67.83/34.93	   new_rem(Neg(x0), Pos(Succ(x1)))
67.83/34.93	   new_primModNatS1(Zero, x0)
67.83/34.93	   new_primEqInt(x0)
67.83/34.93	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.83/34.93	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.83/34.93	   new_rem(Pos(x0), Neg(Zero))
67.83/34.93	   new_rem(Neg(x0), Pos(Zero))
67.83/34.93	   new_primMinusNatS0(x0)
67.83/34.93	   new_primEqInt2
67.83/34.93	   new_esEs(Neg(Zero))
67.83/34.93	   new_esEs(Neg(Succ(x0)))
67.83/34.93	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.83/34.93	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.83/34.93	
67.83/34.93	We have to consider all minimal (P,Q,R)-chains.
67.83/34.93	----------------------------------------
67.83/34.93	
67.83/34.93	(420) TransformationProof (EQUIVALENT)
67.83/34.93	By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS0(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0)))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]:
67.83/34.93	
67.83/34.93	   (new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0)))))),new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0)))))))
67.83/34.93	
67.83/34.93	
67.83/34.93	----------------------------------------
67.83/34.93	
67.83/34.93	(421)
67.83/34.93	Obligation:
67.83/34.93	Q DP problem:
67.83/34.93	The TRS P consists of the following rules:
67.83/34.93	
67.83/34.93	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.83/34.93	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0))))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0))))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, Zero, x0, Zero))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Pos(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, Zero, x0, Zero))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0))))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS1, Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0))))))
67.83/34.93	
67.83/34.93	The TRS R consists of the following rules:
67.83/34.93	
67.83/34.93	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.83/34.93	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.83/34.93	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.83/34.93	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.83/34.93	   new_primMinusNatS2(Zero, Zero) -> Zero
67.83/34.93	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.83/34.93	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.83/34.93	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.83/34.93	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.83/34.93	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.83/34.93	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.83/34.93	   new_primModNatS1(Zero, vuz54200) -> Zero
67.83/34.93	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.83/34.93	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.83/34.93	   new_error -> error([])
67.83/34.93	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.83/34.93	   new_primEqInt2 -> True
67.83/34.93	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.83/34.93	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.83/34.93	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.83/34.93	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.83/34.93	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.83/34.93	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.83/34.93	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.83/34.93	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.83/34.93	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.83/34.93	   new_primMinusNatS1 -> Zero
67.83/34.93	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.83/34.93	   new_primEqInt1 -> True
67.83/34.93	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.83/34.93	   new_primEqInt0(vuz3260) -> False
67.83/34.93	   new_primEqInt(vuz3250) -> False
67.83/34.93	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.83/34.93	
67.83/34.93	The set Q consists of the following terms:
67.83/34.93	
67.83/34.93	   new_rem(Neg(x0), Neg(Zero))
67.83/34.93	   new_primEqInt1
67.83/34.93	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.83/34.93	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.83/34.93	   new_primMinusNatS1
67.83/34.93	   new_rem(Neg(x0), Neg(Succ(x1)))
67.83/34.93	   new_primMinusNatS2(Succ(x0), Zero)
67.83/34.93	   new_primModNatS1(Succ(Zero), Succ(x0))
67.83/34.93	   new_primMinusNatS2(Zero, Zero)
67.83/34.93	   new_error
67.83/34.93	   new_primModNatS1(Succ(Zero), Zero)
67.83/34.93	   new_rem(Pos(x0), Pos(Zero))
67.83/34.93	   new_primModNatS01(x0, x1, Zero, Zero)
67.83/34.93	   new_primEqInt0(x0)
67.83/34.93	   new_esEs(Pos(Zero))
67.83/34.93	   new_esEs(Pos(Succ(x0)))
67.83/34.93	   new_rem(Pos(x0), Pos(Succ(x1)))
67.83/34.93	   new_primModNatS02(x0, x1)
67.83/34.93	   new_primMinusNatS2(Zero, Succ(x0))
67.83/34.93	   new_rem(Pos(x0), Neg(Succ(x1)))
67.83/34.93	   new_rem(Neg(x0), Pos(Succ(x1)))
67.83/34.93	   new_primModNatS1(Zero, x0)
67.83/34.93	   new_primEqInt(x0)
67.83/34.93	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.83/34.93	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.83/34.93	   new_rem(Pos(x0), Neg(Zero))
67.83/34.93	   new_rem(Neg(x0), Pos(Zero))
67.83/34.93	   new_primMinusNatS0(x0)
67.83/34.93	   new_primEqInt2
67.83/34.93	   new_esEs(Neg(Zero))
67.83/34.93	   new_esEs(Neg(Succ(x0)))
67.83/34.93	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.83/34.93	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.83/34.93	
67.83/34.93	We have to consider all minimal (P,Q,R)-chains.
67.83/34.93	----------------------------------------
67.83/34.93	
67.83/34.93	(422) TransformationProof (EQUIVALENT)
67.83/34.93	By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(new_primMinusNatS1, Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(Zero))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]:
67.83/34.93	
67.83/34.93	   (new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Zero, Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(Zero))))),new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Zero, Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(Zero))))))
67.83/34.93	
67.83/34.93	
67.83/34.93	----------------------------------------
67.83/34.93	
67.83/34.93	(423)
67.83/34.93	Obligation:
67.83/34.93	Q DP problem:
67.83/34.93	The TRS P consists of the following rules:
67.83/34.93	
67.83/34.93	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.83/34.93	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0))))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0))))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, Zero, x0, Zero))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Pos(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, Zero, x0, Zero))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0))))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0))))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Zero, Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.93	
67.83/34.93	The TRS R consists of the following rules:
67.83/34.93	
67.83/34.93	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.83/34.93	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.83/34.93	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.83/34.93	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.83/34.93	   new_primMinusNatS2(Zero, Zero) -> Zero
67.83/34.93	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.83/34.93	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.83/34.93	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.83/34.93	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.83/34.93	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.83/34.93	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.83/34.93	   new_primModNatS1(Zero, vuz54200) -> Zero
67.83/34.93	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.83/34.93	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.83/34.93	   new_error -> error([])
67.83/34.93	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.83/34.93	   new_primEqInt2 -> True
67.83/34.93	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.83/34.93	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.83/34.93	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.83/34.93	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.83/34.93	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.83/34.93	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.83/34.93	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.83/34.93	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.83/34.93	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.83/34.93	   new_primMinusNatS1 -> Zero
67.83/34.93	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.83/34.93	   new_primEqInt1 -> True
67.83/34.93	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.83/34.93	   new_primEqInt0(vuz3260) -> False
67.83/34.93	   new_primEqInt(vuz3250) -> False
67.83/34.93	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.83/34.93	
67.83/34.93	The set Q consists of the following terms:
67.83/34.93	
67.83/34.93	   new_rem(Neg(x0), Neg(Zero))
67.83/34.93	   new_primEqInt1
67.83/34.93	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.83/34.93	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.83/34.93	   new_primMinusNatS1
67.83/34.93	   new_rem(Neg(x0), Neg(Succ(x1)))
67.83/34.93	   new_primMinusNatS2(Succ(x0), Zero)
67.83/34.93	   new_primModNatS1(Succ(Zero), Succ(x0))
67.83/34.93	   new_primMinusNatS2(Zero, Zero)
67.83/34.93	   new_error
67.83/34.93	   new_primModNatS1(Succ(Zero), Zero)
67.83/34.93	   new_rem(Pos(x0), Pos(Zero))
67.83/34.93	   new_primModNatS01(x0, x1, Zero, Zero)
67.83/34.93	   new_primEqInt0(x0)
67.83/34.93	   new_esEs(Pos(Zero))
67.83/34.93	   new_esEs(Pos(Succ(x0)))
67.83/34.93	   new_rem(Pos(x0), Pos(Succ(x1)))
67.83/34.93	   new_primModNatS02(x0, x1)
67.83/34.93	   new_primMinusNatS2(Zero, Succ(x0))
67.83/34.93	   new_rem(Pos(x0), Neg(Succ(x1)))
67.83/34.93	   new_rem(Neg(x0), Pos(Succ(x1)))
67.83/34.93	   new_primModNatS1(Zero, x0)
67.83/34.93	   new_primEqInt(x0)
67.83/34.93	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.83/34.93	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.83/34.93	   new_rem(Pos(x0), Neg(Zero))
67.83/34.93	   new_rem(Neg(x0), Pos(Zero))
67.83/34.93	   new_primMinusNatS0(x0)
67.83/34.93	   new_primEqInt2
67.83/34.93	   new_esEs(Neg(Zero))
67.83/34.93	   new_esEs(Neg(Succ(x0)))
67.83/34.93	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.83/34.93	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.83/34.93	
67.83/34.93	We have to consider all minimal (P,Q,R)-chains.
67.83/34.93	----------------------------------------
67.83/34.93	
67.83/34.93	(424) TransformationProof (EQUIVALENT)
67.83/34.93	By rewriting [LPAR04] the rule new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Zero, Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(Zero))))) at position [0,0,0] we obtained the following new rules [LPAR04]:
67.83/34.93	
67.83/34.93	   (new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Neg(Zero)), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(Zero))))),new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Neg(Zero)), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(Zero))))))
67.83/34.93	
67.83/34.93	
67.83/34.93	----------------------------------------
67.83/34.93	
67.83/34.93	(425)
67.83/34.93	Obligation:
67.83/34.93	Q DP problem:
67.83/34.93	The TRS P consists of the following rules:
67.83/34.93	
67.83/34.93	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.83/34.93	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0))))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0))))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, Zero, x0, Zero))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Pos(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, Zero, x0, Zero))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0))))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0))))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(new_esEs(Neg(Zero)), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.93	
67.83/34.93	The TRS R consists of the following rules:
67.83/34.93	
67.83/34.93	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.83/34.93	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.83/34.93	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.83/34.93	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.83/34.93	   new_primMinusNatS2(Zero, Zero) -> Zero
67.83/34.93	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.83/34.93	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.83/34.93	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.83/34.93	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.83/34.93	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.83/34.93	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.83/34.93	   new_primModNatS1(Zero, vuz54200) -> Zero
67.83/34.93	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.83/34.93	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.83/34.93	   new_error -> error([])
67.83/34.93	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.83/34.93	   new_primEqInt2 -> True
67.83/34.93	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.83/34.93	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.83/34.93	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.83/34.93	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.83/34.93	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.83/34.93	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.83/34.93	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.83/34.93	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.83/34.93	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.83/34.93	   new_primMinusNatS1 -> Zero
67.83/34.93	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.83/34.93	   new_primEqInt1 -> True
67.83/34.93	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.83/34.93	   new_primEqInt0(vuz3260) -> False
67.83/34.93	   new_primEqInt(vuz3250) -> False
67.83/34.93	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.83/34.93	
67.83/34.93	The set Q consists of the following terms:
67.83/34.93	
67.83/34.93	   new_rem(Neg(x0), Neg(Zero))
67.83/34.93	   new_primEqInt1
67.83/34.93	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.83/34.93	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.83/34.93	   new_primMinusNatS1
67.83/34.93	   new_rem(Neg(x0), Neg(Succ(x1)))
67.83/34.93	   new_primMinusNatS2(Succ(x0), Zero)
67.83/34.93	   new_primModNatS1(Succ(Zero), Succ(x0))
67.83/34.93	   new_primMinusNatS2(Zero, Zero)
67.83/34.93	   new_error
67.83/34.93	   new_primModNatS1(Succ(Zero), Zero)
67.83/34.93	   new_rem(Pos(x0), Pos(Zero))
67.83/34.93	   new_primModNatS01(x0, x1, Zero, Zero)
67.83/34.93	   new_primEqInt0(x0)
67.83/34.93	   new_esEs(Pos(Zero))
67.83/34.93	   new_esEs(Pos(Succ(x0)))
67.83/34.93	   new_rem(Pos(x0), Pos(Succ(x1)))
67.83/34.93	   new_primModNatS02(x0, x1)
67.83/34.93	   new_primMinusNatS2(Zero, Succ(x0))
67.83/34.93	   new_rem(Pos(x0), Neg(Succ(x1)))
67.83/34.93	   new_rem(Neg(x0), Pos(Succ(x1)))
67.83/34.93	   new_primModNatS1(Zero, x0)
67.83/34.93	   new_primEqInt(x0)
67.83/34.93	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.83/34.93	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.83/34.93	   new_rem(Pos(x0), Neg(Zero))
67.83/34.93	   new_rem(Neg(x0), Pos(Zero))
67.83/34.93	   new_primMinusNatS0(x0)
67.83/34.93	   new_primEqInt2
67.83/34.93	   new_esEs(Neg(Zero))
67.83/34.93	   new_esEs(Neg(Succ(x0)))
67.83/34.93	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.83/34.93	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.83/34.93	
67.83/34.93	We have to consider all minimal (P,Q,R)-chains.
67.83/34.93	----------------------------------------
67.83/34.93	
67.83/34.93	(426) DependencyGraphProof (EQUIVALENT)
67.83/34.93	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
67.83/34.93	----------------------------------------
67.83/34.93	
67.83/34.93	(427)
67.83/34.93	Obligation:
67.83/34.93	Q DP problem:
67.83/34.93	The TRS P consists of the following rules:
67.83/34.93	
67.83/34.93	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.83/34.93	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0))))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0))))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, Zero, x0, Zero))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Pos(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, Zero, x0, Zero))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0))))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0))))))
67.83/34.93	
67.83/34.93	The TRS R consists of the following rules:
67.83/34.93	
67.83/34.93	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.83/34.93	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.83/34.93	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.83/34.93	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.83/34.93	   new_primMinusNatS2(Zero, Zero) -> Zero
67.83/34.93	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.83/34.93	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.83/34.93	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.83/34.93	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.83/34.93	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.83/34.93	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.83/34.93	   new_primModNatS1(Zero, vuz54200) -> Zero
67.83/34.93	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.83/34.93	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.83/34.93	   new_error -> error([])
67.83/34.93	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.83/34.93	   new_primEqInt2 -> True
67.83/34.93	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.83/34.93	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.83/34.93	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.83/34.93	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.83/34.93	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.83/34.93	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.83/34.93	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.83/34.93	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.83/34.93	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.83/34.93	   new_primMinusNatS1 -> Zero
67.83/34.93	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.83/34.93	   new_primEqInt1 -> True
67.83/34.93	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.83/34.93	   new_primEqInt0(vuz3260) -> False
67.83/34.93	   new_primEqInt(vuz3250) -> False
67.83/34.93	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.83/34.93	
67.83/34.93	The set Q consists of the following terms:
67.83/34.93	
67.83/34.93	   new_rem(Neg(x0), Neg(Zero))
67.83/34.93	   new_primEqInt1
67.83/34.93	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.83/34.93	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.83/34.93	   new_primMinusNatS1
67.83/34.93	   new_rem(Neg(x0), Neg(Succ(x1)))
67.83/34.93	   new_primMinusNatS2(Succ(x0), Zero)
67.83/34.93	   new_primModNatS1(Succ(Zero), Succ(x0))
67.83/34.93	   new_primMinusNatS2(Zero, Zero)
67.83/34.93	   new_error
67.83/34.93	   new_primModNatS1(Succ(Zero), Zero)
67.83/34.93	   new_rem(Pos(x0), Pos(Zero))
67.83/34.93	   new_primModNatS01(x0, x1, Zero, Zero)
67.83/34.93	   new_primEqInt0(x0)
67.83/34.93	   new_esEs(Pos(Zero))
67.83/34.93	   new_esEs(Pos(Succ(x0)))
67.83/34.93	   new_rem(Pos(x0), Pos(Succ(x1)))
67.83/34.93	   new_primModNatS02(x0, x1)
67.83/34.93	   new_primMinusNatS2(Zero, Succ(x0))
67.83/34.93	   new_rem(Pos(x0), Neg(Succ(x1)))
67.83/34.93	   new_rem(Neg(x0), Pos(Succ(x1)))
67.83/34.93	   new_primModNatS1(Zero, x0)
67.83/34.93	   new_primEqInt(x0)
67.83/34.93	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.83/34.93	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.83/34.93	   new_rem(Pos(x0), Neg(Zero))
67.83/34.93	   new_rem(Neg(x0), Pos(Zero))
67.83/34.93	   new_primMinusNatS0(x0)
67.83/34.93	   new_primEqInt2
67.83/34.93	   new_esEs(Neg(Zero))
67.83/34.93	   new_esEs(Neg(Succ(x0)))
67.83/34.93	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.83/34.93	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.83/34.93	
67.83/34.93	We have to consider all minimal (P,Q,R)-chains.
67.83/34.93	----------------------------------------
67.83/34.93	
67.83/34.93	(428) QDPOrderProof (EQUIVALENT)
67.83/34.93	We use the reduction pair processor [LPAR04,JAR06].
67.83/34.93	
67.83/34.93	
67.83/34.93	The following pairs can be oriented strictly and are deleted.
67.83/34.93	
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0))))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x0), Zero))), Neg(Succ(Zero)), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x0), Zero))), Pos(Succ(Zero)), Neg(Succ(Succ(Succ(Succ(x0))))))
67.83/34.93	The remaining pairs can at least be oriented weakly.
67.83/34.93	Used ordering:  Polynomial interpretation [POLO]:
67.83/34.93	
67.83/34.93	   POL(False) = 1
67.83/34.93	   POL(Neg(x_1)) = x_1
67.83/34.93	   POL(Pos(x_1)) = x_1
67.83/34.93	   POL(Succ(x_1)) = 1
67.83/34.93	   POL(True) = 0
67.83/34.93	   POL(Zero) = 0
67.83/34.93	   POL([]) = 1
67.83/34.93	   POL(error(x_1)) = 1 + x_1
67.83/34.93	   POL(new_error) = 1
67.83/34.93	   POL(new_esEs(x_1)) = x_1
67.83/34.93	   POL(new_gcd0Gcd'(x_1, x_2)) = 1
67.83/34.93	   POL(new_gcd0Gcd'0(x_1, x_2)) = 1
67.83/34.93	   POL(new_gcd0Gcd'1(x_1, x_2, x_3)) = x_1
67.83/34.93	   POL(new_primEqInt(x_1)) = 1
67.83/34.93	   POL(new_primEqInt0(x_1)) = 1
67.83/34.93	   POL(new_primEqInt1) = 0
67.83/34.93	   POL(new_primEqInt2) = 0
67.83/34.93	   POL(new_primMinusNatS0(x_1)) = 1 + x_1
67.83/34.93	   POL(new_primMinusNatS1) = 1
67.83/34.93	   POL(new_primMinusNatS2(x_1, x_2)) = 0
67.83/34.93	   POL(new_primModNatS01(x_1, x_2, x_3, x_4)) = 1
67.83/34.93	   POL(new_primModNatS02(x_1, x_2)) = 1
67.83/34.93	   POL(new_primModNatS1(x_1, x_2)) = x_2
67.83/34.93	   POL(new_rem(x_1, x_2)) = 0
67.83/34.93	
67.83/34.93	The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
67.83/34.93	
67.83/34.93	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.83/34.93	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.83/34.93	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.83/34.93	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.83/34.93	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.83/34.93	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.83/34.93	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.83/34.93	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.83/34.93	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.83/34.93	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.83/34.93	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.83/34.93	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.83/34.93	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.83/34.93	   new_primEqInt2 -> True
67.83/34.93	   new_primModNatS1(Zero, vuz54200) -> Zero
67.83/34.93	   new_primEqInt1 -> True
67.83/34.93	   new_primEqInt(vuz3250) -> False
67.83/34.93	   new_primEqInt0(vuz3260) -> False
67.83/34.93	
67.83/34.93	
67.83/34.93	----------------------------------------
67.83/34.93	
67.83/34.93	(429)
67.83/34.93	Obligation:
67.83/34.93	Q DP problem:
67.83/34.93	The TRS P consists of the following rules:
67.83/34.93	
67.83/34.93	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.83/34.93	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0))))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, Zero, x0, Zero))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Pos(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, Zero, x0, Zero))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0))))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.93	
67.83/34.93	The TRS R consists of the following rules:
67.83/34.93	
67.83/34.93	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.83/34.93	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.83/34.93	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.83/34.93	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.83/34.93	   new_primMinusNatS2(Zero, Zero) -> Zero
67.83/34.93	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.83/34.93	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.83/34.93	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.83/34.93	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.83/34.93	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.83/34.93	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.83/34.93	   new_primModNatS1(Zero, vuz54200) -> Zero
67.83/34.93	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.83/34.93	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.83/34.93	   new_error -> error([])
67.83/34.93	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.83/34.93	   new_primEqInt2 -> True
67.83/34.93	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.83/34.93	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.83/34.93	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.83/34.93	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.83/34.93	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.83/34.93	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.83/34.93	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.83/34.93	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.83/34.93	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.83/34.93	   new_primMinusNatS1 -> Zero
67.83/34.93	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.83/34.93	   new_primEqInt1 -> True
67.83/34.93	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.83/34.93	   new_primEqInt0(vuz3260) -> False
67.83/34.93	   new_primEqInt(vuz3250) -> False
67.83/34.93	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.83/34.93	
67.83/34.93	The set Q consists of the following terms:
67.83/34.93	
67.83/34.93	   new_rem(Neg(x0), Neg(Zero))
67.83/34.93	   new_primEqInt1
67.83/34.93	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.83/34.93	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.83/34.93	   new_primMinusNatS1
67.83/34.93	   new_rem(Neg(x0), Neg(Succ(x1)))
67.83/34.93	   new_primMinusNatS2(Succ(x0), Zero)
67.83/34.93	   new_primModNatS1(Succ(Zero), Succ(x0))
67.83/34.93	   new_primMinusNatS2(Zero, Zero)
67.83/34.93	   new_error
67.83/34.93	   new_primModNatS1(Succ(Zero), Zero)
67.83/34.93	   new_rem(Pos(x0), Pos(Zero))
67.83/34.93	   new_primModNatS01(x0, x1, Zero, Zero)
67.83/34.93	   new_primEqInt0(x0)
67.83/34.93	   new_esEs(Pos(Zero))
67.83/34.93	   new_esEs(Pos(Succ(x0)))
67.83/34.93	   new_rem(Pos(x0), Pos(Succ(x1)))
67.83/34.93	   new_primModNatS02(x0, x1)
67.83/34.93	   new_primMinusNatS2(Zero, Succ(x0))
67.83/34.93	   new_rem(Pos(x0), Neg(Succ(x1)))
67.83/34.93	   new_rem(Neg(x0), Pos(Succ(x1)))
67.83/34.93	   new_primModNatS1(Zero, x0)
67.83/34.93	   new_primEqInt(x0)
67.83/34.93	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.83/34.93	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.83/34.93	   new_rem(Pos(x0), Neg(Zero))
67.83/34.93	   new_rem(Neg(x0), Pos(Zero))
67.83/34.93	   new_primMinusNatS0(x0)
67.83/34.93	   new_primEqInt2
67.83/34.93	   new_esEs(Neg(Zero))
67.83/34.93	   new_esEs(Neg(Succ(x0)))
67.83/34.93	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.83/34.93	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.83/34.93	
67.83/34.93	We have to consider all minimal (P,Q,R)-chains.
67.83/34.93	----------------------------------------
67.83/34.93	
67.83/34.93	(430) MNOCProof (EQUIVALENT)
67.83/34.93	We use the modular non-overlap check [FROCOS05] to decrease Q to the empty set.
67.83/34.93	----------------------------------------
67.83/34.93	
67.83/34.93	(431)
67.83/34.93	Obligation:
67.83/34.93	Q DP problem:
67.83/34.93	The TRS P consists of the following rules:
67.83/34.93	
67.83/34.93	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.83/34.93	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0))))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, Zero, x0, Zero))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.93	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Pos(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, Zero, x0, Zero))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0))))))
67.83/34.93	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.93	
67.83/34.93	The TRS R consists of the following rules:
67.83/34.93	
67.83/34.93	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.83/34.93	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.83/34.93	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.83/34.93	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.83/34.93	   new_primMinusNatS2(Zero, Zero) -> Zero
67.83/34.93	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.83/34.93	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.83/34.93	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.83/34.93	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.83/34.93	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.83/34.93	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.83/34.93	   new_primModNatS1(Zero, vuz54200) -> Zero
67.83/34.93	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.83/34.93	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.83/34.93	   new_error -> error([])
67.83/34.93	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.83/34.93	   new_primEqInt2 -> True
67.83/34.93	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.83/34.93	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.83/34.93	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.83/34.93	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.83/34.93	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.83/34.93	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.83/34.93	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.83/34.93	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.83/34.93	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.83/34.93	   new_primMinusNatS1 -> Zero
67.83/34.93	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.83/34.93	   new_primEqInt1 -> True
67.83/34.93	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.83/34.93	   new_primEqInt0(vuz3260) -> False
67.83/34.93	   new_primEqInt(vuz3250) -> False
67.83/34.93	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.83/34.93	
67.83/34.93	Q is empty.
67.83/34.93	We have to consider all (P,Q,R)-chains.
67.83/34.93	----------------------------------------
67.83/34.93	
67.83/34.93	(432) InductionCalculusProof (EQUIVALENT)
67.83/34.93	Note that final constraints are written in bold face.
67.83/34.93	
67.83/34.93	
67.83/34.93	
67.83/34.93	For Pair new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542) the following chains were created:
67.83/34.93	*We consider the chain new_gcd0Gcd'0(x2, x3) -> new_gcd0Gcd'(x3, x2), new_gcd0Gcd'(Neg(Succ(Succ(x4))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x4))), Neg(Succ(Zero))) which results in the following constraint:
67.83/34.93	
67.83/34.93	(1)    (new_gcd0Gcd'(x3, x2)=new_gcd0Gcd'(Neg(Succ(Succ(x4))), Neg(Succ(Zero)))  ==>  new_gcd0Gcd'0(x2, x3)_>=_new_gcd0Gcd'(x3, x2))
67.83/34.93	
67.83/34.93	
67.83/34.93	
67.83/34.93	We simplified constraint (1) using rules (I), (II), (III) which results in the following new constraint:
67.83/34.93	
67.83/34.93	(2)    (new_gcd0Gcd'0(Neg(Succ(Zero)), Neg(Succ(Succ(x4))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(x4))), Neg(Succ(Zero))))
67.83/34.93	
67.83/34.93	
67.83/34.93	
67.83/34.93	
67.83/34.93	*We consider the chain new_gcd0Gcd'0(x7, x8) -> new_gcd0Gcd'(x8, x7), new_gcd0Gcd'(Pos(Succ(Succ(x9))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x9))), Pos(Succ(Zero))) which results in the following constraint:
67.83/34.93	
67.83/34.93	(1)    (new_gcd0Gcd'(x8, x7)=new_gcd0Gcd'(Pos(Succ(Succ(x9))), Pos(Succ(Zero)))  ==>  new_gcd0Gcd'0(x7, x8)_>=_new_gcd0Gcd'(x8, x7))
67.83/34.93	
67.83/34.93	
67.83/34.93	
67.83/34.93	We simplified constraint (1) using rules (I), (II), (III) which results in the following new constraint:
67.83/34.93	
67.83/34.93	(2)    (new_gcd0Gcd'0(Pos(Succ(Zero)), Pos(Succ(Succ(x9))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(x9))), Pos(Succ(Zero))))
67.83/34.93	
67.83/34.93	
67.83/34.93	
67.83/34.93	
67.83/34.93	*We consider the chain new_gcd0Gcd'0(x10, x11) -> new_gcd0Gcd'(x11, x10), new_gcd0Gcd'(Neg(Succ(Succ(x12))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x12))), Pos(Succ(Zero))) which results in the following constraint:
67.83/34.93	
67.83/34.93	(1)    (new_gcd0Gcd'(x11, x10)=new_gcd0Gcd'(Neg(Succ(Succ(x12))), Pos(Succ(Zero)))  ==>  new_gcd0Gcd'0(x10, x11)_>=_new_gcd0Gcd'(x11, x10))
67.83/34.93	
67.83/34.93	
67.83/34.93	
67.83/34.93	We simplified constraint (1) using rules (I), (II), (III) which results in the following new constraint:
67.83/34.93	
67.83/34.93	(2)    (new_gcd0Gcd'0(Pos(Succ(Zero)), Neg(Succ(Succ(x12))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(x12))), Pos(Succ(Zero))))
67.83/34.93	
67.83/34.93	
67.83/34.93	
67.83/34.93	
67.83/34.93	*We consider the chain new_gcd0Gcd'0(x13, x14) -> new_gcd0Gcd'(x14, x13), new_gcd0Gcd'(Pos(Succ(Succ(x15))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x15))), Neg(Succ(Zero))) which results in the following constraint:
67.83/34.93	
67.83/34.93	(1)    (new_gcd0Gcd'(x14, x13)=new_gcd0Gcd'(Pos(Succ(Succ(x15))), Neg(Succ(Zero)))  ==>  new_gcd0Gcd'0(x13, x14)_>=_new_gcd0Gcd'(x14, x13))
67.83/34.93	
67.83/34.93	
67.83/34.93	
67.83/34.93	We simplified constraint (1) using rules (I), (II), (III) which results in the following new constraint:
67.83/34.93	
67.83/34.93	(2)    (new_gcd0Gcd'0(Neg(Succ(Zero)), Pos(Succ(Succ(x15))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(x15))), Neg(Succ(Zero))))
67.83/34.93	
67.83/34.93	
67.83/34.93	
67.83/34.93	
67.83/34.93	*We consider the chain new_gcd0Gcd'0(x16, x17) -> new_gcd0Gcd'(x17, x16), new_gcd0Gcd'(Neg(Succ(Succ(Succ(x18)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x18)))), Neg(Succ(Succ(Zero)))) which results in the following constraint:
67.83/34.93	
67.83/34.93	(1)    (new_gcd0Gcd'(x17, x16)=new_gcd0Gcd'(Neg(Succ(Succ(Succ(x18)))), Neg(Succ(Succ(Zero))))  ==>  new_gcd0Gcd'0(x16, x17)_>=_new_gcd0Gcd'(x17, x16))
67.83/34.93	
67.83/34.93	
67.83/34.93	
67.83/34.93	We simplified constraint (1) using rules (I), (II), (III) which results in the following new constraint:
67.83/34.93	
67.83/34.93	(2)    (new_gcd0Gcd'0(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x18)))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(x18)))), Neg(Succ(Succ(Zero)))))
67.83/34.93	
67.83/34.93	
67.83/34.93	
67.83/34.93	
67.83/34.93	*We consider the chain new_gcd0Gcd'0(x19, x20) -> new_gcd0Gcd'(x20, x19), new_gcd0Gcd'(Pos(Succ(Succ(Succ(x21)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x21)))), Pos(Succ(Succ(Zero)))) which results in the following constraint:
67.83/34.93	
67.83/34.93	(1)    (new_gcd0Gcd'(x20, x19)=new_gcd0Gcd'(Pos(Succ(Succ(Succ(x21)))), Pos(Succ(Succ(Zero))))  ==>  new_gcd0Gcd'0(x19, x20)_>=_new_gcd0Gcd'(x20, x19))
67.83/34.93	
67.83/34.93	
67.83/34.93	
67.83/34.93	We simplified constraint (1) using rules (I), (II), (III) which results in the following new constraint:
67.83/34.93	
67.83/34.93	(2)    (new_gcd0Gcd'0(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x21)))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(x21)))), Pos(Succ(Succ(Zero)))))
67.83/34.93	
67.83/34.93	
67.83/34.93	
67.83/34.93	
67.83/34.93	*We consider the chain new_gcd0Gcd'0(x22, x23) -> new_gcd0Gcd'(x23, x22), new_gcd0Gcd'(Neg(Succ(Succ(Succ(x24)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x24)))), Pos(Succ(Succ(Zero)))) which results in the following constraint:
67.83/34.93	
67.83/34.93	(1)    (new_gcd0Gcd'(x23, x22)=new_gcd0Gcd'(Neg(Succ(Succ(Succ(x24)))), Pos(Succ(Succ(Zero))))  ==>  new_gcd0Gcd'0(x22, x23)_>=_new_gcd0Gcd'(x23, x22))
67.83/34.93	
67.83/34.93	
67.83/34.93	
67.83/34.93	We simplified constraint (1) using rules (I), (II), (III) which results in the following new constraint:
67.83/34.93	
67.83/34.93	(2)    (new_gcd0Gcd'0(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x24)))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(x24)))), Pos(Succ(Succ(Zero)))))
67.83/34.93	
67.83/34.93	
67.83/34.93	
67.83/34.93	
67.83/34.93	*We consider the chain new_gcd0Gcd'0(x25, x26) -> new_gcd0Gcd'(x26, x25), new_gcd0Gcd'(Pos(Succ(Succ(Succ(x27)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x27)))), Neg(Succ(Succ(Zero)))) which results in the following constraint:
67.83/34.93	
67.83/34.93	(1)    (new_gcd0Gcd'(x26, x25)=new_gcd0Gcd'(Pos(Succ(Succ(Succ(x27)))), Neg(Succ(Succ(Zero))))  ==>  new_gcd0Gcd'0(x25, x26)_>=_new_gcd0Gcd'(x26, x25))
67.83/34.93	
67.83/34.93	
67.83/34.93	
67.83/34.93	We simplified constraint (1) using rules (I), (II), (III) which results in the following new constraint:
67.83/34.93	
67.83/34.93	(2)    (new_gcd0Gcd'0(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x27)))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(x27)))), Neg(Succ(Succ(Zero)))))
67.83/34.93	
67.83/34.93	
67.83/34.93	
67.83/34.93	
67.83/34.93	*We consider the chain new_gcd0Gcd'0(x28, x29) -> new_gcd0Gcd'(x29, x28), new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x30))))), Neg(Succ(Succ(Succ(Succ(x31)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x31)), Succ(Succ(x30)), x31, x30))), Neg(Succ(Succ(Succ(Succ(x30))))), Neg(Succ(Succ(Succ(Succ(x31)))))) which results in the following constraint:
67.83/34.93	
67.83/34.93	(1)    (new_gcd0Gcd'(x29, x28)=new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x30))))), Neg(Succ(Succ(Succ(Succ(x31))))))  ==>  new_gcd0Gcd'0(x28, x29)_>=_new_gcd0Gcd'(x29, x28))
67.83/34.93	
67.83/34.93	
67.83/34.93	
67.83/34.93	We simplified constraint (1) using rules (I), (II), (III) which results in the following new constraint:
67.83/34.93	
67.83/34.93	(2)    (new_gcd0Gcd'0(Neg(Succ(Succ(Succ(Succ(x31))))), Neg(Succ(Succ(Succ(Succ(x30))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x30))))), Neg(Succ(Succ(Succ(Succ(x31)))))))
67.83/34.93	
67.83/34.93	
67.83/34.93	
67.83/34.93	
67.83/34.93	*We consider the chain new_gcd0Gcd'0(x32, x33) -> new_gcd0Gcd'(x33, x32), new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x34))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x34))))), Neg(Succ(Succ(Succ(Zero))))) which results in the following constraint:
67.83/34.93	
67.83/34.93	(1)    (new_gcd0Gcd'(x33, x32)=new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x34))))), Neg(Succ(Succ(Succ(Zero)))))  ==>  new_gcd0Gcd'0(x32, x33)_>=_new_gcd0Gcd'(x33, x32))
67.83/34.93	
67.83/34.93	
67.83/34.93	
67.83/34.93	We simplified constraint (1) using rules (I), (II), (III) which results in the following new constraint:
67.83/34.93	
67.83/34.93	(2)    (new_gcd0Gcd'0(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x34))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x34))))), Neg(Succ(Succ(Succ(Zero))))))
67.83/34.93	
67.83/34.93	
67.83/34.93	
67.83/34.93	
67.83/34.93	*We consider the chain new_gcd0Gcd'0(x35, x36) -> new_gcd0Gcd'(x36, x35), new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x37)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x37), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x37)))))) which results in the following constraint:
67.83/34.93	
67.83/34.93	(1)    (new_gcd0Gcd'(x36, x35)=new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x37))))))  ==>  new_gcd0Gcd'0(x35, x36)_>=_new_gcd0Gcd'(x36, x35))
67.83/34.93	
67.83/34.93	
67.83/34.93	
67.83/34.93	We simplified constraint (1) using rules (I), (II), (III) which results in the following new constraint:
67.83/34.93	
67.83/34.93	(2)    (new_gcd0Gcd'0(Neg(Succ(Succ(Succ(Succ(x37))))), Neg(Succ(Succ(Succ(Zero)))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x37)))))))
67.83/34.93	
67.83/34.93	
67.83/34.93	
67.83/34.93	
67.83/34.93	*We consider the chain new_gcd0Gcd'0(x38, x39) -> new_gcd0Gcd'(x39, x38), new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x40)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x40, Zero, x40, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x40)))))) which results in the following constraint:
67.83/34.93	
67.83/34.93	(1)    (new_gcd0Gcd'(x39, x38)=new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x40))))))  ==>  new_gcd0Gcd'0(x38, x39)_>=_new_gcd0Gcd'(x39, x38))
67.83/34.93	
67.83/34.93	
67.83/34.93	
67.83/34.93	We simplified constraint (1) using rules (I), (II), (III) which results in the following new constraint:
67.83/34.93	
67.83/34.93	(2)    (new_gcd0Gcd'0(Neg(Succ(Succ(Succ(Succ(x40))))), Neg(Succ(Succ(Zero))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x40)))))))
67.83/34.93	
67.83/34.93	
67.83/34.93	
67.83/34.93	
67.83/34.93	*We consider the chain new_gcd0Gcd'0(x41, x42) -> new_gcd0Gcd'(x42, x41), new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) which results in the following constraint:
67.83/34.93	
67.83/34.93	(1)    (new_gcd0Gcd'(x42, x41)=new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero)))))  ==>  new_gcd0Gcd'0(x41, x42)_>=_new_gcd0Gcd'(x42, x41))
67.83/34.93	
67.83/34.93	
67.83/34.93	
67.83/34.93	We simplified constraint (1) using rules (I), (II), (III) which results in the following new constraint:
67.83/34.93	
67.83/34.93	(2)    (new_gcd0Gcd'0(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Zero))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))))
67.83/34.93	
67.83/34.93	
67.83/34.93	
67.83/34.93	
67.83/34.93	*We consider the chain new_gcd0Gcd'0(x43, x44) -> new_gcd0Gcd'(x44, x43), new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x45))))), Pos(Succ(Succ(Succ(Succ(x46)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x46)), Succ(Succ(x45)), x46, x45))), Pos(Succ(Succ(Succ(Succ(x45))))), Pos(Succ(Succ(Succ(Succ(x46)))))) which results in the following constraint:
67.83/34.93	
67.83/34.93	(1)    (new_gcd0Gcd'(x44, x43)=new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x45))))), Pos(Succ(Succ(Succ(Succ(x46))))))  ==>  new_gcd0Gcd'0(x43, x44)_>=_new_gcd0Gcd'(x44, x43))
67.83/34.93	
67.83/34.93	
67.83/34.93	
67.83/34.93	We simplified constraint (1) using rules (I), (II), (III) which results in the following new constraint:
67.83/34.93	
67.83/34.93	(2)    (new_gcd0Gcd'0(Pos(Succ(Succ(Succ(Succ(x46))))), Pos(Succ(Succ(Succ(Succ(x45))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x45))))), Pos(Succ(Succ(Succ(Succ(x46)))))))
67.83/34.93	
67.83/34.93	
67.83/34.93	
67.83/34.93	
67.83/34.93	*We consider the chain new_gcd0Gcd'0(x47, x48) -> new_gcd0Gcd'(x48, x47), new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x49))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(Succ(x49))))), Pos(Succ(Succ(Succ(Zero))))) which results in the following constraint:
67.83/34.93	
67.83/34.93	(1)    (new_gcd0Gcd'(x48, x47)=new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x49))))), Pos(Succ(Succ(Succ(Zero)))))  ==>  new_gcd0Gcd'0(x47, x48)_>=_new_gcd0Gcd'(x48, x47))
67.83/34.93	
67.83/34.93	
67.83/34.93	
67.83/34.93	We simplified constraint (1) using rules (I), (II), (III) which results in the following new constraint:
67.83/34.93	
67.83/34.93	(2)    (new_gcd0Gcd'0(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x49))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x49))))), Pos(Succ(Succ(Succ(Zero))))))
67.83/34.93	
67.83/34.93	
67.83/34.93	
67.83/34.93	
67.83/34.93	*We consider the chain new_gcd0Gcd'0(x50, x51) -> new_gcd0Gcd'(x51, x50), new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x52)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x52), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x52)))))) which results in the following constraint:
67.83/34.93	
67.83/34.93	(1)    (new_gcd0Gcd'(x51, x50)=new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x52))))))  ==>  new_gcd0Gcd'0(x50, x51)_>=_new_gcd0Gcd'(x51, x50))
67.83/34.93	
67.83/34.93	
67.83/34.93	
67.83/34.93	We simplified constraint (1) using rules (I), (II), (III) which results in the following new constraint:
67.83/34.93	
67.83/34.93	(2)    (new_gcd0Gcd'0(Pos(Succ(Succ(Succ(Succ(x52))))), Pos(Succ(Succ(Succ(Zero)))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x52)))))))
67.83/34.93	
67.83/34.93	
67.83/34.93	
67.83/34.93	
67.83/34.93	*We consider the chain new_gcd0Gcd'0(x53, x54) -> new_gcd0Gcd'(x54, x53), new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x55)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x55, Zero, x55, Zero))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x55)))))) which results in the following constraint:
67.83/34.93	
67.83/34.93	(1)    (new_gcd0Gcd'(x54, x53)=new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x55))))))  ==>  new_gcd0Gcd'0(x53, x54)_>=_new_gcd0Gcd'(x54, x53))
67.83/34.93	
67.83/34.93	
67.83/34.93	
67.83/34.93	We simplified constraint (1) using rules (I), (II), (III) which results in the following new constraint:
67.83/34.93	
67.83/34.93	(2)    (new_gcd0Gcd'0(Pos(Succ(Succ(Succ(Succ(x55))))), Pos(Succ(Succ(Zero))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x55)))))))
67.83/34.93	
67.83/34.93	
67.83/34.93	
67.83/34.93	
67.83/34.93	*We consider the chain new_gcd0Gcd'0(x56, x57) -> new_gcd0Gcd'(x57, x56), new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) which results in the following constraint:
67.83/34.93	
67.83/34.93	(1)    (new_gcd0Gcd'(x57, x56)=new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero)))))  ==>  new_gcd0Gcd'0(x56, x57)_>=_new_gcd0Gcd'(x57, x56))
67.83/34.93	
67.83/34.93	
67.83/34.93	
67.83/34.93	We simplified constraint (1) using rules (I), (II), (III) which results in the following new constraint:
67.83/34.93	
67.83/34.93	(2)    (new_gcd0Gcd'0(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Zero))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))))
67.83/34.93	
67.83/34.93	
67.83/34.93	
67.83/34.93	
67.83/34.93	*We consider the chain new_gcd0Gcd'0(x58, x59) -> new_gcd0Gcd'(x59, x58), new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x60))))), Pos(Succ(Succ(Succ(Succ(x61)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x61)), Succ(Succ(x60)), x61, x60))), Neg(Succ(Succ(Succ(Succ(x60))))), Pos(Succ(Succ(Succ(Succ(x61)))))) which results in the following constraint:
67.83/34.93	
67.83/34.93	(1)    (new_gcd0Gcd'(x59, x58)=new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x60))))), Pos(Succ(Succ(Succ(Succ(x61))))))  ==>  new_gcd0Gcd'0(x58, x59)_>=_new_gcd0Gcd'(x59, x58))
67.83/34.93	
67.83/34.93	
67.83/34.93	
67.83/34.93	We simplified constraint (1) using rules (I), (II), (III) which results in the following new constraint:
67.83/34.93	
67.83/34.93	(2)    (new_gcd0Gcd'0(Pos(Succ(Succ(Succ(Succ(x61))))), Neg(Succ(Succ(Succ(Succ(x60))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x60))))), Pos(Succ(Succ(Succ(Succ(x61)))))))
67.83/34.93	
67.83/34.93	
67.83/34.93	
67.83/34.93	
67.83/34.93	*We consider the chain new_gcd0Gcd'0(x62, x63) -> new_gcd0Gcd'(x63, x62), new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x64))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x64))))), Pos(Succ(Succ(Succ(Zero))))) which results in the following constraint:
67.83/34.93	
67.83/34.93	(1)    (new_gcd0Gcd'(x63, x62)=new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x64))))), Pos(Succ(Succ(Succ(Zero)))))  ==>  new_gcd0Gcd'0(x62, x63)_>=_new_gcd0Gcd'(x63, x62))
67.83/34.93	
67.83/34.93	
67.83/34.93	
67.83/34.93	We simplified constraint (1) using rules (I), (II), (III) which results in the following new constraint:
67.83/34.93	
67.83/34.93	(2)    (new_gcd0Gcd'0(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x64))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x64))))), Pos(Succ(Succ(Succ(Zero))))))
67.83/34.93	
67.83/34.93	
67.83/34.93	
67.83/34.93	
67.83/34.93	*We consider the chain new_gcd0Gcd'0(x65, x66) -> new_gcd0Gcd'(x66, x65), new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x67)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x67), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x67)))))) which results in the following constraint:
67.83/34.93	
67.83/34.93	(1)    (new_gcd0Gcd'(x66, x65)=new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x67))))))  ==>  new_gcd0Gcd'0(x65, x66)_>=_new_gcd0Gcd'(x66, x65))
67.83/34.93	
67.83/34.93	
67.83/34.93	
67.83/34.93	We simplified constraint (1) using rules (I), (II), (III) which results in the following new constraint:
67.83/34.93	
67.83/34.93	(2)    (new_gcd0Gcd'0(Pos(Succ(Succ(Succ(Succ(x67))))), Neg(Succ(Succ(Succ(Zero)))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x67)))))))
67.83/34.93	
67.83/34.93	
67.83/34.93	
67.83/34.93	
67.83/34.93	*We consider the chain new_gcd0Gcd'0(x68, x69) -> new_gcd0Gcd'(x69, x68), new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x70)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x70, Zero, x70, Zero))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x70)))))) which results in the following constraint:
67.83/34.93	
67.83/34.93	(1)    (new_gcd0Gcd'(x69, x68)=new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x70))))))  ==>  new_gcd0Gcd'0(x68, x69)_>=_new_gcd0Gcd'(x69, x68))
67.83/34.93	
67.83/34.93	
67.83/34.93	
67.83/34.93	We simplified constraint (1) using rules (I), (II), (III) which results in the following new constraint:
67.83/34.93	
67.83/34.93	(2)    (new_gcd0Gcd'0(Pos(Succ(Succ(Succ(Succ(x70))))), Neg(Succ(Succ(Zero))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x70)))))))
67.83/34.93	
67.83/34.93	
67.83/34.93	
67.83/34.93	
67.83/34.93	*We consider the chain new_gcd0Gcd'0(x71, x72) -> new_gcd0Gcd'(x72, x71), new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) which results in the following constraint:
67.83/34.93	
67.83/34.93	(1)    (new_gcd0Gcd'(x72, x71)=new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero)))))  ==>  new_gcd0Gcd'0(x71, x72)_>=_new_gcd0Gcd'(x72, x71))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (1) using rules (I), (II), (III) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(2)    (new_gcd0Gcd'0(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Zero))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	*We consider the chain new_gcd0Gcd'0(x73, x74) -> new_gcd0Gcd'(x74, x73), new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x75))))), Neg(Succ(Succ(Succ(Succ(x76)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x76)), Succ(Succ(x75)), x76, x75))), Pos(Succ(Succ(Succ(Succ(x75))))), Neg(Succ(Succ(Succ(Succ(x76)))))) which results in the following constraint:
67.83/34.94	
67.83/34.94	(1)    (new_gcd0Gcd'(x74, x73)=new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x75))))), Neg(Succ(Succ(Succ(Succ(x76))))))  ==>  new_gcd0Gcd'0(x73, x74)_>=_new_gcd0Gcd'(x74, x73))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (1) using rules (I), (II), (III) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(2)    (new_gcd0Gcd'0(Neg(Succ(Succ(Succ(Succ(x76))))), Pos(Succ(Succ(Succ(Succ(x75))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x75))))), Neg(Succ(Succ(Succ(Succ(x76)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	*We consider the chain new_gcd0Gcd'0(x77, x78) -> new_gcd0Gcd'(x78, x77), new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x79))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(Succ(x79))))), Neg(Succ(Succ(Succ(Zero))))) which results in the following constraint:
67.83/34.94	
67.83/34.94	(1)    (new_gcd0Gcd'(x78, x77)=new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x79))))), Neg(Succ(Succ(Succ(Zero)))))  ==>  new_gcd0Gcd'0(x77, x78)_>=_new_gcd0Gcd'(x78, x77))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (1) using rules (I), (II), (III) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(2)    (new_gcd0Gcd'0(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x79))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x79))))), Neg(Succ(Succ(Succ(Zero))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	*We consider the chain new_gcd0Gcd'0(x80, x81) -> new_gcd0Gcd'(x81, x80), new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x82)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x82), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x82)))))) which results in the following constraint:
67.83/34.94	
67.83/34.94	(1)    (new_gcd0Gcd'(x81, x80)=new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x82))))))  ==>  new_gcd0Gcd'0(x80, x81)_>=_new_gcd0Gcd'(x81, x80))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (1) using rules (I), (II), (III) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(2)    (new_gcd0Gcd'0(Neg(Succ(Succ(Succ(Succ(x82))))), Pos(Succ(Succ(Succ(Zero)))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x82)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	*We consider the chain new_gcd0Gcd'0(x83, x84) -> new_gcd0Gcd'(x84, x83), new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x85)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x85, Zero, x85, Zero))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x85)))))) which results in the following constraint:
67.83/34.94	
67.83/34.94	(1)    (new_gcd0Gcd'(x84, x83)=new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x85))))))  ==>  new_gcd0Gcd'0(x83, x84)_>=_new_gcd0Gcd'(x84, x83))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (1) using rules (I), (II), (III) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(2)    (new_gcd0Gcd'0(Neg(Succ(Succ(Succ(Succ(x85))))), Pos(Succ(Succ(Zero))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x85)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	*We consider the chain new_gcd0Gcd'0(x86, x87) -> new_gcd0Gcd'(x87, x86), new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) which results in the following constraint:
67.83/34.94	
67.83/34.94	(1)    (new_gcd0Gcd'(x87, x86)=new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero)))))  ==>  new_gcd0Gcd'0(x86, x87)_>=_new_gcd0Gcd'(x87, x86))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (1) using rules (I), (II), (III) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(2)    (new_gcd0Gcd'0(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Zero))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	For Pair new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero))) the following chains were created:
67.83/34.94	*We consider the chain new_gcd0Gcd'(Neg(Succ(Succ(x90))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x90))), Neg(Succ(Zero))), new_gcd0Gcd'1(False, x91, x92) -> new_gcd0Gcd'0(x91, new_rem(x92, x91)) which results in the following constraint:
67.83/34.94	
67.83/34.94	(1)    (new_gcd0Gcd'1(False, Neg(Succ(Succ(x90))), Neg(Succ(Zero)))=new_gcd0Gcd'1(False, x91, x92)  ==>  new_gcd0Gcd'(Neg(Succ(Succ(x90))), Neg(Succ(Zero)))_>=_new_gcd0Gcd'1(False, Neg(Succ(Succ(x90))), Neg(Succ(Zero))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (1) using rules (I), (II), (IV) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(2)    (new_gcd0Gcd'(Neg(Succ(Succ(x90))), Neg(Succ(Zero)))_>=_new_gcd0Gcd'1(False, Neg(Succ(Succ(x90))), Neg(Succ(Zero))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	For Pair new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542)) the following chains were created:
67.83/34.94	*We consider the chain new_gcd0Gcd'1(False, x120, x121) -> new_gcd0Gcd'0(x120, new_rem(x121, x120)), new_gcd0Gcd'0(x122, x123) -> new_gcd0Gcd'(x123, x122) which results in the following constraint:
67.83/34.94	
67.83/34.94	(1)    (new_gcd0Gcd'0(x120, new_rem(x121, x120))=new_gcd0Gcd'0(x122, x123)  ==>  new_gcd0Gcd'1(False, x120, x121)_>=_new_gcd0Gcd'0(x120, new_rem(x121, x120)))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (1) using rules (I), (II), (IV) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(2)    (new_gcd0Gcd'1(False, x120, x121)_>=_new_gcd0Gcd'0(x120, new_rem(x121, x120)))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	For Pair new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero))) the following chains were created:
67.83/34.94	*We consider the chain new_gcd0Gcd'(Pos(Succ(Succ(x184))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x184))), Pos(Succ(Zero))), new_gcd0Gcd'1(False, x185, x186) -> new_gcd0Gcd'0(x185, new_rem(x186, x185)) which results in the following constraint:
67.83/34.94	
67.83/34.94	(1)    (new_gcd0Gcd'1(False, Pos(Succ(Succ(x184))), Pos(Succ(Zero)))=new_gcd0Gcd'1(False, x185, x186)  ==>  new_gcd0Gcd'(Pos(Succ(Succ(x184))), Pos(Succ(Zero)))_>=_new_gcd0Gcd'1(False, Pos(Succ(Succ(x184))), Pos(Succ(Zero))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (1) using rules (I), (II), (IV) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(2)    (new_gcd0Gcd'(Pos(Succ(Succ(x184))), Pos(Succ(Zero)))_>=_new_gcd0Gcd'1(False, Pos(Succ(Succ(x184))), Pos(Succ(Zero))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	For Pair new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero))) the following chains were created:
67.83/34.94	*We consider the chain new_gcd0Gcd'(Neg(Succ(Succ(x216))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x216))), Pos(Succ(Zero))), new_gcd0Gcd'1(False, x217, x218) -> new_gcd0Gcd'0(x217, new_rem(x218, x217)) which results in the following constraint:
67.83/34.94	
67.83/34.94	(1)    (new_gcd0Gcd'1(False, Neg(Succ(Succ(x216))), Pos(Succ(Zero)))=new_gcd0Gcd'1(False, x217, x218)  ==>  new_gcd0Gcd'(Neg(Succ(Succ(x216))), Pos(Succ(Zero)))_>=_new_gcd0Gcd'1(False, Neg(Succ(Succ(x216))), Pos(Succ(Zero))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (1) using rules (I), (II), (IV) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(2)    (new_gcd0Gcd'(Neg(Succ(Succ(x216))), Pos(Succ(Zero)))_>=_new_gcd0Gcd'1(False, Neg(Succ(Succ(x216))), Pos(Succ(Zero))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	For Pair new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero))) the following chains were created:
67.83/34.94	*We consider the chain new_gcd0Gcd'(Pos(Succ(Succ(x248))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x248))), Neg(Succ(Zero))), new_gcd0Gcd'1(False, x249, x250) -> new_gcd0Gcd'0(x249, new_rem(x250, x249)) which results in the following constraint:
67.83/34.94	
67.83/34.94	(1)    (new_gcd0Gcd'1(False, Pos(Succ(Succ(x248))), Neg(Succ(Zero)))=new_gcd0Gcd'1(False, x249, x250)  ==>  new_gcd0Gcd'(Pos(Succ(Succ(x248))), Neg(Succ(Zero)))_>=_new_gcd0Gcd'1(False, Pos(Succ(Succ(x248))), Neg(Succ(Zero))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (1) using rules (I), (II), (IV) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(2)    (new_gcd0Gcd'(Pos(Succ(Succ(x248))), Neg(Succ(Zero)))_>=_new_gcd0Gcd'1(False, Pos(Succ(Succ(x248))), Neg(Succ(Zero))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	For Pair new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) the following chains were created:
67.83/34.94	*We consider the chain new_gcd0Gcd'(Neg(Succ(Succ(Succ(x280)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x280)))), Neg(Succ(Succ(Zero)))), new_gcd0Gcd'1(False, x281, x282) -> new_gcd0Gcd'0(x281, new_rem(x282, x281)) which results in the following constraint:
67.83/34.94	
67.83/34.94	(1)    (new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x280)))), Neg(Succ(Succ(Zero))))=new_gcd0Gcd'1(False, x281, x282)  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Succ(x280)))), Neg(Succ(Succ(Zero))))_>=_new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x280)))), Neg(Succ(Succ(Zero)))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (1) using rules (I), (II), (IV) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(2)    (new_gcd0Gcd'(Neg(Succ(Succ(Succ(x280)))), Neg(Succ(Succ(Zero))))_>=_new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x280)))), Neg(Succ(Succ(Zero)))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	For Pair new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) the following chains were created:
67.83/34.94	*We consider the chain new_gcd0Gcd'(Pos(Succ(Succ(Succ(x312)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x312)))), Pos(Succ(Succ(Zero)))), new_gcd0Gcd'1(False, x313, x314) -> new_gcd0Gcd'0(x313, new_rem(x314, x313)) which results in the following constraint:
67.83/34.94	
67.83/34.94	(1)    (new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x312)))), Pos(Succ(Succ(Zero))))=new_gcd0Gcd'1(False, x313, x314)  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Succ(x312)))), Pos(Succ(Succ(Zero))))_>=_new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x312)))), Pos(Succ(Succ(Zero)))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (1) using rules (I), (II), (IV) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(2)    (new_gcd0Gcd'(Pos(Succ(Succ(Succ(x312)))), Pos(Succ(Succ(Zero))))_>=_new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x312)))), Pos(Succ(Succ(Zero)))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	For Pair new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) the following chains were created:
67.83/34.94	*We consider the chain new_gcd0Gcd'(Neg(Succ(Succ(Succ(x344)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x344)))), Pos(Succ(Succ(Zero)))), new_gcd0Gcd'1(False, x345, x346) -> new_gcd0Gcd'0(x345, new_rem(x346, x345)) which results in the following constraint:
67.83/34.94	
67.83/34.94	(1)    (new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x344)))), Pos(Succ(Succ(Zero))))=new_gcd0Gcd'1(False, x345, x346)  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Succ(x344)))), Pos(Succ(Succ(Zero))))_>=_new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x344)))), Pos(Succ(Succ(Zero)))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (1) using rules (I), (II), (IV) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(2)    (new_gcd0Gcd'(Neg(Succ(Succ(Succ(x344)))), Pos(Succ(Succ(Zero))))_>=_new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x344)))), Pos(Succ(Succ(Zero)))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	For Pair new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) the following chains were created:
67.83/34.94	*We consider the chain new_gcd0Gcd'(Pos(Succ(Succ(Succ(x376)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x376)))), Neg(Succ(Succ(Zero)))), new_gcd0Gcd'1(False, x377, x378) -> new_gcd0Gcd'0(x377, new_rem(x378, x377)) which results in the following constraint:
67.83/34.94	
67.83/34.94	(1)    (new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x376)))), Neg(Succ(Succ(Zero))))=new_gcd0Gcd'1(False, x377, x378)  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Succ(x376)))), Neg(Succ(Succ(Zero))))_>=_new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x376)))), Neg(Succ(Succ(Zero)))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (1) using rules (I), (II), (IV) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(2)    (new_gcd0Gcd'(Pos(Succ(Succ(Succ(x376)))), Neg(Succ(Succ(Zero))))_>=_new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x376)))), Neg(Succ(Succ(Zero)))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	For Pair new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) the following chains were created:
67.83/34.94	*We consider the chain new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x410))))), Neg(Succ(Succ(Succ(Succ(x411)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x411)), Succ(Succ(x410)), x411, x410))), Neg(Succ(Succ(Succ(Succ(x410))))), Neg(Succ(Succ(Succ(Succ(x411)))))), new_gcd0Gcd'1(False, x412, x413) -> new_gcd0Gcd'0(x412, new_rem(x413, x412)) which results in the following constraint:
67.83/34.94	
67.83/34.94	(1)    (new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x411)), Succ(Succ(x410)), x411, x410))), Neg(Succ(Succ(Succ(Succ(x410))))), Neg(Succ(Succ(Succ(Succ(x411))))))=new_gcd0Gcd'1(False, x412, x413)  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x410))))), Neg(Succ(Succ(Succ(Succ(x411))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x411)), Succ(Succ(x410)), x411, x410))), Neg(Succ(Succ(Succ(Succ(x410))))), Neg(Succ(Succ(Succ(Succ(x411)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (1) using rules (I), (II), (IV), (VII) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(2)    (Neg(new_primModNatS01(Succ(Succ(x411)), Succ(Succ(x410)), x411, x410))=x1046 & new_esEs(x1046)=False  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x410))))), Neg(Succ(Succ(Succ(Succ(x411))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x411)), Succ(Succ(x410)), x411, x410))), Neg(Succ(Succ(Succ(Succ(x410))))), Neg(Succ(Succ(Succ(Succ(x411)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_esEs(x1046)=False which results in the following new constraints:
67.83/34.94	
67.83/34.94	(3)    (new_primEqInt2=False & Neg(new_primModNatS01(Succ(Succ(x411)), Succ(Succ(x410)), x411, x410))=Neg(Zero)  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x410))))), Neg(Succ(Succ(Succ(Succ(x411))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x411)), Succ(Succ(x410)), x411, x410))), Neg(Succ(Succ(Succ(Succ(x410))))), Neg(Succ(Succ(Succ(Succ(x411)))))))
67.83/34.94	
67.83/34.94	(4)    (new_primEqInt1=False & Neg(new_primModNatS01(Succ(Succ(x411)), Succ(Succ(x410)), x411, x410))=Pos(Zero)  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x410))))), Neg(Succ(Succ(Succ(Succ(x411))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x411)), Succ(Succ(x410)), x411, x410))), Neg(Succ(Succ(Succ(Succ(x410))))), Neg(Succ(Succ(Succ(Succ(x411)))))))
67.83/34.94	
67.83/34.94	(5)    (new_primEqInt(x1047)=False & Neg(new_primModNatS01(Succ(Succ(x411)), Succ(Succ(x410)), x411, x410))=Pos(Succ(x1047))  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x410))))), Neg(Succ(Succ(Succ(Succ(x411))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x411)), Succ(Succ(x410)), x411, x410))), Neg(Succ(Succ(Succ(Succ(x410))))), Neg(Succ(Succ(Succ(Succ(x411)))))))
67.83/34.94	
67.83/34.94	(6)    (new_primEqInt0(x1048)=False & Neg(new_primModNatS01(Succ(Succ(x411)), Succ(Succ(x410)), x411, x410))=Neg(Succ(x1048))  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x410))))), Neg(Succ(Succ(Succ(Succ(x411))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x411)), Succ(Succ(x410)), x411, x410))), Neg(Succ(Succ(Succ(Succ(x410))))), Neg(Succ(Succ(Succ(Succ(x411)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (3) using rules (I), (II), (VII) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(7)    (new_primEqInt2=False & Succ(Succ(x411))=x1049 & Succ(Succ(x410))=x1050 & new_primModNatS01(x1049, x1050, x411, x410)=Zero  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x410))))), Neg(Succ(Succ(Succ(Succ(x411))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x411)), Succ(Succ(x410)), x411, x410))), Neg(Succ(Succ(Succ(Succ(x410))))), Neg(Succ(Succ(Succ(Succ(x411)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We solved constraint (4) using rules (I), (II).We solved constraint (5) using rules (I), (II).We simplified constraint (6) using rules (I), (II), (VII) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(8)    (new_primEqInt0(x1048)=False & Succ(Succ(x411))=x1051 & Succ(Succ(x410))=x1052 & new_primModNatS01(x1051, x1052, x411, x410)=Succ(x1048)  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x410))))), Neg(Succ(Succ(Succ(Succ(x411))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x411)), Succ(Succ(x410)), x411, x410))), Neg(Succ(Succ(Succ(Succ(x410))))), Neg(Succ(Succ(Succ(Succ(x411)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We solved constraint (7) using rule (V) (with possible (I) afterwards).We simplified constraint (8) using rule (V) (with possible (I) afterwards) using induction on new_primEqInt0(x1048)=False which results in the following new constraint:
67.83/34.94	
67.83/34.94	(9)    (False=False & Succ(Succ(x411))=x1051 & Succ(Succ(x410))=x1052 & new_primModNatS01(x1051, x1052, x411, x410)=Succ(x1053)  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x410))))), Neg(Succ(Succ(Succ(Succ(x411))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x411)), Succ(Succ(x410)), x411, x410))), Neg(Succ(Succ(Succ(Succ(x410))))), Neg(Succ(Succ(Succ(Succ(x411)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (9) using rules (I), (II) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(10)    (Succ(Succ(x411))=x1051 & Succ(Succ(x410))=x1052 & new_primModNatS01(x1051, x1052, x411, x410)=Succ(x1053)  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x410))))), Neg(Succ(Succ(Succ(Succ(x411))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x411)), Succ(Succ(x410)), x411, x410))), Neg(Succ(Succ(Succ(Succ(x410))))), Neg(Succ(Succ(Succ(Succ(x411)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (10) using rule (V) (with possible (I) afterwards) using induction on new_primModNatS01(x1051, x1052, x411, x410)=Succ(x1053) which results in the following new constraints:
67.83/34.94	
67.83/34.94	(11)    (new_primModNatS01(x1057, x1056, x1055, x1054)=Succ(x1053) & Succ(Succ(Succ(x1055)))=x1057 & Succ(Succ(Succ(x1054)))=x1056 & (\/x1058:new_primModNatS01(x1057, x1056, x1055, x1054)=Succ(x1058) & Succ(Succ(x1055))=x1057 & Succ(Succ(x1054))=x1056  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x1054))))), Neg(Succ(Succ(Succ(Succ(x1055))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x1055)), Succ(Succ(x1054)), x1055, x1054))), Neg(Succ(Succ(Succ(Succ(x1054))))), Neg(Succ(Succ(Succ(Succ(x1055)))))))  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(x1054)))))), Neg(Succ(Succ(Succ(Succ(Succ(x1055)))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(Succ(x1055))), Succ(Succ(Succ(x1054))), Succ(x1055), Succ(x1054)))), Neg(Succ(Succ(Succ(Succ(Succ(x1054)))))), Neg(Succ(Succ(Succ(Succ(Succ(x1055))))))))
67.83/34.94	
67.83/34.94	(12)    (Succ(Succ(x1061))=Succ(x1053) & Succ(Succ(Zero))=x1061 & Succ(Succ(Succ(x1059)))=x1060  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(x1059)))))), Neg(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(Zero)), Succ(Succ(Succ(x1059))), Zero, Succ(x1059)))), Neg(Succ(Succ(Succ(Succ(Succ(x1059)))))), Neg(Succ(Succ(Succ(Succ(Zero)))))))
67.83/34.94	
67.83/34.94	(13)    (new_primModNatS02(x1063, x1062)=Succ(x1053) & Succ(Succ(Zero))=x1063 & Succ(Succ(Zero))=x1062  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(Zero)), Succ(Succ(Zero)), Zero, Zero))), Neg(Succ(Succ(Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Succ(Zero)))))))
67.83/34.94	
67.83/34.94	(14)    (new_primModNatS02(x1066, x1065)=Succ(x1053) & Succ(Succ(Succ(x1064)))=x1066 & Succ(Succ(Zero))=x1065  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Succ(Succ(x1064)))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(Succ(x1064))), Succ(Succ(Zero)), Succ(x1064), Zero))), Neg(Succ(Succ(Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Succ(Succ(x1064))))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (11) using rule (IV) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(15)    (new_primModNatS01(x1057, x1056, x1055, x1054)=Succ(x1053) & Succ(Succ(Succ(x1055)))=x1057 & Succ(Succ(Succ(x1054)))=x1056  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(x1054)))))), Neg(Succ(Succ(Succ(Succ(Succ(x1055)))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(Succ(x1055))), Succ(Succ(Succ(x1054))), Succ(x1055), Succ(x1054)))), Neg(Succ(Succ(Succ(Succ(Succ(x1054)))))), Neg(Succ(Succ(Succ(Succ(Succ(x1055))))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (12) using rules (I), (II), (IV) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(16)    (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(x1059)))))), Neg(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(Zero)), Succ(Succ(Succ(x1059))), Zero, Succ(x1059)))), Neg(Succ(Succ(Succ(Succ(Succ(x1059)))))), Neg(Succ(Succ(Succ(Succ(Zero)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (13) using rule (V) (with possible (I) afterwards) using induction on new_primModNatS02(x1063, x1062)=Succ(x1053) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(17)    (new_primModNatS1(new_primMinusNatS2(Succ(x1081), Succ(x1080)), Succ(x1080))=Succ(x1053) & Succ(Succ(Zero))=x1081 & Succ(Succ(Zero))=x1080  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(Zero)), Succ(Succ(Zero)), Zero, Zero))), Neg(Succ(Succ(Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Succ(Zero)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (14) using rule (V) (with possible (I) afterwards) using induction on new_primModNatS02(x1066, x1065)=Succ(x1053) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(18)    (new_primModNatS1(new_primMinusNatS2(Succ(x1087), Succ(x1086)), Succ(x1086))=Succ(x1053) & Succ(Succ(Succ(x1064)))=x1087 & Succ(Succ(Zero))=x1086  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Succ(Succ(x1064)))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(Succ(x1064))), Succ(Succ(Zero)), Succ(x1064), Zero))), Neg(Succ(Succ(Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Succ(Succ(x1064))))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (15) using rule (V) (with possible (I) afterwards) using induction on new_primModNatS01(x1057, x1056, x1055, x1054)=Succ(x1053) which results in the following new constraints:
67.83/34.94	
67.83/34.94	(19)    (new_primModNatS01(x1070, x1069, x1068, x1067)=Succ(x1053) & Succ(Succ(Succ(Succ(x1068))))=x1070 & Succ(Succ(Succ(Succ(x1067))))=x1069 & (\/x1071:new_primModNatS01(x1070, x1069, x1068, x1067)=Succ(x1071) & Succ(Succ(Succ(x1068)))=x1070 & Succ(Succ(Succ(x1067)))=x1069  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(x1067)))))), Neg(Succ(Succ(Succ(Succ(Succ(x1068)))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(Succ(x1068))), Succ(Succ(Succ(x1067))), Succ(x1068), Succ(x1067)))), Neg(Succ(Succ(Succ(Succ(Succ(x1067)))))), Neg(Succ(Succ(Succ(Succ(Succ(x1068))))))))  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Succ(x1067))))))), Neg(Succ(Succ(Succ(Succ(Succ(Succ(x1068))))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(Succ(Succ(x1068)))), Succ(Succ(Succ(Succ(x1067)))), Succ(Succ(x1068)), Succ(Succ(x1067))))), Neg(Succ(Succ(Succ(Succ(Succ(Succ(x1067))))))), Neg(Succ(Succ(Succ(Succ(Succ(Succ(x1068)))))))))
67.83/34.94	
67.83/34.94	(20)    (Succ(Succ(x1074))=Succ(x1053) & Succ(Succ(Succ(Zero)))=x1074 & Succ(Succ(Succ(Succ(x1072))))=x1073  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Succ(x1072))))))), Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Succ(x1072)))), Succ(Zero), Succ(Succ(x1072))))), Neg(Succ(Succ(Succ(Succ(Succ(Succ(x1072))))))), Neg(Succ(Succ(Succ(Succ(Succ(Zero))))))))
67.83/34.94	
67.83/34.94	(21)    (new_primModNatS02(x1076, x1075)=Succ(x1053) & Succ(Succ(Succ(Zero)))=x1076 & Succ(Succ(Succ(Zero)))=x1075  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))), Succ(Zero), Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(Succ(Succ(Succ(Succ(Succ(Zero))))))))
67.83/34.94	
67.83/34.94	(22)    (new_primModNatS02(x1079, x1078)=Succ(x1053) & Succ(Succ(Succ(Succ(x1077))))=x1079 & Succ(Succ(Succ(Zero)))=x1078  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(Succ(Succ(Succ(Succ(Succ(Succ(x1077))))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(Succ(Succ(x1077)))), Succ(Succ(Succ(Zero))), Succ(Succ(x1077)), Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(Succ(Succ(Succ(Succ(Succ(Succ(x1077)))))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (19) using rules (III), (IV) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(23)    (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Succ(x1067))))))), Neg(Succ(Succ(Succ(Succ(Succ(Succ(x1068))))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(Succ(Succ(x1068)))), Succ(Succ(Succ(Succ(x1067)))), Succ(Succ(x1068)), Succ(Succ(x1067))))), Neg(Succ(Succ(Succ(Succ(Succ(Succ(x1067))))))), Neg(Succ(Succ(Succ(Succ(Succ(Succ(x1068)))))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (20) using rules (I), (II), (IV) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(24)    (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Succ(x1072))))))), Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Succ(x1072)))), Succ(Zero), Succ(Succ(x1072))))), Neg(Succ(Succ(Succ(Succ(Succ(Succ(x1072))))))), Neg(Succ(Succ(Succ(Succ(Succ(Zero))))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (21) using rules (III), (IV) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(25)    (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))), Succ(Zero), Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(Succ(Succ(Succ(Succ(Succ(Zero))))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (22) using rules (III), (IV) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(26)    (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(Succ(Succ(Succ(Succ(Succ(Succ(x1077))))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(Succ(Succ(x1077)))), Succ(Succ(Succ(Zero))), Succ(Succ(x1077)), Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(Succ(Succ(Succ(Succ(Succ(Succ(x1077)))))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (17) using rules (III), (IV), (VII) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(27)    (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(Zero)), Succ(Succ(Zero)), Zero, Zero))), Neg(Succ(Succ(Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Succ(Zero)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (18) using rules (III), (IV), (VII) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(28)    (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Succ(Succ(x1064)))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(Succ(x1064))), Succ(Succ(Zero)), Succ(x1064), Zero))), Neg(Succ(Succ(Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Succ(Succ(x1064))))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	For Pair new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) the following chains were created:
67.83/34.94	*We consider the chain new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x470))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x470))))), Neg(Succ(Succ(Succ(Zero))))), new_gcd0Gcd'1(False, x471, x472) -> new_gcd0Gcd'0(x471, new_rem(x472, x471)) which results in the following constraint:
67.83/34.94	
67.83/34.94	(1)    (new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x470))))), Neg(Succ(Succ(Succ(Zero)))))=new_gcd0Gcd'1(False, x471, x472)  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x470))))), Neg(Succ(Succ(Succ(Zero)))))_>=_new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x470))))), Neg(Succ(Succ(Succ(Zero))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (1) using rules (I), (II), (IV) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(2)    (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x470))))), Neg(Succ(Succ(Succ(Zero)))))_>=_new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x470))))), Neg(Succ(Succ(Succ(Zero))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	For Pair new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) the following chains were created:
67.83/34.94	*We consider the chain new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x502)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x502), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x502)))))), new_gcd0Gcd'1(False, x503, x504) -> new_gcd0Gcd'0(x503, new_rem(x504, x503)) which results in the following constraint:
67.83/34.94	
67.83/34.94	(1)    (new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x502), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x502))))))=new_gcd0Gcd'1(False, x503, x504)  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x502))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x502), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x502)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (1) using rules (I), (II), (IV), (VII) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(2)    (Neg(new_primModNatS1(Succ(x502), Succ(Succ(Zero))))=x1092 & new_esEs(x1092)=False  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x502))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x502), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x502)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_esEs(x1092)=False which results in the following new constraints:
67.83/34.94	
67.83/34.94	(3)    (new_primEqInt2=False & Neg(new_primModNatS1(Succ(x502), Succ(Succ(Zero))))=Neg(Zero)  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x502))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x502), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x502)))))))
67.83/34.94	
67.83/34.94	(4)    (new_primEqInt1=False & Neg(new_primModNatS1(Succ(x502), Succ(Succ(Zero))))=Pos(Zero)  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x502))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x502), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x502)))))))
67.83/34.94	
67.83/34.94	(5)    (new_primEqInt(x1093)=False & Neg(new_primModNatS1(Succ(x502), Succ(Succ(Zero))))=Pos(Succ(x1093))  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x502))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x502), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x502)))))))
67.83/34.94	
67.83/34.94	(6)    (new_primEqInt0(x1094)=False & Neg(new_primModNatS1(Succ(x502), Succ(Succ(Zero))))=Neg(Succ(x1094))  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x502))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x502), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x502)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (3) using rules (I), (II), (VII) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(7)    (new_primEqInt2=False & Succ(x502)=x1095 & Succ(Succ(Zero))=x1096 & new_primModNatS1(x1095, x1096)=Zero  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x502))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x502), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x502)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We solved constraint (4) using rules (I), (II).We solved constraint (5) using rules (I), (II).We simplified constraint (6) using rules (I), (II), (VII) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(8)    (new_primEqInt0(x1094)=False & Succ(x502)=x1097 & Succ(Succ(Zero))=x1098 & new_primModNatS1(x1097, x1098)=Succ(x1094)  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x502))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x502), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x502)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We solved constraint (7) using rule (V) (with possible (I) afterwards).We simplified constraint (8) using rule (V) (with possible (I) afterwards) using induction on new_primEqInt0(x1094)=False which results in the following new constraint:
67.83/34.94	
67.83/34.94	(9)    (False=False & Succ(x502)=x1097 & Succ(Succ(Zero))=x1098 & new_primModNatS1(x1097, x1098)=Succ(x1099)  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x502))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x502), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x502)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (9) using rules (I), (II) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(10)    (Succ(x502)=x1097 & Succ(Succ(Zero))=x1098 & new_primModNatS1(x1097, x1098)=Succ(x1099)  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x502))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x502), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x502)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (10) using rule (V) (with possible (I) afterwards) using induction on new_primModNatS1(x1097, x1098)=Succ(x1099) which results in the following new constraints:
67.83/34.94	
67.83/34.94	(11)    (new_primModNatS1(new_primMinusNatS0(x1100), Zero)=Succ(x1099) & Succ(x502)=Succ(Succ(x1100)) & Succ(Succ(Zero))=Zero  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x502))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x502), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x502)))))))
67.83/34.94	
67.83/34.94	(12)    (Succ(Zero)=Succ(x1099) & Succ(x502)=Succ(Zero) & Succ(Succ(Zero))=Succ(x1101)  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x502))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x502), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x502)))))))
67.83/34.94	
67.83/34.94	(13)    (new_primModNatS01(x1103, x1102, x1103, x1102)=Succ(x1099) & Succ(x502)=Succ(Succ(x1103)) & Succ(Succ(Zero))=Succ(x1102)  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x502))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x502), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x502)))))))
67.83/34.94	
67.83/34.94	(14)    (new_primModNatS1(new_primMinusNatS1, Zero)=Succ(x1099) & Succ(x502)=Succ(Zero) & Succ(Succ(Zero))=Zero  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x502))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x502), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x502)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We solved constraint (11) using rules (I), (II).We simplified constraint (12) using rules (I), (II), (III), (IV) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(15)    (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(Zero), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(Zero)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (13) using rules (I), (II), (III), (VII) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(16)    (x1103=x1105 & x1102=x1106 & new_primModNatS01(x1103, x1102, x1105, x1106)=Succ(x1099) & Succ(Zero)=x1102  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(Succ(x1103)))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(Succ(x1103)), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(Succ(x1103))))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We solved constraint (14) using rules (I), (II).We simplified constraint (16) using rule (V) (with possible (I) afterwards) using induction on new_primModNatS01(x1103, x1102, x1105, x1106)=Succ(x1099) which results in the following new constraints:
67.83/34.94	
67.83/34.94	(17)    (new_primModNatS01(x1110, x1109, x1108, x1107)=Succ(x1099) & x1110=Succ(x1108) & x1109=Succ(x1107) & Succ(Zero)=x1109 & (\/x1111:new_primModNatS01(x1110, x1109, x1108, x1107)=Succ(x1111) & x1110=x1108 & x1109=x1107 & Succ(Zero)=x1109  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(Succ(x1110)))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(Succ(x1110)), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(Succ(x1110))))))))  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(Succ(x1110)))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(Succ(x1110)), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(Succ(x1110))))))))
67.83/34.94	
67.83/34.94	(18)    (Succ(Succ(x1114))=Succ(x1099) & x1114=Zero & x1113=Succ(x1112) & Succ(Zero)=x1113  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(Succ(x1114)))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(Succ(x1114)), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(Succ(x1114))))))))
67.83/34.94	
67.83/34.94	(19)    (new_primModNatS02(x1116, x1115)=Succ(x1099) & x1116=Zero & x1115=Zero & Succ(Zero)=x1115  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(Succ(x1116)))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(Succ(x1116)), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(Succ(x1116))))))))
67.83/34.94	
67.83/34.94	(20)    (new_primModNatS02(x1119, x1118)=Succ(x1099) & x1119=Succ(x1117) & x1118=Zero & Succ(Zero)=x1118  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(Succ(x1119)))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(Succ(x1119)), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(Succ(x1119))))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (17) using rules (I), (II), (III), (IV), (VII) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(21)    (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(Succ(Succ(x1108))))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(Succ(Succ(x1108))), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(Succ(Succ(x1108)))))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (18) using rules (I), (II), (III), (IV) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(22)    (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(Succ(Zero)), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(Succ(Zero))))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We solved constraint (19) using rules (I), (II), (III).We solved constraint (20) using rules (I), (II), (III).
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	For Pair new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0)))))) the following chains were created:
67.83/34.94	*We consider the chain new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x534)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x534, Zero, x534, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x534)))))), new_gcd0Gcd'1(False, x535, x536) -> new_gcd0Gcd'0(x535, new_rem(x536, x535)) which results in the following constraint:
67.83/34.94	
67.83/34.94	(1)    (new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x534, Zero, x534, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x534))))))=new_gcd0Gcd'1(False, x535, x536)  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x534))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x534, Zero, x534, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x534)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (1) using rules (I), (II), (IV), (VII) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(2)    (Neg(new_primModNatS01(x534, Zero, x534, Zero))=x1122 & new_esEs(x1122)=False  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x534))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x534, Zero, x534, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x534)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_esEs(x1122)=False which results in the following new constraints:
67.83/34.94	
67.83/34.94	(3)    (new_primEqInt2=False & Neg(new_primModNatS01(x534, Zero, x534, Zero))=Neg(Zero)  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x534))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x534, Zero, x534, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x534)))))))
67.83/34.94	
67.83/34.94	(4)    (new_primEqInt1=False & Neg(new_primModNatS01(x534, Zero, x534, Zero))=Pos(Zero)  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x534))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x534, Zero, x534, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x534)))))))
67.83/34.94	
67.83/34.94	(5)    (new_primEqInt(x1123)=False & Neg(new_primModNatS01(x534, Zero, x534, Zero))=Pos(Succ(x1123))  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x534))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x534, Zero, x534, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x534)))))))
67.83/34.94	
67.83/34.94	(6)    (new_primEqInt0(x1124)=False & Neg(new_primModNatS01(x534, Zero, x534, Zero))=Neg(Succ(x1124))  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x534))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x534, Zero, x534, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x534)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (3) using rules (I), (II), (VII) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(7)    (new_primEqInt2=False & Zero=x1125 & x534=x1126 & Zero=x1127 & new_primModNatS01(x534, x1125, x1126, x1127)=Zero  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x534))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x534, Zero, x534, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x534)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We solved constraint (4) using rules (I), (II).We solved constraint (5) using rules (I), (II).We simplified constraint (6) using rules (I), (II), (VII) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(8)    (new_primEqInt0(x1124)=False & Zero=x1128 & x534=x1129 & Zero=x1130 & new_primModNatS01(x534, x1128, x1129, x1130)=Succ(x1124)  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x534))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x534, Zero, x534, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x534)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We solved constraint (7) using rule (V) (with possible (I) afterwards).We simplified constraint (8) using rule (V) (with possible (I) afterwards) using induction on new_primEqInt0(x1124)=False which results in the following new constraint:
67.83/34.94	
67.83/34.94	(9)    (False=False & Zero=x1128 & x534=x1129 & Zero=x1130 & new_primModNatS01(x534, x1128, x1129, x1130)=Succ(x1131)  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x534))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x534, Zero, x534, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x534)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (9) using rules (I), (II) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(10)    (Zero=x1128 & x534=x1129 & Zero=x1130 & new_primModNatS01(x534, x1128, x1129, x1130)=Succ(x1131)  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x534))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x534, Zero, x534, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x534)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (10) using rule (V) (with possible (I) afterwards) using induction on new_primModNatS01(x534, x1128, x1129, x1130)=Succ(x1131) which results in the following new constraints:
67.83/34.94	
67.83/34.94	(11)    (new_primModNatS01(x1135, x1134, x1133, x1132)=Succ(x1131) & Zero=x1134 & x1135=Succ(x1133) & Zero=Succ(x1132) & (\/x1136:new_primModNatS01(x1135, x1134, x1133, x1132)=Succ(x1136) & Zero=x1134 & x1135=x1133 & Zero=x1132  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x1135))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x1135, Zero, x1135, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x1135)))))))  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x1135))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x1135, Zero, x1135, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x1135)))))))
67.83/34.94	
67.83/34.94	(12)    (Succ(Succ(x1139))=Succ(x1131) & Zero=x1138 & x1139=Zero & Zero=Succ(x1137)  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x1139))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x1139, Zero, x1139, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x1139)))))))
67.83/34.94	
67.83/34.94	(13)    (new_primModNatS02(x1141, x1140)=Succ(x1131) & Zero=x1140 & x1141=Zero & Zero=Zero  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x1141))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x1141, Zero, x1141, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x1141)))))))
67.83/34.94	
67.83/34.94	(14)    (new_primModNatS02(x1144, x1143)=Succ(x1131) & Zero=x1143 & x1144=Succ(x1142) & Zero=Zero  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x1144))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x1144, Zero, x1144, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x1144)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We solved constraint (11) using rules (I), (II).We solved constraint (12) using rules (I), (II).We simplified constraint (13) using rules (I), (II), (III), (VII) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(15)    (Zero=x1145 & new_primModNatS02(x1145, x1140)=Succ(x1131) & Zero=x1140  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Zero, Zero, Zero, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(Zero)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (14) using rules (I), (II), (III), (VII) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(16)    (Succ(x1142)=x1152 & new_primModNatS02(x1152, x1143)=Succ(x1131) & Zero=x1143  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(Succ(x1142)))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x1142), Zero, Succ(x1142), Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(Succ(x1142))))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (15) using rule (V) (with possible (I) afterwards) using induction on new_primModNatS02(x1145, x1140)=Succ(x1131) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(17)    (new_primModNatS1(new_primMinusNatS2(Succ(x1147), Succ(x1146)), Succ(x1146))=Succ(x1131) & Zero=x1147 & Zero=x1146  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Zero, Zero, Zero, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(Zero)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (17) using rules (III), (IV), (VII) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(18)    (new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Zero, Zero, Zero, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(Zero)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (16) using rule (V) (with possible (I) afterwards) using induction on new_primModNatS02(x1152, x1143)=Succ(x1131) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(19)    (new_primModNatS1(new_primMinusNatS2(Succ(x1154), Succ(x1153)), Succ(x1153))=Succ(x1131) & Succ(x1142)=x1154 & Zero=x1153  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(Succ(x1142)))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x1142), Zero, Succ(x1142), Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(Succ(x1142))))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (19) using rules (III), (IV), (VII) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(20)    (new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(Succ(x1142)))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x1142), Zero, Succ(x1142), Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(Succ(x1142))))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	For Pair new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) the following chains were created:
67.83/34.94	*We consider the chain new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))), new_gcd0Gcd'1(False, x564, x565) -> new_gcd0Gcd'0(x564, new_rem(x565, x564)) which results in the following constraint:
67.83/34.94	
67.83/34.94	(1)    (new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero)))))=new_gcd0Gcd'1(False, x564, x565)  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero)))))_>=_new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (1) using rules (I), (II), (IV) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(2)    (new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero)))))_>=_new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	For Pair new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) the following chains were created:
67.83/34.94	*We consider the chain new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x570))))), Pos(Succ(Succ(Succ(Succ(x571)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x571)), Succ(Succ(x570)), x571, x570))), Pos(Succ(Succ(Succ(Succ(x570))))), Pos(Succ(Succ(Succ(Succ(x571)))))), new_gcd0Gcd'1(False, x572, x573) -> new_gcd0Gcd'0(x572, new_rem(x573, x572)) which results in the following constraint:
67.83/34.94	
67.83/34.94	(1)    (new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x571)), Succ(Succ(x570)), x571, x570))), Pos(Succ(Succ(Succ(Succ(x570))))), Pos(Succ(Succ(Succ(Succ(x571))))))=new_gcd0Gcd'1(False, x572, x573)  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x570))))), Pos(Succ(Succ(Succ(Succ(x571))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x571)), Succ(Succ(x570)), x571, x570))), Pos(Succ(Succ(Succ(Succ(x570))))), Pos(Succ(Succ(Succ(Succ(x571)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (1) using rules (I), (II), (IV), (VII) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(2)    (Pos(new_primModNatS01(Succ(Succ(x571)), Succ(Succ(x570)), x571, x570))=x1159 & new_esEs(x1159)=False  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x570))))), Pos(Succ(Succ(Succ(Succ(x571))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x571)), Succ(Succ(x570)), x571, x570))), Pos(Succ(Succ(Succ(Succ(x570))))), Pos(Succ(Succ(Succ(Succ(x571)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_esEs(x1159)=False which results in the following new constraints:
67.83/34.94	
67.83/34.94	(3)    (new_primEqInt2=False & Pos(new_primModNatS01(Succ(Succ(x571)), Succ(Succ(x570)), x571, x570))=Neg(Zero)  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x570))))), Pos(Succ(Succ(Succ(Succ(x571))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x571)), Succ(Succ(x570)), x571, x570))), Pos(Succ(Succ(Succ(Succ(x570))))), Pos(Succ(Succ(Succ(Succ(x571)))))))
67.83/34.94	
67.83/34.94	(4)    (new_primEqInt1=False & Pos(new_primModNatS01(Succ(Succ(x571)), Succ(Succ(x570)), x571, x570))=Pos(Zero)  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x570))))), Pos(Succ(Succ(Succ(Succ(x571))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x571)), Succ(Succ(x570)), x571, x570))), Pos(Succ(Succ(Succ(Succ(x570))))), Pos(Succ(Succ(Succ(Succ(x571)))))))
67.83/34.94	
67.83/34.94	(5)    (new_primEqInt(x1160)=False & Pos(new_primModNatS01(Succ(Succ(x571)), Succ(Succ(x570)), x571, x570))=Pos(Succ(x1160))  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x570))))), Pos(Succ(Succ(Succ(Succ(x571))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x571)), Succ(Succ(x570)), x571, x570))), Pos(Succ(Succ(Succ(Succ(x570))))), Pos(Succ(Succ(Succ(Succ(x571)))))))
67.83/34.94	
67.83/34.94	(6)    (new_primEqInt0(x1161)=False & Pos(new_primModNatS01(Succ(Succ(x571)), Succ(Succ(x570)), x571, x570))=Neg(Succ(x1161))  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x570))))), Pos(Succ(Succ(Succ(Succ(x571))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x571)), Succ(Succ(x570)), x571, x570))), Pos(Succ(Succ(Succ(Succ(x570))))), Pos(Succ(Succ(Succ(Succ(x571)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We solved constraint (3) using rules (I), (II).We simplified constraint (4) using rules (I), (II), (VII) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(7)    (new_primEqInt1=False & Succ(Succ(x571))=x1162 & Succ(Succ(x570))=x1163 & new_primModNatS01(x1162, x1163, x571, x570)=Zero  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x570))))), Pos(Succ(Succ(Succ(Succ(x571))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x571)), Succ(Succ(x570)), x571, x570))), Pos(Succ(Succ(Succ(Succ(x570))))), Pos(Succ(Succ(Succ(Succ(x571)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (5) using rules (I), (II), (VII) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(8)    (new_primEqInt(x1160)=False & Succ(Succ(x571))=x1164 & Succ(Succ(x570))=x1165 & new_primModNatS01(x1164, x1165, x571, x570)=Succ(x1160)  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x570))))), Pos(Succ(Succ(Succ(Succ(x571))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x571)), Succ(Succ(x570)), x571, x570))), Pos(Succ(Succ(Succ(Succ(x570))))), Pos(Succ(Succ(Succ(Succ(x571)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We solved constraint (6) using rules (I), (II).We solved constraint (7) using rule (V) (with possible (I) afterwards).We simplified constraint (8) using rule (V) (with possible (I) afterwards) using induction on new_primEqInt(x1160)=False which results in the following new constraint:
67.83/34.94	
67.83/34.94	(9)    (False=False & Succ(Succ(x571))=x1164 & Succ(Succ(x570))=x1165 & new_primModNatS01(x1164, x1165, x571, x570)=Succ(x1166)  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x570))))), Pos(Succ(Succ(Succ(Succ(x571))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x571)), Succ(Succ(x570)), x571, x570))), Pos(Succ(Succ(Succ(Succ(x570))))), Pos(Succ(Succ(Succ(Succ(x571)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (9) using rules (I), (II) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(10)    (Succ(Succ(x571))=x1164 & Succ(Succ(x570))=x1165 & new_primModNatS01(x1164, x1165, x571, x570)=Succ(x1166)  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x570))))), Pos(Succ(Succ(Succ(Succ(x571))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x571)), Succ(Succ(x570)), x571, x570))), Pos(Succ(Succ(Succ(Succ(x570))))), Pos(Succ(Succ(Succ(Succ(x571)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (10) using rule (V) (with possible (I) afterwards) using induction on new_primModNatS01(x1164, x1165, x571, x570)=Succ(x1166) which results in the following new constraints:
67.83/34.94	
67.83/34.94	(11)    (new_primModNatS01(x1170, x1169, x1168, x1167)=Succ(x1166) & Succ(Succ(Succ(x1168)))=x1170 & Succ(Succ(Succ(x1167)))=x1169 & (\/x1171:new_primModNatS01(x1170, x1169, x1168, x1167)=Succ(x1171) & Succ(Succ(x1168))=x1170 & Succ(Succ(x1167))=x1169  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x1167))))), Pos(Succ(Succ(Succ(Succ(x1168))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x1168)), Succ(Succ(x1167)), x1168, x1167))), Pos(Succ(Succ(Succ(Succ(x1167))))), Pos(Succ(Succ(Succ(Succ(x1168)))))))  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(x1167)))))), Pos(Succ(Succ(Succ(Succ(Succ(x1168)))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(Succ(x1168))), Succ(Succ(Succ(x1167))), Succ(x1168), Succ(x1167)))), Pos(Succ(Succ(Succ(Succ(Succ(x1167)))))), Pos(Succ(Succ(Succ(Succ(Succ(x1168))))))))
67.83/34.94	
67.83/34.94	(12)    (Succ(Succ(x1174))=Succ(x1166) & Succ(Succ(Zero))=x1174 & Succ(Succ(Succ(x1172)))=x1173  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(x1172)))))), Pos(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(Zero)), Succ(Succ(Succ(x1172))), Zero, Succ(x1172)))), Pos(Succ(Succ(Succ(Succ(Succ(x1172)))))), Pos(Succ(Succ(Succ(Succ(Zero)))))))
67.83/34.94	
67.83/34.94	(13)    (new_primModNatS02(x1176, x1175)=Succ(x1166) & Succ(Succ(Zero))=x1176 & Succ(Succ(Zero))=x1175  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(Zero)), Succ(Succ(Zero)), Zero, Zero))), Pos(Succ(Succ(Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Succ(Zero)))))))
67.83/34.94	
67.83/34.94	(14)    (new_primModNatS02(x1179, x1178)=Succ(x1166) & Succ(Succ(Succ(x1177)))=x1179 & Succ(Succ(Zero))=x1178  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Succ(Succ(x1177)))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(Succ(x1177))), Succ(Succ(Zero)), Succ(x1177), Zero))), Pos(Succ(Succ(Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Succ(Succ(x1177))))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (11) using rule (IV) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(15)    (new_primModNatS01(x1170, x1169, x1168, x1167)=Succ(x1166) & Succ(Succ(Succ(x1168)))=x1170 & Succ(Succ(Succ(x1167)))=x1169  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(x1167)))))), Pos(Succ(Succ(Succ(Succ(Succ(x1168)))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(Succ(x1168))), Succ(Succ(Succ(x1167))), Succ(x1168), Succ(x1167)))), Pos(Succ(Succ(Succ(Succ(Succ(x1167)))))), Pos(Succ(Succ(Succ(Succ(Succ(x1168))))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (12) using rules (I), (II), (IV) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(16)    (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(x1172)))))), Pos(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(Zero)), Succ(Succ(Succ(x1172))), Zero, Succ(x1172)))), Pos(Succ(Succ(Succ(Succ(Succ(x1172)))))), Pos(Succ(Succ(Succ(Succ(Zero)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (13) using rule (V) (with possible (I) afterwards) using induction on new_primModNatS02(x1176, x1175)=Succ(x1166) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(17)    (new_primModNatS1(new_primMinusNatS2(Succ(x1194), Succ(x1193)), Succ(x1193))=Succ(x1166) & Succ(Succ(Zero))=x1194 & Succ(Succ(Zero))=x1193  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(Zero)), Succ(Succ(Zero)), Zero, Zero))), Pos(Succ(Succ(Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Succ(Zero)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (14) using rule (V) (with possible (I) afterwards) using induction on new_primModNatS02(x1179, x1178)=Succ(x1166) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(18)    (new_primModNatS1(new_primMinusNatS2(Succ(x1200), Succ(x1199)), Succ(x1199))=Succ(x1166) & Succ(Succ(Succ(x1177)))=x1200 & Succ(Succ(Zero))=x1199  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Succ(Succ(x1177)))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(Succ(x1177))), Succ(Succ(Zero)), Succ(x1177), Zero))), Pos(Succ(Succ(Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Succ(Succ(x1177))))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (15) using rule (V) (with possible (I) afterwards) using induction on new_primModNatS01(x1170, x1169, x1168, x1167)=Succ(x1166) which results in the following new constraints:
67.83/34.94	
67.83/34.94	(19)    (new_primModNatS01(x1183, x1182, x1181, x1180)=Succ(x1166) & Succ(Succ(Succ(Succ(x1181))))=x1183 & Succ(Succ(Succ(Succ(x1180))))=x1182 & (\/x1184:new_primModNatS01(x1183, x1182, x1181, x1180)=Succ(x1184) & Succ(Succ(Succ(x1181)))=x1183 & Succ(Succ(Succ(x1180)))=x1182  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(x1180)))))), Pos(Succ(Succ(Succ(Succ(Succ(x1181)))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(Succ(x1181))), Succ(Succ(Succ(x1180))), Succ(x1181), Succ(x1180)))), Pos(Succ(Succ(Succ(Succ(Succ(x1180)))))), Pos(Succ(Succ(Succ(Succ(Succ(x1181))))))))  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Succ(x1180))))))), Pos(Succ(Succ(Succ(Succ(Succ(Succ(x1181))))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(Succ(Succ(x1181)))), Succ(Succ(Succ(Succ(x1180)))), Succ(Succ(x1181)), Succ(Succ(x1180))))), Pos(Succ(Succ(Succ(Succ(Succ(Succ(x1180))))))), Pos(Succ(Succ(Succ(Succ(Succ(Succ(x1181)))))))))
67.83/34.94	
67.83/34.94	(20)    (Succ(Succ(x1187))=Succ(x1166) & Succ(Succ(Succ(Zero)))=x1187 & Succ(Succ(Succ(Succ(x1185))))=x1186  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Succ(x1185))))))), Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Succ(x1185)))), Succ(Zero), Succ(Succ(x1185))))), Pos(Succ(Succ(Succ(Succ(Succ(Succ(x1185))))))), Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))))
67.83/34.94	
67.83/34.94	(21)    (new_primModNatS02(x1189, x1188)=Succ(x1166) & Succ(Succ(Succ(Zero)))=x1189 & Succ(Succ(Succ(Zero)))=x1188  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))), Succ(Zero), Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))))
67.83/34.94	
67.83/34.94	(22)    (new_primModNatS02(x1192, x1191)=Succ(x1166) & Succ(Succ(Succ(Succ(x1190))))=x1192 & Succ(Succ(Succ(Zero)))=x1191  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(Succ(Succ(Succ(Succ(Succ(Succ(x1190))))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(Succ(Succ(x1190)))), Succ(Succ(Succ(Zero))), Succ(Succ(x1190)), Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(Succ(Succ(Succ(Succ(Succ(Succ(x1190)))))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (19) using rules (III), (IV) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(23)    (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Succ(x1180))))))), Pos(Succ(Succ(Succ(Succ(Succ(Succ(x1181))))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(Succ(Succ(x1181)))), Succ(Succ(Succ(Succ(x1180)))), Succ(Succ(x1181)), Succ(Succ(x1180))))), Pos(Succ(Succ(Succ(Succ(Succ(Succ(x1180))))))), Pos(Succ(Succ(Succ(Succ(Succ(Succ(x1181)))))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (20) using rules (I), (II), (IV) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(24)    (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Succ(x1185))))))), Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Succ(x1185)))), Succ(Zero), Succ(Succ(x1185))))), Pos(Succ(Succ(Succ(Succ(Succ(Succ(x1185))))))), Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (21) using rules (III), (IV) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(25)    (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))), Succ(Zero), Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (22) using rules (III), (IV) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(26)    (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(Succ(Succ(Succ(Succ(Succ(Succ(x1190))))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(Succ(Succ(x1190)))), Succ(Succ(Succ(Zero))), Succ(Succ(x1190)), Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(Succ(Succ(Succ(Succ(Succ(Succ(x1190)))))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (17) using rules (III), (IV), (VII) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(27)    (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(Zero)), Succ(Succ(Zero)), Zero, Zero))), Pos(Succ(Succ(Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Succ(Zero)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (18) using rules (III), (IV), (VII) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(28)    (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Succ(Succ(x1177)))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(Succ(x1177))), Succ(Succ(Zero)), Succ(x1177), Zero))), Pos(Succ(Succ(Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Succ(Succ(x1177))))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	For Pair new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) the following chains were created:
67.83/34.94	*We consider the chain new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x630))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(Succ(x630))))), Pos(Succ(Succ(Succ(Zero))))), new_gcd0Gcd'1(False, x631, x632) -> new_gcd0Gcd'0(x631, new_rem(x632, x631)) which results in the following constraint:
67.83/34.94	
67.83/34.94	(1)    (new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(Succ(x630))))), Pos(Succ(Succ(Succ(Zero)))))=new_gcd0Gcd'1(False, x631, x632)  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x630))))), Pos(Succ(Succ(Succ(Zero)))))_>=_new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(Succ(x630))))), Pos(Succ(Succ(Succ(Zero))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (1) using rules (I), (II), (IV) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(2)    (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x630))))), Pos(Succ(Succ(Succ(Zero)))))_>=_new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(Succ(x630))))), Pos(Succ(Succ(Succ(Zero))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	For Pair new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) the following chains were created:
67.83/34.94	*We consider the chain new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x662)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x662), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x662)))))), new_gcd0Gcd'1(False, x663, x664) -> new_gcd0Gcd'0(x663, new_rem(x664, x663)) which results in the following constraint:
67.83/34.94	
67.83/34.94	(1)    (new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x662), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x662))))))=new_gcd0Gcd'1(False, x663, x664)  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x662))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x662), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x662)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (1) using rules (I), (II), (IV), (VII) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(2)    (Pos(new_primModNatS1(Succ(x662), Succ(Succ(Zero))))=x1205 & new_esEs(x1205)=False  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x662))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x662), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x662)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_esEs(x1205)=False which results in the following new constraints:
67.83/34.94	
67.83/34.94	(3)    (new_primEqInt2=False & Pos(new_primModNatS1(Succ(x662), Succ(Succ(Zero))))=Neg(Zero)  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x662))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x662), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x662)))))))
67.83/34.94	
67.83/34.94	(4)    (new_primEqInt1=False & Pos(new_primModNatS1(Succ(x662), Succ(Succ(Zero))))=Pos(Zero)  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x662))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x662), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x662)))))))
67.83/34.94	
67.83/34.94	(5)    (new_primEqInt(x1206)=False & Pos(new_primModNatS1(Succ(x662), Succ(Succ(Zero))))=Pos(Succ(x1206))  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x662))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x662), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x662)))))))
67.83/34.94	
67.83/34.94	(6)    (new_primEqInt0(x1207)=False & Pos(new_primModNatS1(Succ(x662), Succ(Succ(Zero))))=Neg(Succ(x1207))  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x662))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x662), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x662)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We solved constraint (3) using rules (I), (II).We simplified constraint (4) using rules (I), (II), (VII) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(7)    (new_primEqInt1=False & Succ(x662)=x1208 & Succ(Succ(Zero))=x1209 & new_primModNatS1(x1208, x1209)=Zero  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x662))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x662), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x662)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (5) using rules (I), (II), (VII) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(8)    (new_primEqInt(x1206)=False & Succ(x662)=x1210 & Succ(Succ(Zero))=x1211 & new_primModNatS1(x1210, x1211)=Succ(x1206)  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x662))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x662), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x662)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We solved constraint (6) using rules (I), (II).We solved constraint (7) using rule (V) (with possible (I) afterwards).We simplified constraint (8) using rule (V) (with possible (I) afterwards) using induction on new_primEqInt(x1206)=False which results in the following new constraint:
67.83/34.94	
67.83/34.94	(9)    (False=False & Succ(x662)=x1210 & Succ(Succ(Zero))=x1211 & new_primModNatS1(x1210, x1211)=Succ(x1212)  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x662))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x662), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x662)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (9) using rules (I), (II) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(10)    (Succ(x662)=x1210 & Succ(Succ(Zero))=x1211 & new_primModNatS1(x1210, x1211)=Succ(x1212)  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x662))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x662), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x662)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (10) using rule (V) (with possible (I) afterwards) using induction on new_primModNatS1(x1210, x1211)=Succ(x1212) which results in the following new constraints:
67.83/34.94	
67.83/34.94	(11)    (new_primModNatS1(new_primMinusNatS0(x1213), Zero)=Succ(x1212) & Succ(x662)=Succ(Succ(x1213)) & Succ(Succ(Zero))=Zero  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x662))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x662), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x662)))))))
67.83/34.94	
67.83/34.94	(12)    (Succ(Zero)=Succ(x1212) & Succ(x662)=Succ(Zero) & Succ(Succ(Zero))=Succ(x1214)  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x662))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x662), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x662)))))))
67.83/34.94	
67.83/34.94	(13)    (new_primModNatS01(x1216, x1215, x1216, x1215)=Succ(x1212) & Succ(x662)=Succ(Succ(x1216)) & Succ(Succ(Zero))=Succ(x1215)  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x662))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x662), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x662)))))))
67.83/34.94	
67.83/34.94	(14)    (new_primModNatS1(new_primMinusNatS1, Zero)=Succ(x1212) & Succ(x662)=Succ(Zero) & Succ(Succ(Zero))=Zero  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x662))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x662), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x662)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We solved constraint (11) using rules (I), (II).We simplified constraint (12) using rules (I), (II), (III), (IV) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(15)    (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(Zero), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(Zero)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (13) using rules (I), (II), (III), (VII) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(16)    (x1216=x1218 & x1215=x1219 & new_primModNatS01(x1216, x1215, x1218, x1219)=Succ(x1212) & Succ(Zero)=x1215  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(Succ(x1216)))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(Succ(x1216)), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(Succ(x1216))))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We solved constraint (14) using rules (I), (II).We simplified constraint (16) using rule (V) (with possible (I) afterwards) using induction on new_primModNatS01(x1216, x1215, x1218, x1219)=Succ(x1212) which results in the following new constraints:
67.83/34.94	
67.83/34.94	(17)    (new_primModNatS01(x1223, x1222, x1221, x1220)=Succ(x1212) & x1223=Succ(x1221) & x1222=Succ(x1220) & Succ(Zero)=x1222 & (\/x1224:new_primModNatS01(x1223, x1222, x1221, x1220)=Succ(x1224) & x1223=x1221 & x1222=x1220 & Succ(Zero)=x1222  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(Succ(x1223)))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(Succ(x1223)), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(Succ(x1223))))))))  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(Succ(x1223)))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(Succ(x1223)), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(Succ(x1223))))))))
67.83/34.94	
67.83/34.94	(18)    (Succ(Succ(x1227))=Succ(x1212) & x1227=Zero & x1226=Succ(x1225) & Succ(Zero)=x1226  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(Succ(x1227)))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(Succ(x1227)), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(Succ(x1227))))))))
67.83/34.94	
67.83/34.94	(19)    (new_primModNatS02(x1229, x1228)=Succ(x1212) & x1229=Zero & x1228=Zero & Succ(Zero)=x1228  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(Succ(x1229)))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(Succ(x1229)), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(Succ(x1229))))))))
67.83/34.94	
67.83/34.94	(20)    (new_primModNatS02(x1232, x1231)=Succ(x1212) & x1232=Succ(x1230) & x1231=Zero & Succ(Zero)=x1231  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(Succ(x1232)))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(Succ(x1232)), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(Succ(x1232))))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (17) using rules (I), (II), (III), (IV), (VII) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(21)    (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(Succ(Succ(x1221))))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(Succ(Succ(x1221))), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(Succ(Succ(x1221)))))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (18) using rules (I), (II), (III), (IV) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(22)    (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(Succ(Zero)), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We solved constraint (19) using rules (I), (II), (III).We solved constraint (20) using rules (I), (II), (III).
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	For Pair new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, Zero, x0, Zero))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0)))))) the following chains were created:
67.83/34.94	*We consider the chain new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x694)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x694, Zero, x694, Zero))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x694)))))), new_gcd0Gcd'1(False, x695, x696) -> new_gcd0Gcd'0(x695, new_rem(x696, x695)) which results in the following constraint:
67.83/34.94	
67.83/34.94	(1)    (new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x694, Zero, x694, Zero))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x694))))))=new_gcd0Gcd'1(False, x695, x696)  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x694))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x694, Zero, x694, Zero))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x694)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (1) using rules (I), (II), (IV), (VII) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(2)    (Pos(new_primModNatS01(x694, Zero, x694, Zero))=x1235 & new_esEs(x1235)=False  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x694))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x694, Zero, x694, Zero))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x694)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_esEs(x1235)=False which results in the following new constraints:
67.83/34.94	
67.83/34.94	(3)    (new_primEqInt2=False & Pos(new_primModNatS01(x694, Zero, x694, Zero))=Neg(Zero)  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x694))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x694, Zero, x694, Zero))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x694)))))))
67.83/34.94	
67.83/34.94	(4)    (new_primEqInt1=False & Pos(new_primModNatS01(x694, Zero, x694, Zero))=Pos(Zero)  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x694))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x694, Zero, x694, Zero))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x694)))))))
67.83/34.94	
67.83/34.94	(5)    (new_primEqInt(x1236)=False & Pos(new_primModNatS01(x694, Zero, x694, Zero))=Pos(Succ(x1236))  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x694))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x694, Zero, x694, Zero))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x694)))))))
67.83/34.94	
67.83/34.94	(6)    (new_primEqInt0(x1237)=False & Pos(new_primModNatS01(x694, Zero, x694, Zero))=Neg(Succ(x1237))  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x694))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x694, Zero, x694, Zero))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x694)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We solved constraint (3) using rules (I), (II).We simplified constraint (4) using rules (I), (II), (VII) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(7)    (new_primEqInt1=False & Zero=x1238 & x694=x1239 & Zero=x1240 & new_primModNatS01(x694, x1238, x1239, x1240)=Zero  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x694))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x694, Zero, x694, Zero))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x694)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (5) using rules (I), (II), (VII) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(8)    (new_primEqInt(x1236)=False & Zero=x1241 & x694=x1242 & Zero=x1243 & new_primModNatS01(x694, x1241, x1242, x1243)=Succ(x1236)  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x694))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x694, Zero, x694, Zero))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x694)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We solved constraint (6) using rules (I), (II).We solved constraint (7) using rule (V) (with possible (I) afterwards).We simplified constraint (8) using rule (V) (with possible (I) afterwards) using induction on new_primEqInt(x1236)=False which results in the following new constraint:
67.83/34.94	
67.83/34.94	(9)    (False=False & Zero=x1241 & x694=x1242 & Zero=x1243 & new_primModNatS01(x694, x1241, x1242, x1243)=Succ(x1244)  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x694))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x694, Zero, x694, Zero))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x694)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (9) using rules (I), (II) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(10)    (Zero=x1241 & x694=x1242 & Zero=x1243 & new_primModNatS01(x694, x1241, x1242, x1243)=Succ(x1244)  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x694))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x694, Zero, x694, Zero))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x694)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (10) using rule (V) (with possible (I) afterwards) using induction on new_primModNatS01(x694, x1241, x1242, x1243)=Succ(x1244) which results in the following new constraints:
67.83/34.94	
67.83/34.94	(11)    (new_primModNatS01(x1248, x1247, x1246, x1245)=Succ(x1244) & Zero=x1247 & x1248=Succ(x1246) & Zero=Succ(x1245) & (\/x1249:new_primModNatS01(x1248, x1247, x1246, x1245)=Succ(x1249) & Zero=x1247 & x1248=x1246 & Zero=x1245  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x1248))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x1248, Zero, x1248, Zero))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x1248)))))))  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x1248))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x1248, Zero, x1248, Zero))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x1248)))))))
67.83/34.94	
67.83/34.94	(12)    (Succ(Succ(x1252))=Succ(x1244) & Zero=x1251 & x1252=Zero & Zero=Succ(x1250)  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x1252))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x1252, Zero, x1252, Zero))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x1252)))))))
67.83/34.94	
67.83/34.94	(13)    (new_primModNatS02(x1254, x1253)=Succ(x1244) & Zero=x1253 & x1254=Zero & Zero=Zero  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x1254))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x1254, Zero, x1254, Zero))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x1254)))))))
67.83/34.94	
67.83/34.94	(14)    (new_primModNatS02(x1257, x1256)=Succ(x1244) & Zero=x1256 & x1257=Succ(x1255) & Zero=Zero  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x1257))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x1257, Zero, x1257, Zero))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x1257)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We solved constraint (11) using rules (I), (II).We solved constraint (12) using rules (I), (II).We simplified constraint (13) using rules (I), (II), (III), (VII) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(15)    (Zero=x1258 & new_primModNatS02(x1258, x1253)=Succ(x1244) & Zero=x1253  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Zero, Zero, Zero, Zero))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(Zero)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (14) using rules (I), (II), (III), (VII) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(16)    (Succ(x1255)=x1265 & new_primModNatS02(x1265, x1256)=Succ(x1244) & Zero=x1256  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(Succ(x1255)))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x1255), Zero, Succ(x1255), Zero))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(Succ(x1255))))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (15) using rule (V) (with possible (I) afterwards) using induction on new_primModNatS02(x1258, x1253)=Succ(x1244) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(17)    (new_primModNatS1(new_primMinusNatS2(Succ(x1260), Succ(x1259)), Succ(x1259))=Succ(x1244) & Zero=x1260 & Zero=x1259  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Zero, Zero, Zero, Zero))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(Zero)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (17) using rules (III), (IV), (VII) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(18)    (new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Zero, Zero, Zero, Zero))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(Zero)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (16) using rule (V) (with possible (I) afterwards) using induction on new_primModNatS02(x1265, x1256)=Succ(x1244) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(19)    (new_primModNatS1(new_primMinusNatS2(Succ(x1267), Succ(x1266)), Succ(x1266))=Succ(x1244) & Succ(x1255)=x1267 & Zero=x1266  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(Succ(x1255)))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x1255), Zero, Succ(x1255), Zero))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(Succ(x1255))))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (19) using rules (III), (IV), (VII) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(20)    (new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(Succ(x1255)))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x1255), Zero, Succ(x1255), Zero))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(Succ(x1255))))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	For Pair new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) the following chains were created:
67.83/34.94	*We consider the chain new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))), new_gcd0Gcd'1(False, x724, x725) -> new_gcd0Gcd'0(x724, new_rem(x725, x724)) which results in the following constraint:
67.83/34.94	
67.83/34.94	(1)    (new_gcd0Gcd'1(False, Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero)))))=new_gcd0Gcd'1(False, x724, x725)  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero)))))_>=_new_gcd0Gcd'1(False, Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (1) using rules (I), (II), (IV) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(2)    (new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero)))))_>=_new_gcd0Gcd'1(False, Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	For Pair new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) the following chains were created:
67.83/34.94	*We consider the chain new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x730))))), Pos(Succ(Succ(Succ(Succ(x731)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x731)), Succ(Succ(x730)), x731, x730))), Neg(Succ(Succ(Succ(Succ(x730))))), Pos(Succ(Succ(Succ(Succ(x731)))))), new_gcd0Gcd'1(False, x732, x733) -> new_gcd0Gcd'0(x732, new_rem(x733, x732)) which results in the following constraint:
67.83/34.94	
67.83/34.94	(1)    (new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x731)), Succ(Succ(x730)), x731, x730))), Neg(Succ(Succ(Succ(Succ(x730))))), Pos(Succ(Succ(Succ(Succ(x731))))))=new_gcd0Gcd'1(False, x732, x733)  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x730))))), Pos(Succ(Succ(Succ(Succ(x731))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x731)), Succ(Succ(x730)), x731, x730))), Neg(Succ(Succ(Succ(Succ(x730))))), Pos(Succ(Succ(Succ(Succ(x731)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (1) using rules (I), (II), (IV), (VII) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(2)    (Pos(new_primModNatS01(Succ(Succ(x731)), Succ(Succ(x730)), x731, x730))=x1272 & new_esEs(x1272)=False  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x730))))), Pos(Succ(Succ(Succ(Succ(x731))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x731)), Succ(Succ(x730)), x731, x730))), Neg(Succ(Succ(Succ(Succ(x730))))), Pos(Succ(Succ(Succ(Succ(x731)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_esEs(x1272)=False which results in the following new constraints:
67.83/34.94	
67.83/34.94	(3)    (new_primEqInt2=False & Pos(new_primModNatS01(Succ(Succ(x731)), Succ(Succ(x730)), x731, x730))=Neg(Zero)  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x730))))), Pos(Succ(Succ(Succ(Succ(x731))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x731)), Succ(Succ(x730)), x731, x730))), Neg(Succ(Succ(Succ(Succ(x730))))), Pos(Succ(Succ(Succ(Succ(x731)))))))
67.83/34.94	
67.83/34.94	(4)    (new_primEqInt1=False & Pos(new_primModNatS01(Succ(Succ(x731)), Succ(Succ(x730)), x731, x730))=Pos(Zero)  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x730))))), Pos(Succ(Succ(Succ(Succ(x731))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x731)), Succ(Succ(x730)), x731, x730))), Neg(Succ(Succ(Succ(Succ(x730))))), Pos(Succ(Succ(Succ(Succ(x731)))))))
67.83/34.94	
67.83/34.94	(5)    (new_primEqInt(x1273)=False & Pos(new_primModNatS01(Succ(Succ(x731)), Succ(Succ(x730)), x731, x730))=Pos(Succ(x1273))  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x730))))), Pos(Succ(Succ(Succ(Succ(x731))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x731)), Succ(Succ(x730)), x731, x730))), Neg(Succ(Succ(Succ(Succ(x730))))), Pos(Succ(Succ(Succ(Succ(x731)))))))
67.83/34.94	
67.83/34.94	(6)    (new_primEqInt0(x1274)=False & Pos(new_primModNatS01(Succ(Succ(x731)), Succ(Succ(x730)), x731, x730))=Neg(Succ(x1274))  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x730))))), Pos(Succ(Succ(Succ(Succ(x731))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x731)), Succ(Succ(x730)), x731, x730))), Neg(Succ(Succ(Succ(Succ(x730))))), Pos(Succ(Succ(Succ(Succ(x731)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We solved constraint (3) using rules (I), (II).We simplified constraint (4) using rules (I), (II), (VII) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(7)    (new_primEqInt1=False & Succ(Succ(x731))=x1275 & Succ(Succ(x730))=x1276 & new_primModNatS01(x1275, x1276, x731, x730)=Zero  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x730))))), Pos(Succ(Succ(Succ(Succ(x731))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x731)), Succ(Succ(x730)), x731, x730))), Neg(Succ(Succ(Succ(Succ(x730))))), Pos(Succ(Succ(Succ(Succ(x731)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (5) using rules (I), (II), (VII) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(8)    (new_primEqInt(x1273)=False & Succ(Succ(x731))=x1277 & Succ(Succ(x730))=x1278 & new_primModNatS01(x1277, x1278, x731, x730)=Succ(x1273)  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x730))))), Pos(Succ(Succ(Succ(Succ(x731))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x731)), Succ(Succ(x730)), x731, x730))), Neg(Succ(Succ(Succ(Succ(x730))))), Pos(Succ(Succ(Succ(Succ(x731)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We solved constraint (6) using rules (I), (II).We solved constraint (7) using rule (V) (with possible (I) afterwards).We simplified constraint (8) using rule (V) (with possible (I) afterwards) using induction on new_primEqInt(x1273)=False which results in the following new constraint:
67.83/34.94	
67.83/34.94	(9)    (False=False & Succ(Succ(x731))=x1277 & Succ(Succ(x730))=x1278 & new_primModNatS01(x1277, x1278, x731, x730)=Succ(x1279)  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x730))))), Pos(Succ(Succ(Succ(Succ(x731))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x731)), Succ(Succ(x730)), x731, x730))), Neg(Succ(Succ(Succ(Succ(x730))))), Pos(Succ(Succ(Succ(Succ(x731)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (9) using rules (I), (II) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(10)    (Succ(Succ(x731))=x1277 & Succ(Succ(x730))=x1278 & new_primModNatS01(x1277, x1278, x731, x730)=Succ(x1279)  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x730))))), Pos(Succ(Succ(Succ(Succ(x731))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x731)), Succ(Succ(x730)), x731, x730))), Neg(Succ(Succ(Succ(Succ(x730))))), Pos(Succ(Succ(Succ(Succ(x731)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (10) using rule (V) (with possible (I) afterwards) using induction on new_primModNatS01(x1277, x1278, x731, x730)=Succ(x1279) which results in the following new constraints:
67.83/34.94	
67.83/34.94	(11)    (new_primModNatS01(x1283, x1282, x1281, x1280)=Succ(x1279) & Succ(Succ(Succ(x1281)))=x1283 & Succ(Succ(Succ(x1280)))=x1282 & (\/x1284:new_primModNatS01(x1283, x1282, x1281, x1280)=Succ(x1284) & Succ(Succ(x1281))=x1283 & Succ(Succ(x1280))=x1282  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x1280))))), Pos(Succ(Succ(Succ(Succ(x1281))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x1281)), Succ(Succ(x1280)), x1281, x1280))), Neg(Succ(Succ(Succ(Succ(x1280))))), Pos(Succ(Succ(Succ(Succ(x1281)))))))  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(x1280)))))), Pos(Succ(Succ(Succ(Succ(Succ(x1281)))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(Succ(x1281))), Succ(Succ(Succ(x1280))), Succ(x1281), Succ(x1280)))), Neg(Succ(Succ(Succ(Succ(Succ(x1280)))))), Pos(Succ(Succ(Succ(Succ(Succ(x1281))))))))
67.83/34.94	
67.83/34.94	(12)    (Succ(Succ(x1287))=Succ(x1279) & Succ(Succ(Zero))=x1287 & Succ(Succ(Succ(x1285)))=x1286  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(x1285)))))), Pos(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(Zero)), Succ(Succ(Succ(x1285))), Zero, Succ(x1285)))), Neg(Succ(Succ(Succ(Succ(Succ(x1285)))))), Pos(Succ(Succ(Succ(Succ(Zero)))))))
67.83/34.94	
67.83/34.94	(13)    (new_primModNatS02(x1289, x1288)=Succ(x1279) & Succ(Succ(Zero))=x1289 & Succ(Succ(Zero))=x1288  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(Zero)), Succ(Succ(Zero)), Zero, Zero))), Neg(Succ(Succ(Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Succ(Zero)))))))
67.83/34.94	
67.83/34.94	(14)    (new_primModNatS02(x1292, x1291)=Succ(x1279) & Succ(Succ(Succ(x1290)))=x1292 & Succ(Succ(Zero))=x1291  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Succ(Succ(x1290)))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(Succ(x1290))), Succ(Succ(Zero)), Succ(x1290), Zero))), Neg(Succ(Succ(Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Succ(Succ(x1290))))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (11) using rule (IV) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(15)    (new_primModNatS01(x1283, x1282, x1281, x1280)=Succ(x1279) & Succ(Succ(Succ(x1281)))=x1283 & Succ(Succ(Succ(x1280)))=x1282  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(x1280)))))), Pos(Succ(Succ(Succ(Succ(Succ(x1281)))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(Succ(x1281))), Succ(Succ(Succ(x1280))), Succ(x1281), Succ(x1280)))), Neg(Succ(Succ(Succ(Succ(Succ(x1280)))))), Pos(Succ(Succ(Succ(Succ(Succ(x1281))))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (12) using rules (I), (II), (IV) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(16)    (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(x1285)))))), Pos(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(Zero)), Succ(Succ(Succ(x1285))), Zero, Succ(x1285)))), Neg(Succ(Succ(Succ(Succ(Succ(x1285)))))), Pos(Succ(Succ(Succ(Succ(Zero)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (13) using rule (V) (with possible (I) afterwards) using induction on new_primModNatS02(x1289, x1288)=Succ(x1279) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(17)    (new_primModNatS1(new_primMinusNatS2(Succ(x1307), Succ(x1306)), Succ(x1306))=Succ(x1279) & Succ(Succ(Zero))=x1307 & Succ(Succ(Zero))=x1306  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(Zero)), Succ(Succ(Zero)), Zero, Zero))), Neg(Succ(Succ(Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Succ(Zero)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (14) using rule (V) (with possible (I) afterwards) using induction on new_primModNatS02(x1292, x1291)=Succ(x1279) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(18)    (new_primModNatS1(new_primMinusNatS2(Succ(x1313), Succ(x1312)), Succ(x1312))=Succ(x1279) & Succ(Succ(Succ(x1290)))=x1313 & Succ(Succ(Zero))=x1312  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Succ(Succ(x1290)))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(Succ(x1290))), Succ(Succ(Zero)), Succ(x1290), Zero))), Neg(Succ(Succ(Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Succ(Succ(x1290))))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (15) using rule (V) (with possible (I) afterwards) using induction on new_primModNatS01(x1283, x1282, x1281, x1280)=Succ(x1279) which results in the following new constraints:
67.83/34.94	
67.83/34.94	(19)    (new_primModNatS01(x1296, x1295, x1294, x1293)=Succ(x1279) & Succ(Succ(Succ(Succ(x1294))))=x1296 & Succ(Succ(Succ(Succ(x1293))))=x1295 & (\/x1297:new_primModNatS01(x1296, x1295, x1294, x1293)=Succ(x1297) & Succ(Succ(Succ(x1294)))=x1296 & Succ(Succ(Succ(x1293)))=x1295  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(x1293)))))), Pos(Succ(Succ(Succ(Succ(Succ(x1294)))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(Succ(x1294))), Succ(Succ(Succ(x1293))), Succ(x1294), Succ(x1293)))), Neg(Succ(Succ(Succ(Succ(Succ(x1293)))))), Pos(Succ(Succ(Succ(Succ(Succ(x1294))))))))  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Succ(x1293))))))), Pos(Succ(Succ(Succ(Succ(Succ(Succ(x1294))))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(Succ(Succ(x1294)))), Succ(Succ(Succ(Succ(x1293)))), Succ(Succ(x1294)), Succ(Succ(x1293))))), Neg(Succ(Succ(Succ(Succ(Succ(Succ(x1293))))))), Pos(Succ(Succ(Succ(Succ(Succ(Succ(x1294)))))))))
67.83/34.94	
67.83/34.94	(20)    (Succ(Succ(x1300))=Succ(x1279) & Succ(Succ(Succ(Zero)))=x1300 & Succ(Succ(Succ(Succ(x1298))))=x1299  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Succ(x1298))))))), Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Succ(x1298)))), Succ(Zero), Succ(Succ(x1298))))), Neg(Succ(Succ(Succ(Succ(Succ(Succ(x1298))))))), Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))))
67.83/34.94	
67.83/34.94	(21)    (new_primModNatS02(x1302, x1301)=Succ(x1279) & Succ(Succ(Succ(Zero)))=x1302 & Succ(Succ(Succ(Zero)))=x1301  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))), Succ(Zero), Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))))
67.83/34.94	
67.83/34.94	(22)    (new_primModNatS02(x1305, x1304)=Succ(x1279) & Succ(Succ(Succ(Succ(x1303))))=x1305 & Succ(Succ(Succ(Zero)))=x1304  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(Succ(Succ(Succ(Succ(Succ(Succ(x1303))))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(Succ(Succ(x1303)))), Succ(Succ(Succ(Zero))), Succ(Succ(x1303)), Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(Succ(Succ(Succ(Succ(Succ(Succ(x1303)))))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (19) using rules (III), (IV) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(23)    (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Succ(x1293))))))), Pos(Succ(Succ(Succ(Succ(Succ(Succ(x1294))))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(Succ(Succ(x1294)))), Succ(Succ(Succ(Succ(x1293)))), Succ(Succ(x1294)), Succ(Succ(x1293))))), Neg(Succ(Succ(Succ(Succ(Succ(Succ(x1293))))))), Pos(Succ(Succ(Succ(Succ(Succ(Succ(x1294)))))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (20) using rules (I), (II), (IV) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(24)    (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Succ(x1298))))))), Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Succ(x1298)))), Succ(Zero), Succ(Succ(x1298))))), Neg(Succ(Succ(Succ(Succ(Succ(Succ(x1298))))))), Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (21) using rules (III), (IV) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(25)    (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))), Succ(Zero), Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (22) using rules (III), (IV) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(26)    (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(Succ(Succ(Succ(Succ(Succ(Succ(x1303))))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(Succ(Succ(x1303)))), Succ(Succ(Succ(Zero))), Succ(Succ(x1303)), Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(Succ(Succ(Succ(Succ(Succ(Succ(x1303)))))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (17) using rules (III), (IV), (VII) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(27)    (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(Zero)), Succ(Succ(Zero)), Zero, Zero))), Neg(Succ(Succ(Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Succ(Zero)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (18) using rules (III), (IV), (VII) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(28)    (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Succ(Succ(x1290)))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(Succ(x1290))), Succ(Succ(Zero)), Succ(x1290), Zero))), Neg(Succ(Succ(Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Succ(Succ(x1290))))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	For Pair new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) the following chains were created:
67.83/34.94	*We consider the chain new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x790))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x790))))), Pos(Succ(Succ(Succ(Zero))))), new_gcd0Gcd'1(False, x791, x792) -> new_gcd0Gcd'0(x791, new_rem(x792, x791)) which results in the following constraint:
67.83/34.94	
67.83/34.94	(1)    (new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x790))))), Pos(Succ(Succ(Succ(Zero)))))=new_gcd0Gcd'1(False, x791, x792)  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x790))))), Pos(Succ(Succ(Succ(Zero)))))_>=_new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x790))))), Pos(Succ(Succ(Succ(Zero))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (1) using rules (I), (II), (IV) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(2)    (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x790))))), Pos(Succ(Succ(Succ(Zero)))))_>=_new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x790))))), Pos(Succ(Succ(Succ(Zero))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	For Pair new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) the following chains were created:
67.83/34.94	*We consider the chain new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x822)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x822), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x822)))))), new_gcd0Gcd'1(False, x823, x824) -> new_gcd0Gcd'0(x823, new_rem(x824, x823)) which results in the following constraint:
67.83/34.94	
67.83/34.94	(1)    (new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x822), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x822))))))=new_gcd0Gcd'1(False, x823, x824)  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x822))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x822), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x822)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (1) using rules (I), (II), (IV), (VII) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(2)    (Pos(new_primModNatS1(Succ(x822), Succ(Succ(Zero))))=x1318 & new_esEs(x1318)=False  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x822))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x822), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x822)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_esEs(x1318)=False which results in the following new constraints:
67.83/34.94	
67.83/34.94	(3)    (new_primEqInt2=False & Pos(new_primModNatS1(Succ(x822), Succ(Succ(Zero))))=Neg(Zero)  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x822))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x822), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x822)))))))
67.83/34.94	
67.83/34.94	(4)    (new_primEqInt1=False & Pos(new_primModNatS1(Succ(x822), Succ(Succ(Zero))))=Pos(Zero)  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x822))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x822), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x822)))))))
67.83/34.94	
67.83/34.94	(5)    (new_primEqInt(x1319)=False & Pos(new_primModNatS1(Succ(x822), Succ(Succ(Zero))))=Pos(Succ(x1319))  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x822))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x822), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x822)))))))
67.83/34.94	
67.83/34.94	(6)    (new_primEqInt0(x1320)=False & Pos(new_primModNatS1(Succ(x822), Succ(Succ(Zero))))=Neg(Succ(x1320))  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x822))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x822), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x822)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We solved constraint (3) using rules (I), (II).We simplified constraint (4) using rules (I), (II), (VII) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(7)    (new_primEqInt1=False & Succ(x822)=x1321 & Succ(Succ(Zero))=x1322 & new_primModNatS1(x1321, x1322)=Zero  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x822))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x822), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x822)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (5) using rules (I), (II), (VII) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(8)    (new_primEqInt(x1319)=False & Succ(x822)=x1323 & Succ(Succ(Zero))=x1324 & new_primModNatS1(x1323, x1324)=Succ(x1319)  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x822))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x822), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x822)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We solved constraint (6) using rules (I), (II).We solved constraint (7) using rule (V) (with possible (I) afterwards).We simplified constraint (8) using rule (V) (with possible (I) afterwards) using induction on new_primEqInt(x1319)=False which results in the following new constraint:
67.83/34.94	
67.83/34.94	(9)    (False=False & Succ(x822)=x1323 & Succ(Succ(Zero))=x1324 & new_primModNatS1(x1323, x1324)=Succ(x1325)  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x822))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x822), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x822)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (9) using rules (I), (II) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(10)    (Succ(x822)=x1323 & Succ(Succ(Zero))=x1324 & new_primModNatS1(x1323, x1324)=Succ(x1325)  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x822))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x822), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x822)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (10) using rule (V) (with possible (I) afterwards) using induction on new_primModNatS1(x1323, x1324)=Succ(x1325) which results in the following new constraints:
67.83/34.94	
67.83/34.94	(11)    (new_primModNatS1(new_primMinusNatS0(x1326), Zero)=Succ(x1325) & Succ(x822)=Succ(Succ(x1326)) & Succ(Succ(Zero))=Zero  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x822))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x822), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x822)))))))
67.83/34.94	
67.83/34.94	(12)    (Succ(Zero)=Succ(x1325) & Succ(x822)=Succ(Zero) & Succ(Succ(Zero))=Succ(x1327)  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x822))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x822), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x822)))))))
67.83/34.94	
67.83/34.94	(13)    (new_primModNatS01(x1329, x1328, x1329, x1328)=Succ(x1325) & Succ(x822)=Succ(Succ(x1329)) & Succ(Succ(Zero))=Succ(x1328)  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x822))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x822), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x822)))))))
67.83/34.94	
67.83/34.94	(14)    (new_primModNatS1(new_primMinusNatS1, Zero)=Succ(x1325) & Succ(x822)=Succ(Zero) & Succ(Succ(Zero))=Zero  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x822))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x822), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x822)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We solved constraint (11) using rules (I), (II).We simplified constraint (12) using rules (I), (II), (III), (IV) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(15)    (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(Zero), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(Zero)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (13) using rules (I), (II), (III), (VII) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(16)    (x1329=x1331 & x1328=x1332 & new_primModNatS01(x1329, x1328, x1331, x1332)=Succ(x1325) & Succ(Zero)=x1328  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(Succ(x1329)))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(Succ(x1329)), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(Succ(x1329))))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We solved constraint (14) using rules (I), (II).We simplified constraint (16) using rule (V) (with possible (I) afterwards) using induction on new_primModNatS01(x1329, x1328, x1331, x1332)=Succ(x1325) which results in the following new constraints:
67.83/34.94	
67.83/34.94	(17)    (new_primModNatS01(x1336, x1335, x1334, x1333)=Succ(x1325) & x1336=Succ(x1334) & x1335=Succ(x1333) & Succ(Zero)=x1335 & (\/x1337:new_primModNatS01(x1336, x1335, x1334, x1333)=Succ(x1337) & x1336=x1334 & x1335=x1333 & Succ(Zero)=x1335  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(Succ(x1336)))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(Succ(x1336)), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(Succ(x1336))))))))  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(Succ(x1336)))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(Succ(x1336)), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(Succ(x1336))))))))
67.83/34.94	
67.83/34.94	(18)    (Succ(Succ(x1340))=Succ(x1325) & x1340=Zero & x1339=Succ(x1338) & Succ(Zero)=x1339  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(Succ(x1340)))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(Succ(x1340)), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(Succ(x1340))))))))
67.83/34.94	
67.83/34.94	(19)    (new_primModNatS02(x1342, x1341)=Succ(x1325) & x1342=Zero & x1341=Zero & Succ(Zero)=x1341  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(Succ(x1342)))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(Succ(x1342)), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(Succ(x1342))))))))
67.83/34.94	
67.83/34.94	(20)    (new_primModNatS02(x1345, x1344)=Succ(x1325) & x1345=Succ(x1343) & x1344=Zero & Succ(Zero)=x1344  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(Succ(x1345)))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(Succ(x1345)), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(Succ(x1345))))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (17) using rules (I), (II), (III), (IV), (VII) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(21)    (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(Succ(Succ(x1334))))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(Succ(Succ(x1334))), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(Succ(Succ(x1334)))))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (18) using rules (I), (II), (III), (IV) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(22)    (new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(Succ(Zero)), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We solved constraint (19) using rules (I), (II), (III).We solved constraint (20) using rules (I), (II), (III).
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	For Pair new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0)))))) the following chains were created:
67.83/34.94	*We consider the chain new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x854)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x854, Zero, x854, Zero))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x854)))))), new_gcd0Gcd'1(False, x855, x856) -> new_gcd0Gcd'0(x855, new_rem(x856, x855)) which results in the following constraint:
67.83/34.94	
67.83/34.94	(1)    (new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x854, Zero, x854, Zero))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x854))))))=new_gcd0Gcd'1(False, x855, x856)  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x854))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x854, Zero, x854, Zero))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x854)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (1) using rules (I), (II), (IV), (VII) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(2)    (Pos(new_primModNatS01(x854, Zero, x854, Zero))=x1348 & new_esEs(x1348)=False  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x854))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x854, Zero, x854, Zero))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x854)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_esEs(x1348)=False which results in the following new constraints:
67.83/34.94	
67.83/34.94	(3)    (new_primEqInt2=False & Pos(new_primModNatS01(x854, Zero, x854, Zero))=Neg(Zero)  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x854))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x854, Zero, x854, Zero))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x854)))))))
67.83/34.94	
67.83/34.94	(4)    (new_primEqInt1=False & Pos(new_primModNatS01(x854, Zero, x854, Zero))=Pos(Zero)  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x854))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x854, Zero, x854, Zero))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x854)))))))
67.83/34.94	
67.83/34.94	(5)    (new_primEqInt(x1349)=False & Pos(new_primModNatS01(x854, Zero, x854, Zero))=Pos(Succ(x1349))  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x854))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x854, Zero, x854, Zero))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x854)))))))
67.83/34.94	
67.83/34.94	(6)    (new_primEqInt0(x1350)=False & Pos(new_primModNatS01(x854, Zero, x854, Zero))=Neg(Succ(x1350))  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x854))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x854, Zero, x854, Zero))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x854)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We solved constraint (3) using rules (I), (II).We simplified constraint (4) using rules (I), (II), (VII) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(7)    (new_primEqInt1=False & Zero=x1351 & x854=x1352 & Zero=x1353 & new_primModNatS01(x854, x1351, x1352, x1353)=Zero  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x854))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x854, Zero, x854, Zero))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x854)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (5) using rules (I), (II), (VII) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(8)    (new_primEqInt(x1349)=False & Zero=x1354 & x854=x1355 & Zero=x1356 & new_primModNatS01(x854, x1354, x1355, x1356)=Succ(x1349)  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x854))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x854, Zero, x854, Zero))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x854)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We solved constraint (6) using rules (I), (II).We solved constraint (7) using rule (V) (with possible (I) afterwards).We simplified constraint (8) using rule (V) (with possible (I) afterwards) using induction on new_primEqInt(x1349)=False which results in the following new constraint:
67.83/34.94	
67.83/34.94	(9)    (False=False & Zero=x1354 & x854=x1355 & Zero=x1356 & new_primModNatS01(x854, x1354, x1355, x1356)=Succ(x1357)  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x854))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x854, Zero, x854, Zero))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x854)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (9) using rules (I), (II) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(10)    (Zero=x1354 & x854=x1355 & Zero=x1356 & new_primModNatS01(x854, x1354, x1355, x1356)=Succ(x1357)  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x854))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x854, Zero, x854, Zero))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x854)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (10) using rule (V) (with possible (I) afterwards) using induction on new_primModNatS01(x854, x1354, x1355, x1356)=Succ(x1357) which results in the following new constraints:
67.83/34.94	
67.83/34.94	(11)    (new_primModNatS01(x1361, x1360, x1359, x1358)=Succ(x1357) & Zero=x1360 & x1361=Succ(x1359) & Zero=Succ(x1358) & (\/x1362:new_primModNatS01(x1361, x1360, x1359, x1358)=Succ(x1362) & Zero=x1360 & x1361=x1359 & Zero=x1358  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x1361))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x1361, Zero, x1361, Zero))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x1361)))))))  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x1361))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x1361, Zero, x1361, Zero))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x1361)))))))
67.83/34.94	
67.83/34.94	(12)    (Succ(Succ(x1365))=Succ(x1357) & Zero=x1364 & x1365=Zero & Zero=Succ(x1363)  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x1365))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x1365, Zero, x1365, Zero))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x1365)))))))
67.83/34.94	
67.83/34.94	(13)    (new_primModNatS02(x1367, x1366)=Succ(x1357) & Zero=x1366 & x1367=Zero & Zero=Zero  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x1367))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x1367, Zero, x1367, Zero))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x1367)))))))
67.83/34.94	
67.83/34.94	(14)    (new_primModNatS02(x1370, x1369)=Succ(x1357) & Zero=x1369 & x1370=Succ(x1368) & Zero=Zero  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x1370))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x1370, Zero, x1370, Zero))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x1370)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We solved constraint (11) using rules (I), (II).We solved constraint (12) using rules (I), (II).We simplified constraint (13) using rules (I), (II), (III), (VII) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(15)    (Zero=x1371 & new_primModNatS02(x1371, x1366)=Succ(x1357) & Zero=x1366  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Zero, Zero, Zero, Zero))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(Zero)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (14) using rules (I), (II), (III), (VII) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(16)    (Succ(x1368)=x1378 & new_primModNatS02(x1378, x1369)=Succ(x1357) & Zero=x1369  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(Succ(x1368)))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x1368), Zero, Succ(x1368), Zero))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(Succ(x1368))))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (15) using rule (V) (with possible (I) afterwards) using induction on new_primModNatS02(x1371, x1366)=Succ(x1357) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(17)    (new_primModNatS1(new_primMinusNatS2(Succ(x1373), Succ(x1372)), Succ(x1372))=Succ(x1357) & Zero=x1373 & Zero=x1372  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Zero, Zero, Zero, Zero))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(Zero)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (17) using rules (III), (IV), (VII) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(18)    (new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Zero, Zero, Zero, Zero))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(Zero)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (16) using rule (V) (with possible (I) afterwards) using induction on new_primModNatS02(x1378, x1369)=Succ(x1357) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(19)    (new_primModNatS1(new_primMinusNatS2(Succ(x1380), Succ(x1379)), Succ(x1379))=Succ(x1357) & Succ(x1368)=x1380 & Zero=x1379  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(Succ(x1368)))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x1368), Zero, Succ(x1368), Zero))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(Succ(x1368))))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (19) using rules (III), (IV), (VII) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(20)    (new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(Succ(x1368)))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x1368), Zero, Succ(x1368), Zero))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(Succ(x1368))))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	For Pair new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) the following chains were created:
67.83/34.94	*We consider the chain new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))), new_gcd0Gcd'1(False, x884, x885) -> new_gcd0Gcd'0(x884, new_rem(x885, x884)) which results in the following constraint:
67.83/34.94	
67.83/34.94	(1)    (new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero)))))=new_gcd0Gcd'1(False, x884, x885)  ==>  new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero)))))_>=_new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (1) using rules (I), (II), (IV) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(2)    (new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero)))))_>=_new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	For Pair new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Pos(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) the following chains were created:
67.83/34.94	*We consider the chain new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x890))))), Neg(Succ(Succ(Succ(Succ(x891)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x891)), Succ(Succ(x890)), x891, x890))), Pos(Succ(Succ(Succ(Succ(x890))))), Neg(Succ(Succ(Succ(Succ(x891)))))), new_gcd0Gcd'1(False, x892, x893) -> new_gcd0Gcd'0(x892, new_rem(x893, x892)) which results in the following constraint:
67.83/34.94	
67.83/34.94	(1)    (new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x891)), Succ(Succ(x890)), x891, x890))), Pos(Succ(Succ(Succ(Succ(x890))))), Neg(Succ(Succ(Succ(Succ(x891))))))=new_gcd0Gcd'1(False, x892, x893)  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x890))))), Neg(Succ(Succ(Succ(Succ(x891))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x891)), Succ(Succ(x890)), x891, x890))), Pos(Succ(Succ(Succ(Succ(x890))))), Neg(Succ(Succ(Succ(Succ(x891)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (1) using rules (I), (II), (IV), (VII) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(2)    (Neg(new_primModNatS01(Succ(Succ(x891)), Succ(Succ(x890)), x891, x890))=x1385 & new_esEs(x1385)=False  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x890))))), Neg(Succ(Succ(Succ(Succ(x891))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x891)), Succ(Succ(x890)), x891, x890))), Pos(Succ(Succ(Succ(Succ(x890))))), Neg(Succ(Succ(Succ(Succ(x891)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_esEs(x1385)=False which results in the following new constraints:
67.83/34.94	
67.83/34.94	(3)    (new_primEqInt2=False & Neg(new_primModNatS01(Succ(Succ(x891)), Succ(Succ(x890)), x891, x890))=Neg(Zero)  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x890))))), Neg(Succ(Succ(Succ(Succ(x891))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x891)), Succ(Succ(x890)), x891, x890))), Pos(Succ(Succ(Succ(Succ(x890))))), Neg(Succ(Succ(Succ(Succ(x891)))))))
67.83/34.94	
67.83/34.94	(4)    (new_primEqInt1=False & Neg(new_primModNatS01(Succ(Succ(x891)), Succ(Succ(x890)), x891, x890))=Pos(Zero)  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x890))))), Neg(Succ(Succ(Succ(Succ(x891))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x891)), Succ(Succ(x890)), x891, x890))), Pos(Succ(Succ(Succ(Succ(x890))))), Neg(Succ(Succ(Succ(Succ(x891)))))))
67.83/34.94	
67.83/34.94	(5)    (new_primEqInt(x1386)=False & Neg(new_primModNatS01(Succ(Succ(x891)), Succ(Succ(x890)), x891, x890))=Pos(Succ(x1386))  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x890))))), Neg(Succ(Succ(Succ(Succ(x891))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x891)), Succ(Succ(x890)), x891, x890))), Pos(Succ(Succ(Succ(Succ(x890))))), Neg(Succ(Succ(Succ(Succ(x891)))))))
67.83/34.94	
67.83/34.94	(6)    (new_primEqInt0(x1387)=False & Neg(new_primModNatS01(Succ(Succ(x891)), Succ(Succ(x890)), x891, x890))=Neg(Succ(x1387))  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x890))))), Neg(Succ(Succ(Succ(Succ(x891))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x891)), Succ(Succ(x890)), x891, x890))), Pos(Succ(Succ(Succ(Succ(x890))))), Neg(Succ(Succ(Succ(Succ(x891)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (3) using rules (I), (II), (VII) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(7)    (new_primEqInt2=False & Succ(Succ(x891))=x1388 & Succ(Succ(x890))=x1389 & new_primModNatS01(x1388, x1389, x891, x890)=Zero  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x890))))), Neg(Succ(Succ(Succ(Succ(x891))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x891)), Succ(Succ(x890)), x891, x890))), Pos(Succ(Succ(Succ(Succ(x890))))), Neg(Succ(Succ(Succ(Succ(x891)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We solved constraint (4) using rules (I), (II).We solved constraint (5) using rules (I), (II).We simplified constraint (6) using rules (I), (II), (VII) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(8)    (new_primEqInt0(x1387)=False & Succ(Succ(x891))=x1390 & Succ(Succ(x890))=x1391 & new_primModNatS01(x1390, x1391, x891, x890)=Succ(x1387)  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x890))))), Neg(Succ(Succ(Succ(Succ(x891))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x891)), Succ(Succ(x890)), x891, x890))), Pos(Succ(Succ(Succ(Succ(x890))))), Neg(Succ(Succ(Succ(Succ(x891)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We solved constraint (7) using rule (V) (with possible (I) afterwards).We simplified constraint (8) using rule (V) (with possible (I) afterwards) using induction on new_primEqInt0(x1387)=False which results in the following new constraint:
67.83/34.94	
67.83/34.94	(9)    (False=False & Succ(Succ(x891))=x1390 & Succ(Succ(x890))=x1391 & new_primModNatS01(x1390, x1391, x891, x890)=Succ(x1392)  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x890))))), Neg(Succ(Succ(Succ(Succ(x891))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x891)), Succ(Succ(x890)), x891, x890))), Pos(Succ(Succ(Succ(Succ(x890))))), Neg(Succ(Succ(Succ(Succ(x891)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (9) using rules (I), (II) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(10)    (Succ(Succ(x891))=x1390 & Succ(Succ(x890))=x1391 & new_primModNatS01(x1390, x1391, x891, x890)=Succ(x1392)  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x890))))), Neg(Succ(Succ(Succ(Succ(x891))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x891)), Succ(Succ(x890)), x891, x890))), Pos(Succ(Succ(Succ(Succ(x890))))), Neg(Succ(Succ(Succ(Succ(x891)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (10) using rule (V) (with possible (I) afterwards) using induction on new_primModNatS01(x1390, x1391, x891, x890)=Succ(x1392) which results in the following new constraints:
67.83/34.94	
67.83/34.94	(11)    (new_primModNatS01(x1396, x1395, x1394, x1393)=Succ(x1392) & Succ(Succ(Succ(x1394)))=x1396 & Succ(Succ(Succ(x1393)))=x1395 & (\/x1397:new_primModNatS01(x1396, x1395, x1394, x1393)=Succ(x1397) & Succ(Succ(x1394))=x1396 & Succ(Succ(x1393))=x1395  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x1393))))), Neg(Succ(Succ(Succ(Succ(x1394))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x1394)), Succ(Succ(x1393)), x1394, x1393))), Pos(Succ(Succ(Succ(Succ(x1393))))), Neg(Succ(Succ(Succ(Succ(x1394)))))))  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(x1393)))))), Neg(Succ(Succ(Succ(Succ(Succ(x1394)))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(Succ(x1394))), Succ(Succ(Succ(x1393))), Succ(x1394), Succ(x1393)))), Pos(Succ(Succ(Succ(Succ(Succ(x1393)))))), Neg(Succ(Succ(Succ(Succ(Succ(x1394))))))))
67.83/34.94	
67.83/34.94	(12)    (Succ(Succ(x1400))=Succ(x1392) & Succ(Succ(Zero))=x1400 & Succ(Succ(Succ(x1398)))=x1399  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(x1398)))))), Neg(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(Zero)), Succ(Succ(Succ(x1398))), Zero, Succ(x1398)))), Pos(Succ(Succ(Succ(Succ(Succ(x1398)))))), Neg(Succ(Succ(Succ(Succ(Zero)))))))
67.83/34.94	
67.83/34.94	(13)    (new_primModNatS02(x1402, x1401)=Succ(x1392) & Succ(Succ(Zero))=x1402 & Succ(Succ(Zero))=x1401  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(Zero)), Succ(Succ(Zero)), Zero, Zero))), Pos(Succ(Succ(Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Succ(Zero)))))))
67.83/34.94	
67.83/34.94	(14)    (new_primModNatS02(x1405, x1404)=Succ(x1392) & Succ(Succ(Succ(x1403)))=x1405 & Succ(Succ(Zero))=x1404  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Succ(Succ(x1403)))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(Succ(x1403))), Succ(Succ(Zero)), Succ(x1403), Zero))), Pos(Succ(Succ(Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Succ(Succ(x1403))))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (11) using rule (IV) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(15)    (new_primModNatS01(x1396, x1395, x1394, x1393)=Succ(x1392) & Succ(Succ(Succ(x1394)))=x1396 & Succ(Succ(Succ(x1393)))=x1395  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(x1393)))))), Neg(Succ(Succ(Succ(Succ(Succ(x1394)))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(Succ(x1394))), Succ(Succ(Succ(x1393))), Succ(x1394), Succ(x1393)))), Pos(Succ(Succ(Succ(Succ(Succ(x1393)))))), Neg(Succ(Succ(Succ(Succ(Succ(x1394))))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (12) using rules (I), (II), (IV) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(16)    (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(x1398)))))), Neg(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(Zero)), Succ(Succ(Succ(x1398))), Zero, Succ(x1398)))), Pos(Succ(Succ(Succ(Succ(Succ(x1398)))))), Neg(Succ(Succ(Succ(Succ(Zero)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (13) using rule (V) (with possible (I) afterwards) using induction on new_primModNatS02(x1402, x1401)=Succ(x1392) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(17)    (new_primModNatS1(new_primMinusNatS2(Succ(x1420), Succ(x1419)), Succ(x1419))=Succ(x1392) & Succ(Succ(Zero))=x1420 & Succ(Succ(Zero))=x1419  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(Zero)), Succ(Succ(Zero)), Zero, Zero))), Pos(Succ(Succ(Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Succ(Zero)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (14) using rule (V) (with possible (I) afterwards) using induction on new_primModNatS02(x1405, x1404)=Succ(x1392) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(18)    (new_primModNatS1(new_primMinusNatS2(Succ(x1426), Succ(x1425)), Succ(x1425))=Succ(x1392) & Succ(Succ(Succ(x1403)))=x1426 & Succ(Succ(Zero))=x1425  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Succ(Succ(x1403)))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(Succ(x1403))), Succ(Succ(Zero)), Succ(x1403), Zero))), Pos(Succ(Succ(Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Succ(Succ(x1403))))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (15) using rule (V) (with possible (I) afterwards) using induction on new_primModNatS01(x1396, x1395, x1394, x1393)=Succ(x1392) which results in the following new constraints:
67.83/34.94	
67.83/34.94	(19)    (new_primModNatS01(x1409, x1408, x1407, x1406)=Succ(x1392) & Succ(Succ(Succ(Succ(x1407))))=x1409 & Succ(Succ(Succ(Succ(x1406))))=x1408 & (\/x1410:new_primModNatS01(x1409, x1408, x1407, x1406)=Succ(x1410) & Succ(Succ(Succ(x1407)))=x1409 & Succ(Succ(Succ(x1406)))=x1408  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(x1406)))))), Neg(Succ(Succ(Succ(Succ(Succ(x1407)))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(Succ(x1407))), Succ(Succ(Succ(x1406))), Succ(x1407), Succ(x1406)))), Pos(Succ(Succ(Succ(Succ(Succ(x1406)))))), Neg(Succ(Succ(Succ(Succ(Succ(x1407))))))))  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Succ(x1406))))))), Neg(Succ(Succ(Succ(Succ(Succ(Succ(x1407))))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(Succ(Succ(x1407)))), Succ(Succ(Succ(Succ(x1406)))), Succ(Succ(x1407)), Succ(Succ(x1406))))), Pos(Succ(Succ(Succ(Succ(Succ(Succ(x1406))))))), Neg(Succ(Succ(Succ(Succ(Succ(Succ(x1407)))))))))
67.83/34.94	
67.83/34.94	(20)    (Succ(Succ(x1413))=Succ(x1392) & Succ(Succ(Succ(Zero)))=x1413 & Succ(Succ(Succ(Succ(x1411))))=x1412  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Succ(x1411))))))), Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Succ(x1411)))), Succ(Zero), Succ(Succ(x1411))))), Pos(Succ(Succ(Succ(Succ(Succ(Succ(x1411))))))), Neg(Succ(Succ(Succ(Succ(Succ(Zero))))))))
67.83/34.94	
67.83/34.94	(21)    (new_primModNatS02(x1415, x1414)=Succ(x1392) & Succ(Succ(Succ(Zero)))=x1415 & Succ(Succ(Succ(Zero)))=x1414  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))), Succ(Zero), Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(Succ(Succ(Succ(Succ(Succ(Zero))))))))
67.83/34.94	
67.83/34.94	(22)    (new_primModNatS02(x1418, x1417)=Succ(x1392) & Succ(Succ(Succ(Succ(x1416))))=x1418 & Succ(Succ(Succ(Zero)))=x1417  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(Succ(Succ(Succ(Succ(Succ(Succ(x1416))))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(Succ(Succ(x1416)))), Succ(Succ(Succ(Zero))), Succ(Succ(x1416)), Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(Succ(Succ(Succ(Succ(Succ(Succ(x1416)))))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (19) using rules (III), (IV) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(23)    (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Succ(x1406))))))), Neg(Succ(Succ(Succ(Succ(Succ(Succ(x1407))))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(Succ(Succ(x1407)))), Succ(Succ(Succ(Succ(x1406)))), Succ(Succ(x1407)), Succ(Succ(x1406))))), Pos(Succ(Succ(Succ(Succ(Succ(Succ(x1406))))))), Neg(Succ(Succ(Succ(Succ(Succ(Succ(x1407)))))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (20) using rules (I), (II), (IV) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(24)    (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Succ(x1411))))))), Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Succ(x1411)))), Succ(Zero), Succ(Succ(x1411))))), Pos(Succ(Succ(Succ(Succ(Succ(Succ(x1411))))))), Neg(Succ(Succ(Succ(Succ(Succ(Zero))))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (21) using rules (III), (IV) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(25)    (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))), Succ(Zero), Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(Succ(Succ(Succ(Succ(Succ(Zero))))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (22) using rules (III), (IV) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(26)    (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(Succ(Succ(Succ(Succ(Succ(Succ(x1416))))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(Succ(Succ(x1416)))), Succ(Succ(Succ(Zero))), Succ(Succ(x1416)), Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(Succ(Succ(Succ(Succ(Succ(Succ(x1416)))))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (17) using rules (III), (IV), (VII) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(27)    (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(Zero)), Succ(Succ(Zero)), Zero, Zero))), Pos(Succ(Succ(Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Succ(Zero)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (18) using rules (III), (IV), (VII) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(28)    (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Succ(Succ(x1403)))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(Succ(x1403))), Succ(Succ(Zero)), Succ(x1403), Zero))), Pos(Succ(Succ(Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Succ(Succ(x1403))))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	For Pair new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) the following chains were created:
67.83/34.94	*We consider the chain new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x950))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(Succ(x950))))), Neg(Succ(Succ(Succ(Zero))))), new_gcd0Gcd'1(False, x951, x952) -> new_gcd0Gcd'0(x951, new_rem(x952, x951)) which results in the following constraint:
67.83/34.94	
67.83/34.94	(1)    (new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(Succ(x950))))), Neg(Succ(Succ(Succ(Zero)))))=new_gcd0Gcd'1(False, x951, x952)  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x950))))), Neg(Succ(Succ(Succ(Zero)))))_>=_new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(Succ(x950))))), Neg(Succ(Succ(Succ(Zero))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (1) using rules (I), (II), (IV) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(2)    (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x950))))), Neg(Succ(Succ(Succ(Zero)))))_>=_new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(Succ(x950))))), Neg(Succ(Succ(Succ(Zero))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	For Pair new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) the following chains were created:
67.83/34.94	*We consider the chain new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x982)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x982), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x982)))))), new_gcd0Gcd'1(False, x983, x984) -> new_gcd0Gcd'0(x983, new_rem(x984, x983)) which results in the following constraint:
67.83/34.94	
67.83/34.94	(1)    (new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x982), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x982))))))=new_gcd0Gcd'1(False, x983, x984)  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x982))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x982), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x982)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (1) using rules (I), (II), (IV), (VII) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(2)    (Neg(new_primModNatS1(Succ(x982), Succ(Succ(Zero))))=x1431 & new_esEs(x1431)=False  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x982))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x982), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x982)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_esEs(x1431)=False which results in the following new constraints:
67.83/34.94	
67.83/34.94	(3)    (new_primEqInt2=False & Neg(new_primModNatS1(Succ(x982), Succ(Succ(Zero))))=Neg(Zero)  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x982))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x982), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x982)))))))
67.83/34.94	
67.83/34.94	(4)    (new_primEqInt1=False & Neg(new_primModNatS1(Succ(x982), Succ(Succ(Zero))))=Pos(Zero)  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x982))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x982), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x982)))))))
67.83/34.94	
67.83/34.94	(5)    (new_primEqInt(x1432)=False & Neg(new_primModNatS1(Succ(x982), Succ(Succ(Zero))))=Pos(Succ(x1432))  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x982))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x982), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x982)))))))
67.83/34.94	
67.83/34.94	(6)    (new_primEqInt0(x1433)=False & Neg(new_primModNatS1(Succ(x982), Succ(Succ(Zero))))=Neg(Succ(x1433))  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x982))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x982), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x982)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (3) using rules (I), (II), (VII) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(7)    (new_primEqInt2=False & Succ(x982)=x1434 & Succ(Succ(Zero))=x1435 & new_primModNatS1(x1434, x1435)=Zero  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x982))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x982), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x982)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We solved constraint (4) using rules (I), (II).We solved constraint (5) using rules (I), (II).We simplified constraint (6) using rules (I), (II), (VII) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(8)    (new_primEqInt0(x1433)=False & Succ(x982)=x1436 & Succ(Succ(Zero))=x1437 & new_primModNatS1(x1436, x1437)=Succ(x1433)  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x982))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x982), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x982)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We solved constraint (7) using rule (V) (with possible (I) afterwards).We simplified constraint (8) using rule (V) (with possible (I) afterwards) using induction on new_primEqInt0(x1433)=False which results in the following new constraint:
67.83/34.94	
67.83/34.94	(9)    (False=False & Succ(x982)=x1436 & Succ(Succ(Zero))=x1437 & new_primModNatS1(x1436, x1437)=Succ(x1438)  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x982))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x982), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x982)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (9) using rules (I), (II) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(10)    (Succ(x982)=x1436 & Succ(Succ(Zero))=x1437 & new_primModNatS1(x1436, x1437)=Succ(x1438)  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x982))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x982), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x982)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (10) using rule (V) (with possible (I) afterwards) using induction on new_primModNatS1(x1436, x1437)=Succ(x1438) which results in the following new constraints:
67.83/34.94	
67.83/34.94	(11)    (new_primModNatS1(new_primMinusNatS0(x1439), Zero)=Succ(x1438) & Succ(x982)=Succ(Succ(x1439)) & Succ(Succ(Zero))=Zero  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x982))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x982), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x982)))))))
67.83/34.94	
67.83/34.94	(12)    (Succ(Zero)=Succ(x1438) & Succ(x982)=Succ(Zero) & Succ(Succ(Zero))=Succ(x1440)  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x982))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x982), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x982)))))))
67.83/34.94	
67.83/34.94	(13)    (new_primModNatS01(x1442, x1441, x1442, x1441)=Succ(x1438) & Succ(x982)=Succ(Succ(x1442)) & Succ(Succ(Zero))=Succ(x1441)  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x982))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x982), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x982)))))))
67.83/34.94	
67.83/34.94	(14)    (new_primModNatS1(new_primMinusNatS1, Zero)=Succ(x1438) & Succ(x982)=Succ(Zero) & Succ(Succ(Zero))=Zero  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x982))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x982), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x982)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We solved constraint (11) using rules (I), (II).We simplified constraint (12) using rules (I), (II), (III), (IV) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(15)    (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(Zero), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(Zero)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (13) using rules (I), (II), (III), (VII) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(16)    (x1442=x1444 & x1441=x1445 & new_primModNatS01(x1442, x1441, x1444, x1445)=Succ(x1438) & Succ(Zero)=x1441  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(Succ(x1442)))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(Succ(x1442)), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(Succ(x1442))))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We solved constraint (14) using rules (I), (II).We simplified constraint (16) using rule (V) (with possible (I) afterwards) using induction on new_primModNatS01(x1442, x1441, x1444, x1445)=Succ(x1438) which results in the following new constraints:
67.83/34.94	
67.83/34.94	(17)    (new_primModNatS01(x1449, x1448, x1447, x1446)=Succ(x1438) & x1449=Succ(x1447) & x1448=Succ(x1446) & Succ(Zero)=x1448 & (\/x1450:new_primModNatS01(x1449, x1448, x1447, x1446)=Succ(x1450) & x1449=x1447 & x1448=x1446 & Succ(Zero)=x1448  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(Succ(x1449)))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(Succ(x1449)), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(Succ(x1449))))))))  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(Succ(x1449)))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(Succ(x1449)), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(Succ(x1449))))))))
67.83/34.94	
67.83/34.94	(18)    (Succ(Succ(x1453))=Succ(x1438) & x1453=Zero & x1452=Succ(x1451) & Succ(Zero)=x1452  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(Succ(x1453)))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(Succ(x1453)), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(Succ(x1453))))))))
67.83/34.94	
67.83/34.94	(19)    (new_primModNatS02(x1455, x1454)=Succ(x1438) & x1455=Zero & x1454=Zero & Succ(Zero)=x1454  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(Succ(x1455)))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(Succ(x1455)), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(Succ(x1455))))))))
67.83/34.94	
67.83/34.94	(20)    (new_primModNatS02(x1458, x1457)=Succ(x1438) & x1458=Succ(x1456) & x1457=Zero & Succ(Zero)=x1457  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(Succ(x1458)))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(Succ(x1458)), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(Succ(x1458))))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (17) using rules (I), (II), (III), (IV), (VII) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(21)    (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(Succ(Succ(x1447))))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(Succ(Succ(x1447))), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(Succ(Succ(x1447)))))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (18) using rules (I), (II), (III), (IV) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(22)    (new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(Succ(Zero)), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(Succ(Zero))))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We solved constraint (19) using rules (I), (II), (III).We solved constraint (20) using rules (I), (II), (III).
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	For Pair new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, Zero, x0, Zero))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0)))))) the following chains were created:
67.83/34.94	*We consider the chain new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x1014)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x1014, Zero, x1014, Zero))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x1014)))))), new_gcd0Gcd'1(False, x1015, x1016) -> new_gcd0Gcd'0(x1015, new_rem(x1016, x1015)) which results in the following constraint:
67.83/34.94	
67.83/34.94	(1)    (new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x1014, Zero, x1014, Zero))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x1014))))))=new_gcd0Gcd'1(False, x1015, x1016)  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x1014))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x1014, Zero, x1014, Zero))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x1014)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (1) using rules (I), (II), (IV), (VII) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(2)    (Neg(new_primModNatS01(x1014, Zero, x1014, Zero))=x1461 & new_esEs(x1461)=False  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x1014))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x1014, Zero, x1014, Zero))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x1014)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_esEs(x1461)=False which results in the following new constraints:
67.83/34.94	
67.83/34.94	(3)    (new_primEqInt2=False & Neg(new_primModNatS01(x1014, Zero, x1014, Zero))=Neg(Zero)  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x1014))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x1014, Zero, x1014, Zero))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x1014)))))))
67.83/34.94	
67.83/34.94	(4)    (new_primEqInt1=False & Neg(new_primModNatS01(x1014, Zero, x1014, Zero))=Pos(Zero)  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x1014))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x1014, Zero, x1014, Zero))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x1014)))))))
67.83/34.94	
67.83/34.94	(5)    (new_primEqInt(x1462)=False & Neg(new_primModNatS01(x1014, Zero, x1014, Zero))=Pos(Succ(x1462))  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x1014))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x1014, Zero, x1014, Zero))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x1014)))))))
67.83/34.94	
67.83/34.94	(6)    (new_primEqInt0(x1463)=False & Neg(new_primModNatS01(x1014, Zero, x1014, Zero))=Neg(Succ(x1463))  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x1014))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x1014, Zero, x1014, Zero))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x1014)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (3) using rules (I), (II), (VII) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(7)    (new_primEqInt2=False & Zero=x1464 & x1014=x1465 & Zero=x1466 & new_primModNatS01(x1014, x1464, x1465, x1466)=Zero  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x1014))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x1014, Zero, x1014, Zero))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x1014)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We solved constraint (4) using rules (I), (II).We solved constraint (5) using rules (I), (II).We simplified constraint (6) using rules (I), (II), (VII) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(8)    (new_primEqInt0(x1463)=False & Zero=x1467 & x1014=x1468 & Zero=x1469 & new_primModNatS01(x1014, x1467, x1468, x1469)=Succ(x1463)  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x1014))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x1014, Zero, x1014, Zero))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x1014)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We solved constraint (7) using rule (V) (with possible (I) afterwards).We simplified constraint (8) using rule (V) (with possible (I) afterwards) using induction on new_primEqInt0(x1463)=False which results in the following new constraint:
67.83/34.94	
67.83/34.94	(9)    (False=False & Zero=x1467 & x1014=x1468 & Zero=x1469 & new_primModNatS01(x1014, x1467, x1468, x1469)=Succ(x1470)  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x1014))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x1014, Zero, x1014, Zero))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x1014)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (9) using rules (I), (II) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(10)    (Zero=x1467 & x1014=x1468 & Zero=x1469 & new_primModNatS01(x1014, x1467, x1468, x1469)=Succ(x1470)  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x1014))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x1014, Zero, x1014, Zero))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x1014)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (10) using rule (V) (with possible (I) afterwards) using induction on new_primModNatS01(x1014, x1467, x1468, x1469)=Succ(x1470) which results in the following new constraints:
67.83/34.94	
67.83/34.94	(11)    (new_primModNatS01(x1474, x1473, x1472, x1471)=Succ(x1470) & Zero=x1473 & x1474=Succ(x1472) & Zero=Succ(x1471) & (\/x1475:new_primModNatS01(x1474, x1473, x1472, x1471)=Succ(x1475) & Zero=x1473 & x1474=x1472 & Zero=x1471  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x1474))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x1474, Zero, x1474, Zero))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x1474)))))))  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x1474))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x1474, Zero, x1474, Zero))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x1474)))))))
67.83/34.94	
67.83/34.94	(12)    (Succ(Succ(x1478))=Succ(x1470) & Zero=x1477 & x1478=Zero & Zero=Succ(x1476)  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x1478))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x1478, Zero, x1478, Zero))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x1478)))))))
67.83/34.94	
67.83/34.94	(13)    (new_primModNatS02(x1480, x1479)=Succ(x1470) & Zero=x1479 & x1480=Zero & Zero=Zero  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x1480))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x1480, Zero, x1480, Zero))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x1480)))))))
67.83/34.94	
67.83/34.94	(14)    (new_primModNatS02(x1483, x1482)=Succ(x1470) & Zero=x1482 & x1483=Succ(x1481) & Zero=Zero  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x1483))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x1483, Zero, x1483, Zero))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x1483)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We solved constraint (11) using rules (I), (II).We solved constraint (12) using rules (I), (II).We simplified constraint (13) using rules (I), (II), (III), (VII) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(15)    (Zero=x1484 & new_primModNatS02(x1484, x1479)=Succ(x1470) & Zero=x1479  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Zero, Zero, Zero, Zero))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(Zero)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (14) using rules (I), (II), (III), (VII) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(16)    (Succ(x1481)=x1491 & new_primModNatS02(x1491, x1482)=Succ(x1470) & Zero=x1482  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(Succ(x1481)))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x1481), Zero, Succ(x1481), Zero))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(Succ(x1481))))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (15) using rule (V) (with possible (I) afterwards) using induction on new_primModNatS02(x1484, x1479)=Succ(x1470) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(17)    (new_primModNatS1(new_primMinusNatS2(Succ(x1486), Succ(x1485)), Succ(x1485))=Succ(x1470) & Zero=x1486 & Zero=x1485  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Zero, Zero, Zero, Zero))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(Zero)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (17) using rules (III), (IV), (VII) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(18)    (new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Zero, Zero, Zero, Zero))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(Zero)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (16) using rule (V) (with possible (I) afterwards) using induction on new_primModNatS02(x1491, x1482)=Succ(x1470) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(19)    (new_primModNatS1(new_primMinusNatS2(Succ(x1493), Succ(x1492)), Succ(x1492))=Succ(x1470) & Succ(x1481)=x1493 & Zero=x1492  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(Succ(x1481)))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x1481), Zero, Succ(x1481), Zero))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(Succ(x1481))))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (19) using rules (III), (IV), (VII) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(20)    (new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(Succ(x1481)))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x1481), Zero, Succ(x1481), Zero))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(Succ(x1481))))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	For Pair new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) the following chains were created:
67.83/34.94	*We consider the chain new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))), new_gcd0Gcd'1(False, x1044, x1045) -> new_gcd0Gcd'0(x1044, new_rem(x1045, x1044)) which results in the following constraint:
67.83/34.94	
67.83/34.94	(1)    (new_gcd0Gcd'1(False, Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero)))))=new_gcd0Gcd'1(False, x1044, x1045)  ==>  new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero)))))_>=_new_gcd0Gcd'1(False, Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	We simplified constraint (1) using rules (I), (II), (IV) which results in the following new constraint:
67.83/34.94	
67.83/34.94	(2)    (new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero)))))_>=_new_gcd0Gcd'1(False, Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	
67.83/34.94	To summarize, we get the following constraints P__>=_ for the following pairs.
67.83/34.94	
67.83/34.94	*new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.83/34.94	
67.83/34.94	*(new_gcd0Gcd'0(Neg(Succ(Zero)), Neg(Succ(Succ(x4))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(x4))), Neg(Succ(Zero))))
67.83/34.94	
67.83/34.94	
67.83/34.94	*(new_gcd0Gcd'0(Pos(Succ(Zero)), Pos(Succ(Succ(x9))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(x9))), Pos(Succ(Zero))))
67.83/34.94	
67.83/34.94	
67.83/34.94	*(new_gcd0Gcd'0(Pos(Succ(Zero)), Neg(Succ(Succ(x12))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(x12))), Pos(Succ(Zero))))
67.83/34.94	
67.83/34.94	
67.83/34.94	*(new_gcd0Gcd'0(Neg(Succ(Zero)), Pos(Succ(Succ(x15))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(x15))), Neg(Succ(Zero))))
67.83/34.94	
67.83/34.94	
67.83/34.94	*(new_gcd0Gcd'0(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x18)))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(x18)))), Neg(Succ(Succ(Zero)))))
67.83/34.94	
67.83/34.94	
67.83/34.94	*(new_gcd0Gcd'0(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x21)))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(x21)))), Pos(Succ(Succ(Zero)))))
67.83/34.94	
67.83/34.94	
67.83/34.94	*(new_gcd0Gcd'0(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(x24)))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(x24)))), Pos(Succ(Succ(Zero)))))
67.83/34.94	
67.83/34.94	
67.83/34.94	*(new_gcd0Gcd'0(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(x27)))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(x27)))), Neg(Succ(Succ(Zero)))))
67.83/34.94	
67.83/34.94	
67.83/34.94	*(new_gcd0Gcd'0(Neg(Succ(Succ(Succ(Succ(x31))))), Neg(Succ(Succ(Succ(Succ(x30))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x30))))), Neg(Succ(Succ(Succ(Succ(x31)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	*(new_gcd0Gcd'0(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x34))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x34))))), Neg(Succ(Succ(Succ(Zero))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	*(new_gcd0Gcd'0(Neg(Succ(Succ(Succ(Succ(x37))))), Neg(Succ(Succ(Succ(Zero)))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x37)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	*(new_gcd0Gcd'0(Neg(Succ(Succ(Succ(Succ(x40))))), Neg(Succ(Succ(Zero))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x40)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	*(new_gcd0Gcd'0(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Zero))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	*(new_gcd0Gcd'0(Pos(Succ(Succ(Succ(Succ(x46))))), Pos(Succ(Succ(Succ(Succ(x45))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x45))))), Pos(Succ(Succ(Succ(Succ(x46)))))))
67.83/34.94	
67.83/34.94	
67.83/34.94	*(new_gcd0Gcd'0(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x49))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x49))))), Pos(Succ(Succ(Succ(Zero))))))
67.83/34.95	
67.83/34.95	
67.83/34.95	*(new_gcd0Gcd'0(Pos(Succ(Succ(Succ(Succ(x52))))), Pos(Succ(Succ(Succ(Zero)))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x52)))))))
67.83/34.95	
67.83/34.95	
67.83/34.95	*(new_gcd0Gcd'0(Pos(Succ(Succ(Succ(Succ(x55))))), Pos(Succ(Succ(Zero))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x55)))))))
67.83/34.95	
67.83/34.95	
67.83/34.95	*(new_gcd0Gcd'0(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Zero))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))))
67.83/34.95	
67.83/34.95	
67.83/34.95	*(new_gcd0Gcd'0(Pos(Succ(Succ(Succ(Succ(x61))))), Neg(Succ(Succ(Succ(Succ(x60))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x60))))), Pos(Succ(Succ(Succ(Succ(x61)))))))
67.83/34.95	
67.83/34.95	
67.83/34.95	*(new_gcd0Gcd'0(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x64))))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x64))))), Pos(Succ(Succ(Succ(Zero))))))
67.83/34.95	
67.83/34.95	
67.83/34.95	*(new_gcd0Gcd'0(Pos(Succ(Succ(Succ(Succ(x67))))), Neg(Succ(Succ(Succ(Zero)))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x67)))))))
67.83/34.95	
67.83/34.95	
67.83/34.95	*(new_gcd0Gcd'0(Pos(Succ(Succ(Succ(Succ(x70))))), Neg(Succ(Succ(Zero))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x70)))))))
67.83/34.95	
67.83/34.95	
67.83/34.95	*(new_gcd0Gcd'0(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Zero))))_>=_new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))))
67.83/34.95	
67.83/34.95	
67.83/34.95	*(new_gcd0Gcd'0(Neg(Succ(Succ(Succ(Succ(x76))))), Pos(Succ(Succ(Succ(Succ(x75))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x75))))), Neg(Succ(Succ(Succ(Succ(x76)))))))
67.83/34.95	
67.83/34.95	
67.83/34.95	*(new_gcd0Gcd'0(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x79))))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x79))))), Neg(Succ(Succ(Succ(Zero))))))
67.83/34.95	
67.83/34.95	
67.83/34.95	*(new_gcd0Gcd'0(Neg(Succ(Succ(Succ(Succ(x82))))), Pos(Succ(Succ(Succ(Zero)))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x82)))))))
67.83/34.95	
67.83/34.95	
67.83/34.95	*(new_gcd0Gcd'0(Neg(Succ(Succ(Succ(Succ(x85))))), Pos(Succ(Succ(Zero))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x85)))))))
67.83/34.95	
67.83/34.95	
67.83/34.95	*(new_gcd0Gcd'0(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Zero))))_>=_new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))))
67.83/34.95	
67.83/34.95	
67.83/34.95	
67.83/34.95	
67.83/34.95	*new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.83/34.95	
67.83/34.95	*(new_gcd0Gcd'(Neg(Succ(Succ(x90))), Neg(Succ(Zero)))_>=_new_gcd0Gcd'1(False, Neg(Succ(Succ(x90))), Neg(Succ(Zero))))
67.83/34.95	
67.83/34.95	
67.83/34.95	
67.83/34.95	
67.83/34.95	*new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.83/34.95	
67.83/34.95	*(new_gcd0Gcd'1(False, x120, x121)_>=_new_gcd0Gcd'0(x120, new_rem(x121, x120)))
67.83/34.95	
67.83/34.95	
67.83/34.95	
67.83/34.95	
67.83/34.95	*new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.83/34.95	
67.83/34.95	*(new_gcd0Gcd'(Pos(Succ(Succ(x184))), Pos(Succ(Zero)))_>=_new_gcd0Gcd'1(False, Pos(Succ(Succ(x184))), Pos(Succ(Zero))))
67.83/34.95	
67.83/34.95	
67.83/34.95	
67.83/34.95	
67.83/34.95	*new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.83/34.95	
67.83/34.95	*(new_gcd0Gcd'(Neg(Succ(Succ(x216))), Pos(Succ(Zero)))_>=_new_gcd0Gcd'1(False, Neg(Succ(Succ(x216))), Pos(Succ(Zero))))
67.83/34.95	
67.83/34.95	
67.83/34.95	
67.83/34.95	
67.83/34.95	*new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.83/34.95	
67.83/34.95	*(new_gcd0Gcd'(Pos(Succ(Succ(x248))), Neg(Succ(Zero)))_>=_new_gcd0Gcd'1(False, Pos(Succ(Succ(x248))), Neg(Succ(Zero))))
67.83/34.95	
67.83/34.95	
67.83/34.95	
67.83/34.95	
67.83/34.95	*new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.83/34.95	
67.83/34.95	*(new_gcd0Gcd'(Neg(Succ(Succ(Succ(x280)))), Neg(Succ(Succ(Zero))))_>=_new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x280)))), Neg(Succ(Succ(Zero)))))
67.83/34.95	
67.83/34.95	
67.83/34.95	
67.83/34.95	
67.83/34.95	*new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.83/34.95	
67.83/34.95	*(new_gcd0Gcd'(Pos(Succ(Succ(Succ(x312)))), Pos(Succ(Succ(Zero))))_>=_new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x312)))), Pos(Succ(Succ(Zero)))))
67.83/34.95	
67.83/34.95	
67.83/34.95	
67.83/34.95	
67.83/34.95	*new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.83/34.95	
67.83/34.95	*(new_gcd0Gcd'(Neg(Succ(Succ(Succ(x344)))), Pos(Succ(Succ(Zero))))_>=_new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x344)))), Pos(Succ(Succ(Zero)))))
67.83/34.95	
67.83/34.95	
67.83/34.95	
67.83/34.95	
67.83/34.95	*new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.83/34.95	
67.83/34.95	*(new_gcd0Gcd'(Pos(Succ(Succ(Succ(x376)))), Neg(Succ(Succ(Zero))))_>=_new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x376)))), Neg(Succ(Succ(Zero)))))
67.83/34.95	
67.83/34.95	
67.83/34.95	
67.83/34.95	
67.83/34.95	*new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.95	
67.83/34.95	*(new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Succ(x1072))))))), Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Succ(x1072)))), Succ(Zero), Succ(Succ(x1072))))), Neg(Succ(Succ(Succ(Succ(Succ(Succ(x1072))))))), Neg(Succ(Succ(Succ(Succ(Succ(Zero))))))))
67.83/34.95	
67.83/34.95	
67.83/34.95	*(new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(x1059)))))), Neg(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(Zero)), Succ(Succ(Succ(x1059))), Zero, Succ(x1059)))), Neg(Succ(Succ(Succ(Succ(Succ(x1059)))))), Neg(Succ(Succ(Succ(Succ(Zero)))))))
67.83/34.95	
67.83/34.95	
67.83/34.95	*(new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Succ(x1067))))))), Neg(Succ(Succ(Succ(Succ(Succ(Succ(x1068))))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(Succ(Succ(x1068)))), Succ(Succ(Succ(Succ(x1067)))), Succ(Succ(x1068)), Succ(Succ(x1067))))), Neg(Succ(Succ(Succ(Succ(Succ(Succ(x1067))))))), Neg(Succ(Succ(Succ(Succ(Succ(Succ(x1068)))))))))
67.83/34.95	
67.83/34.95	
67.83/34.95	*(new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))), Succ(Zero), Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(Succ(Succ(Succ(Succ(Succ(Zero))))))))
67.83/34.95	
67.83/34.95	
67.83/34.95	*(new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(Succ(Succ(Succ(Succ(Succ(Succ(x1077))))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(Succ(Succ(x1077)))), Succ(Succ(Succ(Zero))), Succ(Succ(x1077)), Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(Succ(Succ(Succ(Succ(Succ(Succ(x1077)))))))))
67.83/34.95	
67.83/34.95	
67.83/34.95	*(new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(Zero)), Succ(Succ(Zero)), Zero, Zero))), Neg(Succ(Succ(Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Succ(Zero)))))))
67.83/34.95	
67.83/34.95	
67.83/34.95	*(new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Succ(Succ(x1064)))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(Succ(x1064))), Succ(Succ(Zero)), Succ(x1064), Zero))), Neg(Succ(Succ(Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Succ(Succ(x1064))))))))
67.83/34.95	
67.83/34.95	
67.83/34.95	
67.83/34.95	
67.83/34.95	*new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.95	
67.83/34.95	*(new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x470))))), Neg(Succ(Succ(Succ(Zero)))))_>=_new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x470))))), Neg(Succ(Succ(Succ(Zero))))))
67.83/34.95	
67.83/34.95	
67.83/34.95	
67.83/34.95	
67.83/34.95	*new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.95	
67.83/34.95	*(new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(Zero), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(Zero)))))))
67.83/34.95	
67.83/34.95	
67.83/34.95	*(new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(Succ(Zero)), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(Succ(Zero))))))))
67.83/34.95	
67.83/34.95	
67.83/34.95	*(new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(Succ(Succ(x1108))))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(Succ(Succ(x1108))), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(Succ(Succ(x1108)))))))))
67.83/34.95	
67.83/34.95	
67.83/34.95	
67.83/34.95	
67.83/34.95	*new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0))))))
67.83/34.95	
67.83/34.95	*(new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Zero, Zero, Zero, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(Zero)))))))
67.83/34.95	
67.83/34.95	
67.83/34.95	*(new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(Succ(x1142)))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x1142), Zero, Succ(x1142), Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(Succ(x1142))))))))
67.83/34.95	
67.83/34.95	
67.83/34.95	
67.83/34.95	
67.83/34.95	*new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.95	
67.83/34.95	*(new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero)))))_>=_new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))))
67.83/34.95	
67.83/34.95	
67.83/34.95	
67.83/34.95	
67.83/34.95	*new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.95	
67.83/34.95	*(new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Succ(x1185))))))), Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Succ(x1185)))), Succ(Zero), Succ(Succ(x1185))))), Pos(Succ(Succ(Succ(Succ(Succ(Succ(x1185))))))), Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))))
67.83/34.95	
67.83/34.95	
67.83/34.95	*(new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(x1172)))))), Pos(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(Zero)), Succ(Succ(Succ(x1172))), Zero, Succ(x1172)))), Pos(Succ(Succ(Succ(Succ(Succ(x1172)))))), Pos(Succ(Succ(Succ(Succ(Zero)))))))
67.83/34.95	
67.83/34.95	
67.83/34.95	*(new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Succ(x1180))))))), Pos(Succ(Succ(Succ(Succ(Succ(Succ(x1181))))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(Succ(Succ(x1181)))), Succ(Succ(Succ(Succ(x1180)))), Succ(Succ(x1181)), Succ(Succ(x1180))))), Pos(Succ(Succ(Succ(Succ(Succ(Succ(x1180))))))), Pos(Succ(Succ(Succ(Succ(Succ(Succ(x1181)))))))))
67.83/34.95	
67.83/34.95	
67.83/34.95	*(new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))), Succ(Zero), Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))))
67.83/34.95	
67.83/34.95	
67.83/34.95	*(new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(Succ(Succ(Succ(Succ(Succ(Succ(x1190))))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(Succ(Succ(x1190)))), Succ(Succ(Succ(Zero))), Succ(Succ(x1190)), Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(Succ(Succ(Succ(Succ(Succ(Succ(x1190)))))))))
67.83/34.95	
67.83/34.95	
67.83/34.95	*(new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(Zero)), Succ(Succ(Zero)), Zero, Zero))), Pos(Succ(Succ(Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Succ(Zero)))))))
67.83/34.95	
67.83/34.95	
67.83/34.95	*(new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Succ(Succ(x1177)))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(Succ(x1177))), Succ(Succ(Zero)), Succ(x1177), Zero))), Pos(Succ(Succ(Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Succ(Succ(x1177))))))))
67.83/34.95	
67.83/34.95	
67.83/34.95	
67.83/34.95	
67.83/34.95	*new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.95	
67.83/34.95	*(new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x630))))), Pos(Succ(Succ(Succ(Zero)))))_>=_new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(Succ(x630))))), Pos(Succ(Succ(Succ(Zero))))))
67.83/34.95	
67.83/34.95	
67.83/34.95	
67.83/34.95	
67.83/34.95	*new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.95	
67.83/34.95	*(new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(Zero), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(Zero)))))))
67.83/34.95	
67.83/34.95	
67.83/34.95	*(new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(Succ(Zero)), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))))
67.83/34.95	
67.83/34.95	
67.83/34.95	*(new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(Succ(Succ(x1221))))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(Succ(Succ(x1221))), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(Succ(Succ(x1221)))))))))
67.83/34.95	
67.83/34.95	
67.83/34.95	
67.83/34.95	
67.83/34.95	*new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, Zero, x0, Zero))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.95	
67.83/34.95	*(new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Zero, Zero, Zero, Zero))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(Zero)))))))
67.83/34.95	
67.83/34.95	
67.83/34.95	*(new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(Succ(x1255)))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x1255), Zero, Succ(x1255), Zero))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(Succ(x1255))))))))
67.83/34.95	
67.83/34.95	
67.83/34.95	
67.83/34.95	
67.83/34.95	*new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.95	
67.83/34.95	*(new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero)))))_>=_new_gcd0Gcd'1(False, Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))))
67.83/34.95	
67.83/34.95	
67.83/34.95	
67.83/34.95	
67.83/34.95	*new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.95	
67.83/34.95	*(new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Succ(x1298))))))), Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Succ(x1298)))), Succ(Zero), Succ(Succ(x1298))))), Neg(Succ(Succ(Succ(Succ(Succ(Succ(x1298))))))), Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))))
67.83/34.95	
67.83/34.95	
67.83/34.95	*(new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(x1285)))))), Pos(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(Zero)), Succ(Succ(Succ(x1285))), Zero, Succ(x1285)))), Neg(Succ(Succ(Succ(Succ(Succ(x1285)))))), Pos(Succ(Succ(Succ(Succ(Zero)))))))
67.83/34.95	
67.83/34.95	
67.83/34.95	*(new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Succ(x1293))))))), Pos(Succ(Succ(Succ(Succ(Succ(Succ(x1294))))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(Succ(Succ(x1294)))), Succ(Succ(Succ(Succ(x1293)))), Succ(Succ(x1294)), Succ(Succ(x1293))))), Neg(Succ(Succ(Succ(Succ(Succ(Succ(x1293))))))), Pos(Succ(Succ(Succ(Succ(Succ(Succ(x1294)))))))))
67.83/34.95	
67.83/34.95	
67.83/34.95	*(new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))), Succ(Zero), Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))))
67.83/34.95	
67.83/34.95	
67.83/34.95	*(new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(Succ(Succ(Succ(Succ(Succ(Succ(x1303))))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(Succ(Succ(x1303)))), Succ(Succ(Succ(Zero))), Succ(Succ(x1303)), Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(Succ(Succ(Succ(Succ(Succ(Succ(x1303)))))))))
67.83/34.95	
67.83/34.95	
67.83/34.95	*(new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(Zero)), Succ(Succ(Zero)), Zero, Zero))), Neg(Succ(Succ(Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Succ(Zero)))))))
67.83/34.95	
67.83/34.95	
67.83/34.95	*(new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Succ(Succ(x1290)))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(Succ(x1290))), Succ(Succ(Zero)), Succ(x1290), Zero))), Neg(Succ(Succ(Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Succ(Succ(x1290))))))))
67.83/34.95	
67.83/34.95	
67.83/34.95	
67.83/34.95	
67.83/34.95	*new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.95	
67.83/34.95	*(new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x790))))), Pos(Succ(Succ(Succ(Zero)))))_>=_new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x790))))), Pos(Succ(Succ(Succ(Zero))))))
67.83/34.95	
67.83/34.95	
67.83/34.95	
67.83/34.95	
67.83/34.95	*new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.95	
67.83/34.95	*(new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(Zero), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(Zero)))))))
67.83/34.95	
67.83/34.95	
67.83/34.95	*(new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(Succ(Zero)), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))))
67.83/34.95	
67.83/34.95	
67.83/34.95	*(new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(Succ(Succ(x1334))))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(Succ(Succ(x1334))), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(Succ(Succ(x1334)))))))))
67.83/34.95	
67.83/34.95	
67.83/34.95	
67.83/34.95	
67.83/34.95	*new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.95	
67.83/34.95	*(new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Zero, Zero, Zero, Zero))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(Zero)))))))
67.83/34.95	
67.83/34.95	
67.83/34.95	*(new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(Succ(x1368)))))))_>=_new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(x1368), Zero, Succ(x1368), Zero))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(Succ(x1368))))))))
67.83/34.95	
67.83/34.95	
67.83/34.95	
67.83/34.95	
67.83/34.95	*new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.95	
67.83/34.95	*(new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero)))))_>=_new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))))
67.83/34.95	
67.83/34.95	
67.83/34.95	
67.83/34.95	
67.83/34.95	*new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Pos(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.95	
67.83/34.95	*(new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Succ(x1411))))))), Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Succ(x1411)))), Succ(Zero), Succ(Succ(x1411))))), Pos(Succ(Succ(Succ(Succ(Succ(Succ(x1411))))))), Neg(Succ(Succ(Succ(Succ(Succ(Zero))))))))
67.83/34.95	
67.83/34.95	
67.83/34.95	*(new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(x1398)))))), Neg(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(Zero)), Succ(Succ(Succ(x1398))), Zero, Succ(x1398)))), Pos(Succ(Succ(Succ(Succ(Succ(x1398)))))), Neg(Succ(Succ(Succ(Succ(Zero)))))))
67.83/34.95	
67.83/34.95	
67.83/34.95	*(new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Succ(x1406))))))), Neg(Succ(Succ(Succ(Succ(Succ(Succ(x1407))))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(Succ(Succ(x1407)))), Succ(Succ(Succ(Succ(x1406)))), Succ(Succ(x1407)), Succ(Succ(x1406))))), Pos(Succ(Succ(Succ(Succ(Succ(Succ(x1406))))))), Neg(Succ(Succ(Succ(Succ(Succ(Succ(x1407)))))))))
67.83/34.95	
67.83/34.95	
67.83/34.95	*(new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Zero))), Succ(Zero), Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(Succ(Succ(Succ(Succ(Succ(Zero))))))))
67.83/34.95	
67.83/34.95	
67.83/34.95	*(new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(Succ(Succ(Succ(Succ(Succ(Succ(x1416))))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(Succ(Succ(x1416)))), Succ(Succ(Succ(Zero))), Succ(Succ(x1416)), Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(Succ(Succ(Succ(Succ(Succ(Succ(x1416)))))))))
67.83/34.95	
67.83/34.95	
67.83/34.95	*(new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(Zero)), Succ(Succ(Zero)), Zero, Zero))), Pos(Succ(Succ(Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Succ(Zero)))))))
67.83/34.95	
67.83/34.95	
67.83/34.95	*(new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Succ(Succ(x1403)))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(Succ(x1403))), Succ(Succ(Zero)), Succ(x1403), Zero))), Pos(Succ(Succ(Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Succ(Succ(x1403))))))))
67.83/34.95	
67.83/34.95	
67.83/34.95	
67.83/34.95	
67.83/34.95	*new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.95	
67.83/34.95	*(new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x950))))), Neg(Succ(Succ(Succ(Zero)))))_>=_new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(Succ(x950))))), Neg(Succ(Succ(Succ(Zero))))))
67.83/34.95	
67.83/34.95	
67.83/34.95	
67.83/34.95	
67.83/34.95	*new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.95	
67.83/34.95	*(new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(Zero), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(Zero)))))))
67.83/34.95	
67.83/34.95	
67.83/34.95	*(new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(Succ(Zero)), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(Succ(Zero))))))))
67.83/34.95	
67.83/34.95	
67.83/34.95	*(new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(Succ(Succ(x1447))))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(Succ(Succ(x1447))), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(Succ(Succ(x1447)))))))))
67.83/34.95	
67.83/34.95	
67.83/34.95	
67.83/34.95	
67.83/34.95	*new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, Zero, x0, Zero))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0))))))
67.83/34.95	
67.83/34.95	*(new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(Zero))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Zero, Zero, Zero, Zero))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(Zero)))))))
67.83/34.95	
67.83/34.95	
67.83/34.95	*(new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(Succ(x1481)))))))_>=_new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(x1481), Zero, Succ(x1481), Zero))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(Succ(x1481))))))))
67.83/34.95	
67.83/34.95	
67.83/34.95	
67.83/34.95	
67.83/34.95	*new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.95	
67.83/34.95	*(new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero)))))_>=_new_gcd0Gcd'1(False, Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))))
67.83/34.95	
67.83/34.95	
67.83/34.95	
67.83/34.95	
67.83/34.95	
67.83/34.95	
67.83/34.95	
67.83/34.95	
67.83/34.95	The constraints for P_> respective P_bound are constructed from P__>=_ where we just replace every occurence of "t _>=_ s" in P__>=_ by  "t > s" respective "t _>=_ c". Here c stands for the fresh constant used for P_bound. 
67.83/34.95	----------------------------------------
67.83/34.95	
67.83/34.95	(433)
67.83/34.95	Obligation:
67.83/34.95	Q DP problem:
67.83/34.95	The TRS P consists of the following rules:
67.83/34.95	
67.83/34.95	   new_gcd0Gcd'0(vuz542, vuz557) -> new_gcd0Gcd'(vuz557, vuz542)
67.83/34.95	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Neg(Succ(Zero)))
67.83/34.95	   new_gcd0Gcd'1(False, vuz542, vuz549) -> new_gcd0Gcd'0(vuz542, new_rem(vuz549, vuz542))
67.83/34.95	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Pos(Succ(Zero)))
67.83/34.95	   new_gcd0Gcd'(Neg(Succ(Succ(x0))), Pos(Succ(Zero))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(x0))), Pos(Succ(Zero)))
67.83/34.95	   new_gcd0Gcd'(Pos(Succ(Succ(x0))), Neg(Succ(Zero))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(x0))), Neg(Succ(Zero)))
67.83/34.95	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.83/34.95	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.83/34.95	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(x2)))), Pos(Succ(Succ(Zero))))
67.83/34.95	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero)))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(x2)))), Neg(Succ(Succ(Zero))))
67.83/34.95	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.95	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.95	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.95	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0))))))
67.83/34.95	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.95	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Pos(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.95	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.95	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.95	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, Zero, x0, Zero))), Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.95	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.95	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Neg(Succ(Succ(Succ(Succ(x3))))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.95	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Succ(Succ(x2))))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.95	   new_gcd0Gcd'(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(Succ(Succ(Succ(x2))))))
67.83/34.95	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Pos(new_primModNatS01(x0, Zero, x0, Zero))), Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Succ(x0))))))
67.83/34.95	   new_gcd0Gcd'(Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Neg(Succ(Succ(Zero))), Pos(Succ(Succ(Succ(Zero)))))
67.83/34.95	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(Succ(Succ(x2)), Succ(Succ(x3)), x2, x3))), Pos(Succ(Succ(Succ(Succ(x3))))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.95	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Succ(Succ(x2))))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.95	   new_gcd0Gcd'(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS1(Succ(x2), Succ(Succ(Zero))))), Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(Succ(Succ(Succ(x2))))))
67.83/34.95	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0)))))) -> new_gcd0Gcd'1(new_esEs(Neg(new_primModNatS01(x0, Zero, x0, Zero))), Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Succ(x0))))))
67.83/34.95	   new_gcd0Gcd'(Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero))))) -> new_gcd0Gcd'1(False, Pos(Succ(Succ(Zero))), Neg(Succ(Succ(Succ(Zero)))))
67.83/34.95	
67.83/34.95	The TRS R consists of the following rules:
67.83/34.95	
67.83/34.95	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS01(vuz594, vuz595, vuz5960, vuz5970)
67.83/34.95	   new_primModNatS1(Succ(Succ(vuz549000)), Zero) -> new_primModNatS1(new_primMinusNatS0(vuz549000), Zero)
67.83/34.95	   new_esEs(Neg(Zero)) -> new_primEqInt2
67.83/34.95	   new_primModNatS1(Succ(Zero), Succ(vuz542000)) -> Succ(Zero)
67.83/34.95	   new_primMinusNatS2(Zero, Zero) -> Zero
67.83/34.95	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.83/34.95	   new_esEs(Pos(Zero)) -> new_primEqInt1
67.83/34.95	   new_primModNatS01(vuz594, vuz595, Zero, Succ(vuz5970)) -> Succ(Succ(vuz594))
67.83/34.95	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.83/34.95	   new_primModNatS1(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS01(vuz549000, vuz542000, vuz549000, vuz542000)
67.83/34.95	   new_rem(Neg(vuz5490), Neg(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.83/34.95	   new_primModNatS1(Zero, vuz54200) -> Zero
67.83/34.95	   new_rem(Pos(vuz5490), Pos(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.83/34.95	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.83/34.95	   new_error -> error([])
67.83/34.95	   new_esEs(Pos(Succ(vuz55100))) -> new_primEqInt(vuz55100)
67.83/34.95	   new_primEqInt2 -> True
67.83/34.95	   new_rem(Neg(vuz5490), Neg(Zero)) -> new_error
67.83/34.95	   new_primModNatS01(vuz594, vuz595, Zero, Zero) -> new_primModNatS02(vuz594, vuz595)
67.83/34.95	   new_rem(Pos(vuz5490), Neg(Zero)) -> new_error
67.83/34.95	   new_rem(Neg(vuz5490), Pos(Zero)) -> new_error
67.83/34.95	   new_esEs(Neg(Succ(vuz55100))) -> new_primEqInt0(vuz55100)
67.83/34.95	   new_primModNatS01(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS02(vuz594, vuz595)
67.83/34.95	   new_primModNatS1(Succ(Zero), Zero) -> new_primModNatS1(new_primMinusNatS1, Zero)
67.83/34.95	   new_primModNatS02(vuz594, vuz595) -> new_primModNatS1(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.83/34.95	   new_rem(Pos(vuz5490), Neg(Succ(vuz54200))) -> Pos(new_primModNatS1(vuz5490, vuz54200))
67.83/34.95	   new_primMinusNatS1 -> Zero
67.83/34.95	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.83/34.95	   new_primEqInt1 -> True
67.83/34.95	   new_rem(Neg(vuz5490), Pos(Succ(vuz54200))) -> Neg(new_primModNatS1(vuz5490, vuz54200))
67.83/34.95	   new_primEqInt0(vuz3260) -> False
67.83/34.95	   new_primEqInt(vuz3250) -> False
67.83/34.95	   new_rem(Pos(vuz5490), Pos(Zero)) -> new_error
67.83/34.95	
67.83/34.95	The set Q consists of the following terms:
67.83/34.95	
67.83/34.95	   new_rem(Neg(x0), Neg(Zero))
67.83/34.95	   new_primEqInt1
67.83/34.95	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
67.83/34.95	   new_primModNatS1(Succ(Succ(x0)), Succ(x1))
67.83/34.95	   new_primMinusNatS1
67.83/34.95	   new_rem(Neg(x0), Neg(Succ(x1)))
67.83/34.95	   new_primMinusNatS2(Succ(x0), Zero)
67.83/34.95	   new_primModNatS1(Succ(Zero), Succ(x0))
67.83/34.95	   new_primMinusNatS2(Zero, Zero)
67.83/34.95	   new_error
67.83/34.95	   new_primModNatS1(Succ(Zero), Zero)
67.83/34.95	   new_rem(Pos(x0), Pos(Zero))
67.83/34.95	   new_primModNatS01(x0, x1, Zero, Zero)
67.83/34.95	   new_primEqInt0(x0)
67.83/34.95	   new_esEs(Pos(Zero))
67.83/34.95	   new_esEs(Pos(Succ(x0)))
67.83/34.95	   new_rem(Pos(x0), Pos(Succ(x1)))
67.83/34.95	   new_primModNatS02(x0, x1)
67.83/34.95	   new_primMinusNatS2(Zero, Succ(x0))
67.83/34.95	   new_rem(Pos(x0), Neg(Succ(x1)))
67.83/34.95	   new_rem(Neg(x0), Pos(Succ(x1)))
67.83/34.95	   new_primModNatS1(Zero, x0)
67.83/34.95	   new_primEqInt(x0)
67.83/34.95	   new_primModNatS01(x0, x1, Zero, Succ(x2))
67.83/34.95	   new_primModNatS1(Succ(Succ(x0)), Zero)
67.83/34.95	   new_rem(Pos(x0), Neg(Zero))
67.83/34.95	   new_rem(Neg(x0), Pos(Zero))
67.83/34.95	   new_primMinusNatS0(x0)
67.83/34.95	   new_primEqInt2
67.83/34.95	   new_esEs(Neg(Zero))
67.83/34.95	   new_esEs(Neg(Succ(x0)))
67.83/34.95	   new_primModNatS01(x0, x1, Succ(x2), Zero)
67.83/34.95	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.83/34.95	
67.83/34.95	We have to consider all minimal (P,Q,R)-chains.
67.83/34.95	----------------------------------------
67.83/34.95	
67.83/34.95	(434)
67.83/34.95	Obligation:
67.83/34.95	Q DP problem:
67.83/34.95	The TRS P consists of the following rules:
67.83/34.95	
67.83/34.95	   new_primQuotInt6(Succ(vuz4010), Succ(vuz4000), vuz403, vuz402, vuz3190, vuz31700) -> new_primQuotInt6(vuz4010, vuz4000, vuz4010, vuz4000, vuz3190, vuz31700)
67.83/34.95	
67.83/34.95	R is empty.
67.83/34.95	Q is empty.
67.83/34.95	We have to consider all minimal (P,Q,R)-chains.
67.83/34.95	----------------------------------------
67.83/34.95	
67.83/34.95	(435) TransformationProof (EQUIVALENT)
67.83/34.95	By instantiating [LPAR04] the rule new_primQuotInt6(Succ(vuz4010), Succ(vuz4000), vuz403, vuz402, vuz3190, vuz31700) -> new_primQuotInt6(vuz4010, vuz4000, vuz4010, vuz4000, vuz3190, vuz31700) we obtained the following new rules [LPAR04]:
67.83/34.95	
67.83/34.95	   (new_primQuotInt6(Succ(x0), Succ(x1), Succ(x0), Succ(x1), z4, z5) -> new_primQuotInt6(x0, x1, x0, x1, z4, z5),new_primQuotInt6(Succ(x0), Succ(x1), Succ(x0), Succ(x1), z4, z5) -> new_primQuotInt6(x0, x1, x0, x1, z4, z5))
67.83/34.95	
67.83/34.95	
67.83/34.95	----------------------------------------
67.83/34.95	
67.83/34.95	(436)
67.83/34.95	Obligation:
67.83/34.95	Q DP problem:
67.83/34.95	The TRS P consists of the following rules:
67.83/34.95	
67.83/34.95	   new_primQuotInt6(Succ(x0), Succ(x1), Succ(x0), Succ(x1), z4, z5) -> new_primQuotInt6(x0, x1, x0, x1, z4, z5)
67.83/34.95	
67.83/34.95	R is empty.
67.83/34.95	Q is empty.
67.83/34.95	We have to consider all minimal (P,Q,R)-chains.
67.83/34.95	----------------------------------------
67.83/34.95	
67.83/34.95	(437) QDPSizeChangeProof (EQUIVALENT)
67.83/34.95	By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 
67.83/34.95	
67.83/34.95	From the DPs we obtained the following set of size-change graphs:
67.83/34.95	*new_primQuotInt6(Succ(x0), Succ(x1), Succ(x0), Succ(x1), z4, z5) -> new_primQuotInt6(x0, x1, x0, x1, z4, z5)
67.83/34.95	The graph contains the following edges 1 > 1, 3 > 1, 2 > 2, 4 > 2, 1 > 3, 3 > 3, 2 > 4, 4 > 4, 5 >= 5, 6 >= 6
67.83/34.95	
67.83/34.95	
67.83/34.95	----------------------------------------
67.83/34.95	
67.83/34.95	(438)
67.83/34.95	YES
67.83/34.95	
67.83/34.95	----------------------------------------
67.83/34.95	
67.83/34.95	(439)
67.83/34.95	Obligation:
67.83/34.95	Q DP problem:
67.83/34.95	The TRS P consists of the following rules:
67.83/34.95	
67.83/34.95	   new_primPlusNat(Succ(vuz33500), Succ(vuz3071000)) -> new_primPlusNat(vuz33500, vuz3071000)
67.83/34.95	
67.83/34.95	R is empty.
67.83/34.95	Q is empty.
67.83/34.95	We have to consider all minimal (P,Q,R)-chains.
67.83/34.95	----------------------------------------
67.83/34.95	
67.83/34.95	(440) QDPSizeChangeProof (EQUIVALENT)
67.83/34.95	By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 
67.83/34.95	
67.83/34.95	From the DPs we obtained the following set of size-change graphs:
67.83/34.95	*new_primPlusNat(Succ(vuz33500), Succ(vuz3071000)) -> new_primPlusNat(vuz33500, vuz3071000)
67.83/34.95	The graph contains the following edges 1 > 1, 2 > 2
67.83/34.95	
67.83/34.95	
67.83/34.95	----------------------------------------
67.83/34.95	
67.83/34.95	(441)
67.83/34.95	YES
67.83/34.95	
67.83/34.95	----------------------------------------
67.83/34.95	
67.83/34.95	(442)
67.83/34.95	Obligation:
67.83/34.95	Q DP problem:
67.83/34.95	The TRS P consists of the following rules:
67.83/34.95	
67.83/34.95	   new_primQuotInt1(Succ(vuz4570), Succ(vuz4560), vuz459, vuz458, vuz3190, vuz31700) -> new_primQuotInt1(vuz4570, vuz4560, vuz4570, vuz4560, vuz3190, vuz31700)
67.83/34.95	
67.83/34.95	R is empty.
67.83/34.95	Q is empty.
67.83/34.95	We have to consider all minimal (P,Q,R)-chains.
67.83/34.95	----------------------------------------
67.83/34.95	
67.83/34.95	(443) TransformationProof (EQUIVALENT)
67.83/34.95	By instantiating [LPAR04] the rule new_primQuotInt1(Succ(vuz4570), Succ(vuz4560), vuz459, vuz458, vuz3190, vuz31700) -> new_primQuotInt1(vuz4570, vuz4560, vuz4570, vuz4560, vuz3190, vuz31700) we obtained the following new rules [LPAR04]:
67.83/34.95	
67.83/34.95	   (new_primQuotInt1(Succ(x0), Succ(x1), Succ(x0), Succ(x1), z4, z5) -> new_primQuotInt1(x0, x1, x0, x1, z4, z5),new_primQuotInt1(Succ(x0), Succ(x1), Succ(x0), Succ(x1), z4, z5) -> new_primQuotInt1(x0, x1, x0, x1, z4, z5))
67.83/34.95	
67.83/34.95	
67.83/34.95	----------------------------------------
67.83/34.95	
67.83/34.95	(444)
67.83/34.95	Obligation:
67.83/34.95	Q DP problem:
67.83/34.95	The TRS P consists of the following rules:
67.83/34.95	
67.83/34.95	   new_primQuotInt1(Succ(x0), Succ(x1), Succ(x0), Succ(x1), z4, z5) -> new_primQuotInt1(x0, x1, x0, x1, z4, z5)
67.83/34.95	
67.83/34.95	R is empty.
67.83/34.95	Q is empty.
67.83/34.95	We have to consider all minimal (P,Q,R)-chains.
67.83/34.95	----------------------------------------
67.83/34.95	
67.83/34.95	(445) QDPSizeChangeProof (EQUIVALENT)
67.83/34.95	By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 
67.83/34.95	
67.83/34.95	From the DPs we obtained the following set of size-change graphs:
67.83/34.95	*new_primQuotInt1(Succ(x0), Succ(x1), Succ(x0), Succ(x1), z4, z5) -> new_primQuotInt1(x0, x1, x0, x1, z4, z5)
67.83/34.95	The graph contains the following edges 1 > 1, 3 > 1, 2 > 2, 4 > 2, 1 > 3, 3 > 3, 2 > 4, 4 > 4, 5 >= 5, 6 >= 6
67.83/34.95	
67.83/34.95	
67.83/34.95	----------------------------------------
67.83/34.95	
67.83/34.95	(446)
67.83/34.95	YES
67.83/34.95	
67.83/34.95	----------------------------------------
67.83/34.95	
67.83/34.95	(447)
67.83/34.95	Obligation:
67.83/34.95	Q DP problem:
67.83/34.95	The TRS P consists of the following rules:
67.83/34.95	
67.83/34.95	   new_primModNatS(Succ(Succ(vuz549000)), Zero) -> new_primModNatS(new_primMinusNatS0(vuz549000), Zero)
67.83/34.95	   new_primModNatS(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS0(vuz549000, vuz542000, vuz549000, vuz542000)
67.83/34.95	   new_primModNatS(Succ(Zero), Zero) -> new_primModNatS(new_primMinusNatS1, Zero)
67.83/34.95	   new_primModNatS0(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.83/34.95	   new_primModNatS0(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS0(vuz594, vuz595, vuz5960, vuz5970)
67.83/34.95	   new_primModNatS0(vuz594, vuz595, Zero, Zero) -> new_primModNatS00(vuz594, vuz595)
67.83/34.95	   new_primModNatS00(vuz594, vuz595) -> new_primModNatS(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.83/34.95	
67.83/34.95	The TRS R consists of the following rules:
67.83/34.95	
67.83/34.95	   new_primMinusNatS1 -> Zero
67.83/34.95	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.83/34.95	   new_primMinusNatS2(Zero, Zero) -> Zero
67.83/34.95	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.83/34.95	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.83/34.95	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.83/34.95	
67.83/34.95	The set Q consists of the following terms:
67.83/34.95	
67.83/34.95	   new_primMinusNatS2(Succ(x0), Zero)
67.83/34.95	   new_primMinusNatS0(x0)
67.83/34.95	   new_primMinusNatS2(Zero, Succ(x0))
67.83/34.95	   new_primMinusNatS2(Zero, Zero)
67.83/34.95	   new_primMinusNatS1
67.83/34.95	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.83/34.95	
67.83/34.95	We have to consider all minimal (P,Q,R)-chains.
67.83/34.95	----------------------------------------
67.83/34.95	
67.83/34.95	(448) DependencyGraphProof (EQUIVALENT)
67.83/34.95	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 2 SCCs with 1 less node.
67.83/34.95	----------------------------------------
67.83/34.95	
67.83/34.95	(449)
67.83/34.95	Complex Obligation (AND)
67.83/34.95	
67.83/34.95	----------------------------------------
67.83/34.95	
67.83/34.95	(450)
67.83/34.95	Obligation:
67.83/34.95	Q DP problem:
67.83/34.95	The TRS P consists of the following rules:
67.83/34.95	
67.83/34.95	   new_primModNatS0(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.83/34.95	   new_primModNatS(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS0(vuz549000, vuz542000, vuz549000, vuz542000)
67.83/34.95	   new_primModNatS0(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS0(vuz594, vuz595, vuz5960, vuz5970)
67.83/34.95	   new_primModNatS0(vuz594, vuz595, Zero, Zero) -> new_primModNatS00(vuz594, vuz595)
67.83/34.95	   new_primModNatS00(vuz594, vuz595) -> new_primModNatS(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.83/34.95	
67.83/34.95	The TRS R consists of the following rules:
67.83/34.95	
67.83/34.95	   new_primMinusNatS1 -> Zero
67.83/34.95	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.83/34.95	   new_primMinusNatS2(Zero, Zero) -> Zero
67.83/34.95	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.83/34.95	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.83/34.95	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.83/34.95	
67.83/34.95	The set Q consists of the following terms:
67.83/34.95	
67.83/34.95	   new_primMinusNatS2(Succ(x0), Zero)
67.83/34.95	   new_primMinusNatS0(x0)
67.83/34.95	   new_primMinusNatS2(Zero, Succ(x0))
67.83/34.95	   new_primMinusNatS2(Zero, Zero)
67.83/34.95	   new_primMinusNatS1
67.83/34.95	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.83/34.95	
67.83/34.95	We have to consider all minimal (P,Q,R)-chains.
67.83/34.95	----------------------------------------
67.83/34.95	
67.83/34.95	(451) QDPOrderProof (EQUIVALENT)
67.83/34.95	We use the reduction pair processor [LPAR04,JAR06].
67.83/34.95	
67.83/34.95	
67.83/34.95	The following pairs can be oriented strictly and are deleted.
67.83/34.95	
67.83/34.95	   new_primModNatS(Succ(Succ(vuz549000)), Succ(vuz542000)) -> new_primModNatS0(vuz549000, vuz542000, vuz549000, vuz542000)
67.83/34.95	The remaining pairs can at least be oriented weakly.
67.83/34.95	Used ordering:  Polynomial interpretation [POLO]:
67.83/34.95	
67.83/34.95	   POL(Succ(x_1)) = 1 + x_1
67.83/34.95	   POL(Zero) = 1
67.83/34.95	   POL(new_primMinusNatS2(x_1, x_2)) = x_1
67.83/34.95	   POL(new_primModNatS(x_1, x_2)) = x_1
67.83/34.95	   POL(new_primModNatS0(x_1, x_2, x_3, x_4)) = 1 + x_1
67.83/34.95	   POL(new_primModNatS00(x_1, x_2)) = 1 + x_1
67.83/34.95	
67.83/34.95	The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
67.83/34.95	
67.83/34.95	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.83/34.95	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.83/34.95	   new_primMinusNatS2(Zero, Zero) -> Zero
67.83/34.95	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.83/34.95	
67.83/34.95	
67.83/34.95	----------------------------------------
67.83/34.95	
67.83/34.95	(452)
67.83/34.95	Obligation:
67.83/34.95	Q DP problem:
67.83/34.95	The TRS P consists of the following rules:
67.83/34.95	
67.83/34.95	   new_primModNatS0(vuz594, vuz595, Succ(vuz5960), Zero) -> new_primModNatS(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.83/34.95	   new_primModNatS0(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS0(vuz594, vuz595, vuz5960, vuz5970)
67.83/34.95	   new_primModNatS0(vuz594, vuz595, Zero, Zero) -> new_primModNatS00(vuz594, vuz595)
67.83/34.95	   new_primModNatS00(vuz594, vuz595) -> new_primModNatS(new_primMinusNatS2(Succ(vuz594), Succ(vuz595)), Succ(vuz595))
67.83/34.95	
67.83/34.95	The TRS R consists of the following rules:
67.83/34.95	
67.83/34.95	   new_primMinusNatS1 -> Zero
67.83/34.95	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.83/34.95	   new_primMinusNatS2(Zero, Zero) -> Zero
67.83/34.95	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.83/34.95	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.83/34.95	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.83/34.95	
67.83/34.95	The set Q consists of the following terms:
67.83/34.95	
67.83/34.95	   new_primMinusNatS2(Succ(x0), Zero)
67.83/34.95	   new_primMinusNatS0(x0)
67.83/34.95	   new_primMinusNatS2(Zero, Succ(x0))
67.83/34.95	   new_primMinusNatS2(Zero, Zero)
67.83/34.95	   new_primMinusNatS1
67.83/34.95	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.83/34.95	
67.83/34.95	We have to consider all minimal (P,Q,R)-chains.
67.83/34.95	----------------------------------------
67.83/34.95	
67.83/34.95	(453) DependencyGraphProof (EQUIVALENT)
67.83/34.95	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 3 less nodes.
67.83/34.95	----------------------------------------
67.83/34.95	
67.83/34.95	(454)
67.83/34.95	Obligation:
67.83/34.95	Q DP problem:
67.83/34.95	The TRS P consists of the following rules:
67.83/34.95	
67.83/34.95	   new_primModNatS0(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS0(vuz594, vuz595, vuz5960, vuz5970)
67.83/34.95	
67.83/34.95	The TRS R consists of the following rules:
67.83/34.95	
67.83/34.95	   new_primMinusNatS1 -> Zero
67.83/34.95	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.83/34.95	   new_primMinusNatS2(Zero, Zero) -> Zero
67.83/34.95	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.83/34.95	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.83/34.95	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.83/34.95	
67.83/34.95	The set Q consists of the following terms:
67.83/34.95	
67.83/34.95	   new_primMinusNatS2(Succ(x0), Zero)
67.83/34.95	   new_primMinusNatS0(x0)
67.83/34.95	   new_primMinusNatS2(Zero, Succ(x0))
67.83/34.95	   new_primMinusNatS2(Zero, Zero)
67.83/34.95	   new_primMinusNatS1
67.83/34.95	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.83/34.95	
67.83/34.95	We have to consider all minimal (P,Q,R)-chains.
67.83/34.95	----------------------------------------
67.83/34.95	
67.83/34.95	(455) QDPSizeChangeProof (EQUIVALENT)
67.83/34.95	By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 
67.83/34.95	
67.83/34.95	From the DPs we obtained the following set of size-change graphs:
67.83/34.95	*new_primModNatS0(vuz594, vuz595, Succ(vuz5960), Succ(vuz5970)) -> new_primModNatS0(vuz594, vuz595, vuz5960, vuz5970)
67.83/34.95	The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 > 4
67.83/34.95	
67.83/34.95	
67.83/34.95	----------------------------------------
67.83/34.95	
67.83/34.95	(456)
67.83/34.95	YES
67.83/34.95	
67.83/34.95	----------------------------------------
67.83/34.95	
67.83/34.95	(457)
67.83/34.95	Obligation:
67.83/34.95	Q DP problem:
67.83/34.95	The TRS P consists of the following rules:
67.83/34.95	
67.83/34.95	   new_primModNatS(Succ(Succ(vuz549000)), Zero) -> new_primModNatS(new_primMinusNatS0(vuz549000), Zero)
67.83/34.95	
67.83/34.95	The TRS R consists of the following rules:
67.83/34.95	
67.83/34.95	   new_primMinusNatS1 -> Zero
67.83/34.95	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.83/34.95	   new_primMinusNatS2(Zero, Zero) -> Zero
67.83/34.95	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.83/34.95	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.83/34.95	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.83/34.95	
67.83/34.95	The set Q consists of the following terms:
67.83/34.95	
67.83/34.95	   new_primMinusNatS2(Succ(x0), Zero)
67.83/34.95	   new_primMinusNatS0(x0)
67.83/34.95	   new_primMinusNatS2(Zero, Succ(x0))
67.83/34.95	   new_primMinusNatS2(Zero, Zero)
67.83/34.95	   new_primMinusNatS1
67.83/34.95	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.83/34.95	
67.83/34.95	We have to consider all minimal (P,Q,R)-chains.
67.83/34.95	----------------------------------------
67.83/34.95	
67.83/34.95	(458) MRRProof (EQUIVALENT)
67.83/34.95	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.
67.83/34.95	
67.83/34.95	Strictly oriented dependency pairs:
67.83/34.95	
67.83/34.95	   new_primModNatS(Succ(Succ(vuz549000)), Zero) -> new_primModNatS(new_primMinusNatS0(vuz549000), Zero)
67.83/34.95	
67.83/34.95	Strictly oriented rules of the TRS R:
67.83/34.95	
67.83/34.95	   new_primMinusNatS2(Succ(vuz5740), Zero) -> Succ(vuz5740)
67.83/34.95	   new_primMinusNatS2(Zero, Zero) -> Zero
67.83/34.95	   new_primMinusNatS2(Succ(vuz5740), Succ(vuz5750)) -> new_primMinusNatS2(vuz5740, vuz5750)
67.83/34.95	   new_primMinusNatS2(Zero, Succ(vuz5750)) -> Zero
67.83/34.95	
67.83/34.95	Used ordering: Polynomial interpretation [POLO]:
67.83/34.95	
67.83/34.95	   POL(Succ(x_1)) = 1 + x_1
67.83/34.95	   POL(Zero) = 2
67.83/34.95	   POL(new_primMinusNatS0(x_1)) = 1 + x_1
67.83/34.95	   POL(new_primMinusNatS1) = 2
67.83/34.95	   POL(new_primMinusNatS2(x_1, x_2)) = 1 + 2*x_1 + 2*x_2
67.83/34.95	   POL(new_primModNatS(x_1, x_2)) = x_1 + x_2
67.83/34.95	
67.83/34.95	
67.83/34.95	----------------------------------------
67.83/34.95	
67.83/34.95	(459)
67.83/34.95	Obligation:
67.83/34.95	Q DP problem:
67.83/34.95	P is empty.
67.83/34.95	The TRS R consists of the following rules:
67.83/34.95	
67.83/34.95	   new_primMinusNatS1 -> Zero
67.83/34.95	   new_primMinusNatS0(vuz41600) -> Succ(vuz41600)
67.83/34.95	
67.83/34.95	The set Q consists of the following terms:
67.83/34.95	
67.83/34.95	   new_primMinusNatS2(Succ(x0), Zero)
67.83/34.95	   new_primMinusNatS0(x0)
67.83/34.95	   new_primMinusNatS2(Zero, Succ(x0))
67.83/34.95	   new_primMinusNatS2(Zero, Zero)
67.83/34.95	   new_primMinusNatS1
67.83/34.95	   new_primMinusNatS2(Succ(x0), Succ(x1))
67.83/34.95	
67.83/34.95	We have to consider all minimal (P,Q,R)-chains.
67.83/34.95	----------------------------------------
67.83/34.95	
67.83/34.95	(460) PisEmptyProof (EQUIVALENT)
67.83/34.95	The TRS P is empty. Hence, there is no (P,Q,R) chain.
67.83/34.95	----------------------------------------
67.83/34.95	
67.83/34.95	(461)
67.83/34.95	YES
67.83/34.95	
67.83/34.95	----------------------------------------
67.83/34.95	
67.83/34.95	(462)
67.83/34.95	Obligation:
67.83/34.95	Q DP problem:
67.83/34.95	The TRS P consists of the following rules:
67.83/34.95	
67.83/34.95	   new_primQuotInt4(Succ(vuz4190), Succ(vuz4180), vuz421, vuz420, vuz31900, vuz3170) -> new_primQuotInt4(vuz4190, vuz4180, vuz4190, vuz4180, vuz31900, vuz3170)
67.83/34.95	
67.83/34.95	R is empty.
67.83/34.95	Q is empty.
67.83/34.95	We have to consider all minimal (P,Q,R)-chains.
67.83/34.95	----------------------------------------
67.83/34.95	
67.83/34.95	(463) TransformationProof (EQUIVALENT)
67.83/34.95	By instantiating [LPAR04] the rule new_primQuotInt4(Succ(vuz4190), Succ(vuz4180), vuz421, vuz420, vuz31900, vuz3170) -> new_primQuotInt4(vuz4190, vuz4180, vuz4190, vuz4180, vuz31900, vuz3170) we obtained the following new rules [LPAR04]:
67.83/34.95	
67.83/34.95	   (new_primQuotInt4(Succ(x0), Succ(x1), Succ(x0), Succ(x1), z4, z5) -> new_primQuotInt4(x0, x1, x0, x1, z4, z5),new_primQuotInt4(Succ(x0), Succ(x1), Succ(x0), Succ(x1), z4, z5) -> new_primQuotInt4(x0, x1, x0, x1, z4, z5))
67.83/34.95	
67.83/34.95	
67.83/34.95	----------------------------------------
67.83/34.95	
67.83/34.95	(464)
67.83/34.95	Obligation:
67.83/34.95	Q DP problem:
67.83/34.95	The TRS P consists of the following rules:
67.83/34.95	
67.83/34.95	   new_primQuotInt4(Succ(x0), Succ(x1), Succ(x0), Succ(x1), z4, z5) -> new_primQuotInt4(x0, x1, x0, x1, z4, z5)
67.83/34.95	
67.83/34.95	R is empty.
67.83/34.95	Q is empty.
67.83/34.95	We have to consider all minimal (P,Q,R)-chains.
67.83/34.95	----------------------------------------
67.83/34.95	
67.83/34.95	(465) QDPSizeChangeProof (EQUIVALENT)
67.83/34.95	By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 
67.83/34.95	
67.83/34.95	From the DPs we obtained the following set of size-change graphs:
67.83/34.95	*new_primQuotInt4(Succ(x0), Succ(x1), Succ(x0), Succ(x1), z4, z5) -> new_primQuotInt4(x0, x1, x0, x1, z4, z5)
67.83/34.95	The graph contains the following edges 1 > 1, 3 > 1, 2 > 2, 4 > 2, 1 > 3, 3 > 3, 2 > 4, 4 > 4, 5 >= 5, 6 >= 6
67.83/34.95	
67.83/34.95	
67.83/34.95	----------------------------------------
67.83/34.95	
67.83/34.95	(466)
67.83/34.95	YES
67.83/34.95	
67.83/34.95	----------------------------------------
67.83/34.95	
67.83/34.95	(467)
67.83/34.95	Obligation:
67.83/34.95	Q DP problem:
67.83/34.95	The TRS P consists of the following rules:
67.83/34.95	
67.83/34.95	   new_primQuotInt3(Succ(vuz4650), Succ(vuz4640), vuz467, vuz466, vuz3190, vuz31700) -> new_primQuotInt3(vuz4650, vuz4640, vuz4650, vuz4640, vuz3190, vuz31700)
67.83/34.95	
67.83/34.95	R is empty.
67.83/34.95	Q is empty.
67.83/34.95	We have to consider all minimal (P,Q,R)-chains.
67.83/34.95	----------------------------------------
67.83/34.95	
67.83/34.95	(468) TransformationProof (EQUIVALENT)
67.83/34.95	By instantiating [LPAR04] the rule new_primQuotInt3(Succ(vuz4650), Succ(vuz4640), vuz467, vuz466, vuz3190, vuz31700) -> new_primQuotInt3(vuz4650, vuz4640, vuz4650, vuz4640, vuz3190, vuz31700) we obtained the following new rules [LPAR04]:
67.83/34.95	
67.83/34.95	   (new_primQuotInt3(Succ(x0), Succ(x1), Succ(x0), Succ(x1), z4, z5) -> new_primQuotInt3(x0, x1, x0, x1, z4, z5),new_primQuotInt3(Succ(x0), Succ(x1), Succ(x0), Succ(x1), z4, z5) -> new_primQuotInt3(x0, x1, x0, x1, z4, z5))
67.83/34.95	
67.83/34.95	
67.83/34.95	----------------------------------------
67.83/34.95	
67.83/34.95	(469)
67.83/34.95	Obligation:
67.83/34.95	Q DP problem:
67.83/34.95	The TRS P consists of the following rules:
67.83/34.95	
67.83/34.95	   new_primQuotInt3(Succ(x0), Succ(x1), Succ(x0), Succ(x1), z4, z5) -> new_primQuotInt3(x0, x1, x0, x1, z4, z5)
67.83/34.95	
67.83/34.95	R is empty.
67.83/34.95	Q is empty.
67.83/34.95	We have to consider all minimal (P,Q,R)-chains.
67.83/34.95	----------------------------------------
67.83/34.95	
67.83/34.95	(470) QDPSizeChangeProof (EQUIVALENT)
67.83/34.95	By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 
67.83/34.95	
67.83/34.95	From the DPs we obtained the following set of size-change graphs:
67.83/34.95	*new_primQuotInt3(Succ(x0), Succ(x1), Succ(x0), Succ(x1), z4, z5) -> new_primQuotInt3(x0, x1, x0, x1, z4, z5)
67.83/34.95	The graph contains the following edges 1 > 1, 3 > 1, 2 > 2, 4 > 2, 1 > 3, 3 > 3, 2 > 4, 4 > 4, 5 >= 5, 6 >= 6
67.83/34.95	
67.83/34.95	
67.83/34.95	----------------------------------------
67.83/34.95	
67.83/34.95	(471)
67.83/34.95	YES
67.83/34.95	
67.83/34.95	----------------------------------------
67.83/34.95	
67.83/34.95	(472)
67.83/34.95	Obligation:
67.83/34.95	Q DP problem:
67.83/34.95	The TRS P consists of the following rules:
67.83/34.95	
67.83/34.95	   new_primQuotInt2(Succ(vuz4310), Succ(vuz4300), vuz433, vuz432, vuz31900, vuz3170) -> new_primQuotInt2(vuz4310, vuz4300, vuz4310, vuz4300, vuz31900, vuz3170)
67.83/34.95	
67.83/34.95	R is empty.
67.83/34.95	Q is empty.
67.83/34.95	We have to consider all minimal (P,Q,R)-chains.
67.83/34.95	----------------------------------------
67.83/34.95	
67.83/34.95	(473) TransformationProof (EQUIVALENT)
67.83/34.95	By instantiating [LPAR04] the rule new_primQuotInt2(Succ(vuz4310), Succ(vuz4300), vuz433, vuz432, vuz31900, vuz3170) -> new_primQuotInt2(vuz4310, vuz4300, vuz4310, vuz4300, vuz31900, vuz3170) we obtained the following new rules [LPAR04]:
67.83/34.95	
67.83/34.95	   (new_primQuotInt2(Succ(x0), Succ(x1), Succ(x0), Succ(x1), z4, z5) -> new_primQuotInt2(x0, x1, x0, x1, z4, z5),new_primQuotInt2(Succ(x0), Succ(x1), Succ(x0), Succ(x1), z4, z5) -> new_primQuotInt2(x0, x1, x0, x1, z4, z5))
67.83/34.95	
67.83/34.95	
67.83/34.95	----------------------------------------
67.83/34.95	
67.83/34.95	(474)
67.83/34.95	Obligation:
67.83/34.95	Q DP problem:
67.83/34.95	The TRS P consists of the following rules:
67.83/34.95	
67.83/34.95	   new_primQuotInt2(Succ(x0), Succ(x1), Succ(x0), Succ(x1), z4, z5) -> new_primQuotInt2(x0, x1, x0, x1, z4, z5)
67.83/34.95	
67.83/34.95	R is empty.
67.83/34.95	Q is empty.
67.83/34.95	We have to consider all minimal (P,Q,R)-chains.
67.83/34.95	----------------------------------------
67.83/34.95	
67.83/34.95	(475) QDPSizeChangeProof (EQUIVALENT)
67.83/34.95	By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 
67.83/34.95	
67.83/34.95	From the DPs we obtained the following set of size-change graphs:
67.83/34.95	*new_primQuotInt2(Succ(x0), Succ(x1), Succ(x0), Succ(x1), z4, z5) -> new_primQuotInt2(x0, x1, x0, x1, z4, z5)
67.83/34.95	The graph contains the following edges 1 > 1, 3 > 1, 2 > 2, 4 > 2, 1 > 3, 3 > 3, 2 > 4, 4 > 4, 5 >= 5, 6 >= 6
67.83/34.95	
67.83/34.95	
67.83/34.95	----------------------------------------
67.83/34.95	
67.83/34.95	(476)
67.83/34.95	YES
67.83/34.95	
67.83/34.95	----------------------------------------
67.83/34.95	
67.83/34.95	(477)
67.83/34.95	Obligation:
67.83/34.95	Q DP problem:
67.83/34.95	The TRS P consists of the following rules:
67.83/34.95	
67.83/34.95	   new_primQuotInt5(Succ(vuz4490), Succ(vuz4480), vuz451, vuz450, vuz31900, vuz3170) -> new_primQuotInt5(vuz4490, vuz4480, vuz4490, vuz4480, vuz31900, vuz3170)
67.83/34.95	
67.83/34.95	R is empty.
67.83/34.95	Q is empty.
67.83/34.95	We have to consider all minimal (P,Q,R)-chains.
67.83/34.95	----------------------------------------
67.83/34.95	
67.83/34.95	(478) TransformationProof (EQUIVALENT)
67.83/34.95	By instantiating [LPAR04] the rule new_primQuotInt5(Succ(vuz4490), Succ(vuz4480), vuz451, vuz450, vuz31900, vuz3170) -> new_primQuotInt5(vuz4490, vuz4480, vuz4490, vuz4480, vuz31900, vuz3170) we obtained the following new rules [LPAR04]:
67.83/34.95	
67.83/34.95	   (new_primQuotInt5(Succ(x0), Succ(x1), Succ(x0), Succ(x1), z4, z5) -> new_primQuotInt5(x0, x1, x0, x1, z4, z5),new_primQuotInt5(Succ(x0), Succ(x1), Succ(x0), Succ(x1), z4, z5) -> new_primQuotInt5(x0, x1, x0, x1, z4, z5))
67.83/34.95	
67.83/34.95	
67.83/34.95	----------------------------------------
67.83/34.95	
67.83/34.95	(479)
67.83/34.95	Obligation:
67.83/34.95	Q DP problem:
67.83/34.95	The TRS P consists of the following rules:
67.83/34.95	
67.83/34.95	   new_primQuotInt5(Succ(x0), Succ(x1), Succ(x0), Succ(x1), z4, z5) -> new_primQuotInt5(x0, x1, x0, x1, z4, z5)
67.83/34.95	
67.83/34.95	R is empty.
67.83/34.95	Q is empty.
67.83/34.95	We have to consider all minimal (P,Q,R)-chains.
67.83/34.95	----------------------------------------
67.83/34.95	
67.83/34.95	(480) QDPSizeChangeProof (EQUIVALENT)
67.83/34.95	By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 
67.83/34.95	
67.83/34.95	From the DPs we obtained the following set of size-change graphs:
67.83/34.95	*new_primQuotInt5(Succ(x0), Succ(x1), Succ(x0), Succ(x1), z4, z5) -> new_primQuotInt5(x0, x1, x0, x1, z4, z5)
67.83/34.95	The graph contains the following edges 1 > 1, 3 > 1, 2 > 2, 4 > 2, 1 > 3, 3 > 3, 2 > 4, 4 > 4, 5 >= 5, 6 >= 6
67.83/34.95	
67.83/34.95	
67.83/34.95	----------------------------------------
67.83/34.95	
67.83/34.95	(481)
67.83/34.95	YES
67.83/34.95	
67.83/34.95	----------------------------------------
67.83/34.95	
67.83/34.95	(482)
67.83/34.95	Obligation:
67.83/34.95	Q DP problem:
67.83/34.95	The TRS P consists of the following rules:
67.83/34.95	
67.83/34.95	   new_primQuotInt(vuz374, Succ(vuz4890), Succ(vuz3770), vuz375) -> new_primQuotInt(vuz374, vuz4890, vuz3770, vuz375)
67.83/34.95	
67.83/34.95	R is empty.
67.83/34.95	Q is empty.
67.83/34.95	We have to consider all minimal (P,Q,R)-chains.
67.83/34.95	----------------------------------------
67.83/34.95	
67.83/34.95	(483) QDPSizeChangeProof (EQUIVALENT)
67.83/34.95	By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 
67.83/34.95	
67.83/34.95	From the DPs we obtained the following set of size-change graphs:
67.83/34.95	*new_primQuotInt(vuz374, Succ(vuz4890), Succ(vuz3770), vuz375) -> new_primQuotInt(vuz374, vuz4890, vuz3770, vuz375)
67.83/34.95	The graph contains the following edges 1 >= 1, 2 > 2, 3 > 3, 4 >= 4
67.83/34.95	
67.83/34.95	
67.83/34.95	----------------------------------------
67.83/34.95	
67.83/34.95	(484)
67.83/34.95	YES
67.83/34.95	
67.83/34.95	----------------------------------------
67.83/34.95	
67.83/34.95	(485)
67.83/34.95	Obligation:
67.83/34.95	Q DP problem:
67.83/34.95	The TRS P consists of the following rules:
67.83/34.95	
67.83/34.95	   new_primQuotInt0(vuz366, Succ(vuz3690), Succ(vuz4830), vuz367) -> new_primQuotInt0(vuz366, vuz3690, vuz4830, vuz367)
67.83/34.95	
67.83/34.95	R is empty.
67.83/34.95	Q is empty.
67.83/34.95	We have to consider all minimal (P,Q,R)-chains.
67.83/34.95	----------------------------------------
67.83/34.95	
67.83/34.95	(486) QDPSizeChangeProof (EQUIVALENT)
67.83/34.95	By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 
67.83/34.95	
67.83/34.95	From the DPs we obtained the following set of size-change graphs:
67.83/34.95	*new_primQuotInt0(vuz366, Succ(vuz3690), Succ(vuz4830), vuz367) -> new_primQuotInt0(vuz366, vuz3690, vuz4830, vuz367)
67.83/34.95	The graph contains the following edges 1 >= 1, 2 > 2, 3 > 3, 4 >= 4
67.83/34.95	
67.83/34.95	
67.83/34.95	----------------------------------------
67.83/34.95	
67.83/34.95	(487)
67.83/34.95	YES
67.83/34.95	
67.83/34.95	----------------------------------------
67.83/34.95	
67.83/34.95	(488) Narrow (COMPLETE)
67.83/34.95	Haskell To QDPs
67.83/34.95	
67.83/34.95	digraph dp_graph {
67.83/34.95	node [outthreshold=100, inthreshold=100];1[label="enumFromThen",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
67.83/34.95	3[label="enumFromThen vuz3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
67.83/34.95	4[label="enumFromThen vuz3 vuz4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
67.83/34.95	5[label="numericEnumFromThen vuz3 vuz4",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
67.83/34.95	6[label="iterate (vuz4 - vuz3 +) vuz3",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3];
67.83/34.95	7[label="vuz3 : iterate (vuz4 - vuz3 +) (vuz4 - vuz3 + vuz3)",fontsize=16,color="green",shape="box"];7 -> 8[label="",style="dashed", color="green", weight=3];
67.83/34.95	8 -> 13[label="",style="dashed", color="red", weight=0];
67.83/34.95	8[label="iterate (vuz4 - vuz3 +) (vuz4 - vuz3 + vuz3)",fontsize=16,color="magenta"];8 -> 14[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	14[label="vuz3",fontsize=16,color="green",shape="box"];13[label="iterate (vuz4 - vuz3 +) (vuz4 - vuz3 + vuz5)",fontsize=16,color="black",shape="triangle"];13 -> 16[label="",style="solid", color="black", weight=3];
67.83/34.95	16[label="vuz4 - vuz3 + vuz5 : iterate (vuz4 - vuz3 +) (vuz4 - vuz3 + (vuz4 - vuz3 + vuz5))",fontsize=16,color="green",shape="box"];16 -> 17[label="",style="dashed", color="green", weight=3];
67.83/34.95	16 -> 18[label="",style="dashed", color="green", weight=3];
67.83/34.95	17[label="vuz4 - vuz3 + vuz5",fontsize=16,color="black",shape="box"];17 -> 5645[label="",style="solid", color="black", weight=3];
67.83/34.95	18 -> 13[label="",style="dashed", color="red", weight=0];
67.83/34.95	18[label="iterate (vuz4 - vuz3 +) (vuz4 - vuz3 + (vuz4 - vuz3 + vuz5))",fontsize=16,color="magenta"];18 -> 20[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	5645 -> 5329[label="",style="dashed", color="red", weight=0];
67.83/34.95	5645[label="vuz4 + (negate vuz3) + vuz5",fontsize=16,color="magenta"];5645 -> 6517[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	5645 -> 6518[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	20[label="vuz4 - vuz3 + vuz5",fontsize=16,color="black",shape="box"];20 -> 5425[label="",style="solid", color="black", weight=3];
67.83/34.95	6517[label="vuz5",fontsize=16,color="green",shape="box"];6518 -> 5329[label="",style="dashed", color="red", weight=0];
67.83/34.95	6518[label="vuz4 + (negate vuz3)",fontsize=16,color="magenta"];6518 -> 7106[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	6518 -> 7107[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	5329[label="vuz306 + vuz307",fontsize=16,color="burlywood",shape="triangle"];10820[label="vuz306/vuz3060 :% vuz3061",fontsize=10,color="white",style="solid",shape="box"];5329 -> 10820[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10820 -> 5964[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	5425 -> 5329[label="",style="dashed", color="red", weight=0];
67.83/34.95	5425[label="vuz4 + (negate vuz3) + vuz5",fontsize=16,color="magenta"];5425 -> 6125[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	5425 -> 6126[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7106[label="negate vuz3",fontsize=16,color="burlywood",shape="triangle"];10821[label="vuz3/vuz30 :% vuz31",fontsize=10,color="white",style="solid",shape="box"];7106 -> 10821[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10821 -> 7111[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	7107[label="vuz4",fontsize=16,color="green",shape="box"];5964[label="vuz3060 :% vuz3061 + vuz307",fontsize=16,color="burlywood",shape="box"];10822[label="vuz307/vuz3070 :% vuz3071",fontsize=10,color="white",style="solid",shape="box"];5964 -> 10822[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10822 -> 7081[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	6125[label="vuz5",fontsize=16,color="green",shape="box"];6126 -> 5329[label="",style="dashed", color="red", weight=0];
67.83/34.95	6126[label="vuz4 + (negate vuz3)",fontsize=16,color="magenta"];6126 -> 7108[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	6126 -> 7109[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7111[label="negate vuz30 :% vuz31",fontsize=16,color="black",shape="box"];7111 -> 7113[label="",style="solid", color="black", weight=3];
67.83/34.95	7081[label="vuz3060 :% vuz3061 + vuz3070 :% vuz3071",fontsize=16,color="black",shape="box"];7081 -> 7110[label="",style="solid", color="black", weight=3];
67.83/34.95	7108 -> 7106[label="",style="dashed", color="red", weight=0];
67.83/34.95	7108[label="negate vuz3",fontsize=16,color="magenta"];7109[label="vuz4",fontsize=16,color="green",shape="box"];7113[label="(negate vuz30) :% vuz31",fontsize=16,color="green",shape="box"];7113 -> 7115[label="",style="dashed", color="green", weight=3];
67.83/34.95	7110[label="reduce (vuz3060 * vuz3071 + vuz3070 * vuz3061) (vuz3061 * vuz3071)",fontsize=16,color="black",shape="box"];7110 -> 7112[label="",style="solid", color="black", weight=3];
67.83/34.95	7115[label="negate vuz30",fontsize=16,color="black",shape="triangle"];7115 -> 7122[label="",style="solid", color="black", weight=3];
67.83/34.95	7112[label="reduce2 (vuz3060 * vuz3071 + vuz3070 * vuz3061) (vuz3061 * vuz3071)",fontsize=16,color="black",shape="box"];7112 -> 7114[label="",style="solid", color="black", weight=3];
67.83/34.95	7122[label="primNegInt vuz30",fontsize=16,color="burlywood",shape="box"];10823[label="vuz30/Pos vuz300",fontsize=10,color="white",style="solid",shape="box"];7122 -> 10823[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10823 -> 7127[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	10824[label="vuz30/Neg vuz300",fontsize=10,color="white",style="solid",shape="box"];7122 -> 10824[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10824 -> 7128[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	7114 -> 7116[label="",style="dashed", color="red", weight=0];
67.83/34.95	7114[label="reduce2Reduce1 (vuz3060 * vuz3071 + vuz3070 * vuz3061) (vuz3061 * vuz3071) (vuz3060 * vuz3071 + vuz3070 * vuz3061) (vuz3061 * vuz3071) (vuz3061 * vuz3071 == fromInt (Pos Zero))",fontsize=16,color="magenta"];7114 -> 7117[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7114 -> 7118[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7114 -> 7119[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7114 -> 7120[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7114 -> 7121[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7127[label="primNegInt (Pos vuz300)",fontsize=16,color="black",shape="box"];7127 -> 7133[label="",style="solid", color="black", weight=3];
67.83/34.95	7128[label="primNegInt (Neg vuz300)",fontsize=16,color="black",shape="box"];7128 -> 7134[label="",style="solid", color="black", weight=3];
67.83/34.95	7117[label="vuz3061 * vuz3071 == fromInt (Pos Zero)",fontsize=16,color="blue",shape="box"];10825[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];7117 -> 10825[label="",style="solid", color="blue", weight=9];
67.83/34.95	10825 -> 7123[label="",style="solid", color="blue", weight=3];
67.83/34.95	10826[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];7117 -> 10826[label="",style="solid", color="blue", weight=9];
67.83/34.95	10826 -> 7124[label="",style="solid", color="blue", weight=3];
67.83/34.95	7118[label="vuz3060",fontsize=16,color="green",shape="box"];7119[label="vuz3071",fontsize=16,color="green",shape="box"];7120[label="vuz3061",fontsize=16,color="green",shape="box"];7121[label="vuz3070",fontsize=16,color="green",shape="box"];7116[label="reduce2Reduce1 (vuz316 * vuz317 + vuz318 * vuz319) (vuz319 * vuz317) (vuz316 * vuz317 + vuz318 * vuz319) (vuz319 * vuz317) vuz320",fontsize=16,color="burlywood",shape="triangle"];10827[label="vuz320/False",fontsize=10,color="white",style="solid",shape="box"];7116 -> 10827[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10827 -> 7125[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	10828[label="vuz320/True",fontsize=10,color="white",style="solid",shape="box"];7116 -> 10828[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10828 -> 7126[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	7133[label="Neg vuz300",fontsize=16,color="green",shape="box"];7134[label="Pos vuz300",fontsize=16,color="green",shape="box"];7123 -> 9987[label="",style="dashed", color="red", weight=0];
67.83/34.95	7123[label="vuz3061 * vuz3071 == fromInt (Pos Zero)",fontsize=16,color="magenta"];7123 -> 9988[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7124[label="vuz3061 * vuz3071 == fromInt (Pos Zero)",fontsize=16,color="black",shape="box"];7124 -> 7130[label="",style="solid", color="black", weight=3];
67.83/34.95	7125[label="reduce2Reduce1 (vuz316 * vuz317 + vuz318 * vuz319) (vuz319 * vuz317) (vuz316 * vuz317 + vuz318 * vuz319) (vuz319 * vuz317) False",fontsize=16,color="black",shape="box"];7125 -> 7131[label="",style="solid", color="black", weight=3];
67.83/34.95	7126[label="reduce2Reduce1 (vuz316 * vuz317 + vuz318 * vuz319) (vuz319 * vuz317) (vuz316 * vuz317 + vuz318 * vuz319) (vuz319 * vuz317) True",fontsize=16,color="black",shape="box"];7126 -> 7132[label="",style="solid", color="black", weight=3];
67.83/34.95	9988[label="vuz3061 * vuz3071",fontsize=16,color="black",shape="triangle"];9988 -> 10015[label="",style="solid", color="black", weight=3];
67.83/34.95	9987[label="vuz551 == fromInt (Pos Zero)",fontsize=16,color="black",shape="triangle"];9987 -> 10016[label="",style="solid", color="black", weight=3];
67.83/34.95	7130[label="error []",fontsize=16,color="red",shape="box"];7131[label="reduce2Reduce0 (vuz316 * vuz317 + vuz318 * vuz319) (vuz319 * vuz317) (vuz316 * vuz317 + vuz318 * vuz319) (vuz319 * vuz317) otherwise",fontsize=16,color="black",shape="box"];7131 -> 7136[label="",style="solid", color="black", weight=3];
67.83/34.95	7132[label="error []",fontsize=16,color="black",shape="box"];7132 -> 7137[label="",style="solid", color="black", weight=3];
67.83/34.95	10015[label="primMulInt vuz3061 vuz3071",fontsize=16,color="burlywood",shape="box"];10829[label="vuz3061/Pos vuz30610",fontsize=10,color="white",style="solid",shape="box"];10015 -> 10829[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10829 -> 10168[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	10830[label="vuz3061/Neg vuz30610",fontsize=10,color="white",style="solid",shape="box"];10015 -> 10830[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10830 -> 10169[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	10016[label="primEqInt vuz551 (fromInt (Pos Zero))",fontsize=16,color="burlywood",shape="box"];10831[label="vuz551/Pos vuz5510",fontsize=10,color="white",style="solid",shape="box"];10016 -> 10831[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10831 -> 10170[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	10832[label="vuz551/Neg vuz5510",fontsize=10,color="white",style="solid",shape="box"];10016 -> 10832[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10832 -> 10171[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	7136[label="reduce2Reduce0 (vuz316 * vuz317 + vuz318 * vuz319) (vuz319 * vuz317) (vuz316 * vuz317 + vuz318 * vuz319) (vuz319 * vuz317) True",fontsize=16,color="black",shape="box"];7136 -> 7140[label="",style="solid", color="black", weight=3];
67.83/34.95	7137[label="error []",fontsize=16,color="red",shape="box"];10168[label="primMulInt (Pos vuz30610) vuz3071",fontsize=16,color="burlywood",shape="box"];10833[label="vuz3071/Pos vuz30710",fontsize=10,color="white",style="solid",shape="box"];10168 -> 10833[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10833 -> 10194[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	10834[label="vuz3071/Neg vuz30710",fontsize=10,color="white",style="solid",shape="box"];10168 -> 10834[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10834 -> 10195[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	10169[label="primMulInt (Neg vuz30610) vuz3071",fontsize=16,color="burlywood",shape="box"];10835[label="vuz3071/Pos vuz30710",fontsize=10,color="white",style="solid",shape="box"];10169 -> 10835[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10835 -> 10196[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	10836[label="vuz3071/Neg vuz30710",fontsize=10,color="white",style="solid",shape="box"];10169 -> 10836[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10836 -> 10197[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	10170[label="primEqInt (Pos vuz5510) (fromInt (Pos Zero))",fontsize=16,color="burlywood",shape="box"];10837[label="vuz5510/Succ vuz55100",fontsize=10,color="white",style="solid",shape="box"];10170 -> 10837[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10837 -> 10198[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	10838[label="vuz5510/Zero",fontsize=10,color="white",style="solid",shape="box"];10170 -> 10838[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10838 -> 10199[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	10171[label="primEqInt (Neg vuz5510) (fromInt (Pos Zero))",fontsize=16,color="burlywood",shape="box"];10839[label="vuz5510/Succ vuz55100",fontsize=10,color="white",style="solid",shape="box"];10171 -> 10839[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10839 -> 10200[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	10840[label="vuz5510/Zero",fontsize=10,color="white",style="solid",shape="box"];10171 -> 10840[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10840 -> 10201[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	7140[label="(vuz316 * vuz317 + vuz318 * vuz319) `quot` reduce2D (vuz316 * vuz317 + vuz318 * vuz319) (vuz319 * vuz317) :% (vuz319 * vuz317 `quot` reduce2D (vuz316 * vuz317 + vuz318 * vuz319) (vuz319 * vuz317))",fontsize=16,color="green",shape="box"];7140 -> 7145[label="",style="dashed", color="green", weight=3];
67.83/34.95	7140 -> 7146[label="",style="dashed", color="green", weight=3];
67.83/34.95	10194[label="primMulInt (Pos vuz30610) (Pos vuz30710)",fontsize=16,color="black",shape="box"];10194 -> 10238[label="",style="solid", color="black", weight=3];
67.83/34.95	10195[label="primMulInt (Pos vuz30610) (Neg vuz30710)",fontsize=16,color="black",shape="box"];10195 -> 10239[label="",style="solid", color="black", weight=3];
67.83/34.95	10196[label="primMulInt (Neg vuz30610) (Pos vuz30710)",fontsize=16,color="black",shape="box"];10196 -> 10240[label="",style="solid", color="black", weight=3];
67.83/34.95	10197[label="primMulInt (Neg vuz30610) (Neg vuz30710)",fontsize=16,color="black",shape="box"];10197 -> 10241[label="",style="solid", color="black", weight=3];
67.83/34.95	10198[label="primEqInt (Pos (Succ vuz55100)) (fromInt (Pos Zero))",fontsize=16,color="black",shape="box"];10198 -> 10242[label="",style="solid", color="black", weight=3];
67.83/34.95	10199[label="primEqInt (Pos Zero) (fromInt (Pos Zero))",fontsize=16,color="black",shape="box"];10199 -> 10243[label="",style="solid", color="black", weight=3];
67.83/34.95	10200[label="primEqInt (Neg (Succ vuz55100)) (fromInt (Pos Zero))",fontsize=16,color="black",shape="box"];10200 -> 10244[label="",style="solid", color="black", weight=3];
67.83/34.95	10201[label="primEqInt (Neg Zero) (fromInt (Pos Zero))",fontsize=16,color="black",shape="box"];10201 -> 10245[label="",style="solid", color="black", weight=3];
67.83/34.95	7145[label="(vuz316 * vuz317 + vuz318 * vuz319) `quot` reduce2D (vuz316 * vuz317 + vuz318 * vuz319) (vuz319 * vuz317)",fontsize=16,color="blue",shape="box"];10841[label="`quot` :: Integer -> Integer -> Integer",fontsize=10,color="white",style="solid",shape="box"];7145 -> 10841[label="",style="solid", color="blue", weight=9];
67.83/34.95	10841 -> 7151[label="",style="solid", color="blue", weight=3];
67.83/34.95	10842[label="`quot` :: Int -> Int -> Int",fontsize=10,color="white",style="solid",shape="box"];7145 -> 10842[label="",style="solid", color="blue", weight=9];
67.83/34.95	10842 -> 7152[label="",style="solid", color="blue", weight=3];
67.83/34.95	7146[label="vuz319 * vuz317 `quot` reduce2D (vuz316 * vuz317 + vuz318 * vuz319) (vuz319 * vuz317)",fontsize=16,color="blue",shape="box"];10843[label="`quot` :: Integer -> Integer -> Integer",fontsize=10,color="white",style="solid",shape="box"];7146 -> 10843[label="",style="solid", color="blue", weight=9];
67.83/34.95	10843 -> 7153[label="",style="solid", color="blue", weight=3];
67.83/34.95	10844[label="`quot` :: Int -> Int -> Int",fontsize=10,color="white",style="solid",shape="box"];7146 -> 10844[label="",style="solid", color="blue", weight=9];
67.83/34.95	10844 -> 7154[label="",style="solid", color="blue", weight=3];
67.83/34.95	10238[label="Pos (primMulNat vuz30610 vuz30710)",fontsize=16,color="green",shape="box"];10238 -> 10260[label="",style="dashed", color="green", weight=3];
67.83/34.95	10239[label="Neg (primMulNat vuz30610 vuz30710)",fontsize=16,color="green",shape="box"];10239 -> 10261[label="",style="dashed", color="green", weight=3];
67.83/34.95	10240[label="Neg (primMulNat vuz30610 vuz30710)",fontsize=16,color="green",shape="box"];10240 -> 10262[label="",style="dashed", color="green", weight=3];
67.83/34.95	10241[label="Pos (primMulNat vuz30610 vuz30710)",fontsize=16,color="green",shape="box"];10241 -> 10263[label="",style="dashed", color="green", weight=3];
67.83/34.95	10242 -> 7519[label="",style="dashed", color="red", weight=0];
67.83/34.95	10242[label="primEqInt (Pos (Succ vuz55100)) (Pos Zero)",fontsize=16,color="magenta"];10242 -> 10264[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	10243 -> 7520[label="",style="dashed", color="red", weight=0];
67.83/34.95	10243[label="primEqInt (Pos Zero) (Pos Zero)",fontsize=16,color="magenta"];10244 -> 7526[label="",style="dashed", color="red", weight=0];
67.83/34.95	10244[label="primEqInt (Neg (Succ vuz55100)) (Pos Zero)",fontsize=16,color="magenta"];10244 -> 10265[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	10245 -> 7527[label="",style="dashed", color="red", weight=0];
67.83/34.95	10245[label="primEqInt (Neg Zero) (Pos Zero)",fontsize=16,color="magenta"];7151[label="(vuz316 * vuz317 + vuz318 * vuz319) `quot` reduce2D (vuz316 * vuz317 + vuz318 * vuz319) (vuz319 * vuz317)",fontsize=16,color="black",shape="box"];7151 -> 7163[label="",style="solid", color="black", weight=3];
67.83/34.95	7152[label="(vuz316 * vuz317 + vuz318 * vuz319) `quot` reduce2D (vuz316 * vuz317 + vuz318 * vuz319) (vuz319 * vuz317)",fontsize=16,color="black",shape="box"];7152 -> 7164[label="",style="solid", color="black", weight=3];
67.83/34.95	7153[label="vuz319 * vuz317 `quot` reduce2D (vuz316 * vuz317 + vuz318 * vuz319) (vuz319 * vuz317)",fontsize=16,color="black",shape="box"];7153 -> 7165[label="",style="solid", color="black", weight=3];
67.83/34.95	7154[label="vuz319 * vuz317 `quot` reduce2D (vuz316 * vuz317 + vuz318 * vuz319) (vuz319 * vuz317)",fontsize=16,color="black",shape="box"];7154 -> 7166[label="",style="solid", color="black", weight=3];
67.83/34.95	10260 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.95	10260[label="primMulNat vuz30610 vuz30710",fontsize=16,color="magenta"];10261 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.95	10261[label="primMulNat vuz30610 vuz30710",fontsize=16,color="magenta"];10261 -> 10279[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	10262 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.95	10262[label="primMulNat vuz30610 vuz30710",fontsize=16,color="magenta"];10262 -> 10280[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	10263 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.95	10263[label="primMulNat vuz30610 vuz30710",fontsize=16,color="magenta"];10263 -> 10281[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	10263 -> 10282[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	10264[label="vuz55100",fontsize=16,color="green",shape="box"];7519[label="primEqInt (Pos (Succ vuz3250)) (Pos Zero)",fontsize=16,color="black",shape="triangle"];7519 -> 7532[label="",style="solid", color="black", weight=3];
67.83/34.95	7520[label="primEqInt (Pos Zero) (Pos Zero)",fontsize=16,color="black",shape="triangle"];7520 -> 7533[label="",style="solid", color="black", weight=3];
67.83/34.95	10265[label="vuz55100",fontsize=16,color="green",shape="box"];7526[label="primEqInt (Neg (Succ vuz3260)) (Pos Zero)",fontsize=16,color="black",shape="triangle"];7526 -> 7547[label="",style="solid", color="black", weight=3];
67.83/34.95	7527[label="primEqInt (Neg Zero) (Pos Zero)",fontsize=16,color="black",shape="triangle"];7527 -> 7548[label="",style="solid", color="black", weight=3];
67.83/34.95	7163[label="error []",fontsize=16,color="red",shape="box"];7164[label="primQuotInt (vuz316 * vuz317 + vuz318 * vuz319) (reduce2D (vuz316 * vuz317 + vuz318 * vuz319) (vuz319 * vuz317))",fontsize=16,color="black",shape="box"];7164 -> 7175[label="",style="solid", color="black", weight=3];
67.83/34.95	7165[label="error []",fontsize=16,color="red",shape="box"];7166[label="primQuotInt (vuz319 * vuz317) (reduce2D (vuz316 * vuz317 + vuz318 * vuz319) (vuz319 * vuz317))",fontsize=16,color="black",shape="box"];7166 -> 7176[label="",style="solid", color="black", weight=3];
67.83/34.95	7480[label="primMulNat vuz30610 vuz30710",fontsize=16,color="burlywood",shape="triangle"];10845[label="vuz30610/Succ vuz306100",fontsize=10,color="white",style="solid",shape="box"];7480 -> 10845[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10845 -> 7492[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	10846[label="vuz30610/Zero",fontsize=10,color="white",style="solid",shape="box"];7480 -> 10846[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10846 -> 7493[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	10279[label="vuz30710",fontsize=16,color="green",shape="box"];10280[label="vuz30610",fontsize=16,color="green",shape="box"];10281[label="vuz30610",fontsize=16,color="green",shape="box"];10282[label="vuz30710",fontsize=16,color="green",shape="box"];7532[label="False",fontsize=16,color="green",shape="box"];7533[label="True",fontsize=16,color="green",shape="box"];7547[label="False",fontsize=16,color="green",shape="box"];7548[label="True",fontsize=16,color="green",shape="box"];7175[label="primQuotInt (primPlusInt (vuz316 * vuz317) (vuz318 * vuz319)) (reduce2D (primPlusInt (vuz316 * vuz317) (vuz318 * vuz319)) (vuz319 * vuz317))",fontsize=16,color="black",shape="box"];7175 -> 7185[label="",style="solid", color="black", weight=3];
67.83/34.95	7176[label="primQuotInt (primMulInt vuz319 vuz317) (reduce2D (vuz316 * vuz317 + vuz318 * vuz319) (primMulInt vuz319 vuz317))",fontsize=16,color="burlywood",shape="box"];10847[label="vuz319/Pos vuz3190",fontsize=10,color="white",style="solid",shape="box"];7176 -> 10847[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10847 -> 7186[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	10848[label="vuz319/Neg vuz3190",fontsize=10,color="white",style="solid",shape="box"];7176 -> 10848[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10848 -> 7187[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	7492[label="primMulNat (Succ vuz306100) vuz30710",fontsize=16,color="burlywood",shape="box"];10849[label="vuz30710/Succ vuz307100",fontsize=10,color="white",style="solid",shape="box"];7492 -> 10849[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10849 -> 7515[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	10850[label="vuz30710/Zero",fontsize=10,color="white",style="solid",shape="box"];7492 -> 10850[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10850 -> 7516[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	7493[label="primMulNat Zero vuz30710",fontsize=16,color="burlywood",shape="box"];10851[label="vuz30710/Succ vuz307100",fontsize=10,color="white",style="solid",shape="box"];7493 -> 10851[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10851 -> 7517[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	10852[label="vuz30710/Zero",fontsize=10,color="white",style="solid",shape="box"];7493 -> 10852[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10852 -> 7518[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	7185[label="primQuotInt (primPlusInt (primMulInt vuz316 vuz317) (vuz318 * vuz319)) (reduce2D (primPlusInt (primMulInt vuz316 vuz317) (vuz318 * vuz319)) (vuz319 * vuz317))",fontsize=16,color="burlywood",shape="box"];10853[label="vuz316/Pos vuz3160",fontsize=10,color="white",style="solid",shape="box"];7185 -> 10853[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10853 -> 7194[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	10854[label="vuz316/Neg vuz3160",fontsize=10,color="white",style="solid",shape="box"];7185 -> 10854[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10854 -> 7195[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	7186[label="primQuotInt (primMulInt (Pos vuz3190) vuz317) (reduce2D (vuz316 * vuz317 + vuz318 * Pos vuz3190) (primMulInt (Pos vuz3190) vuz317))",fontsize=16,color="burlywood",shape="box"];10855[label="vuz317/Pos vuz3170",fontsize=10,color="white",style="solid",shape="box"];7186 -> 10855[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10855 -> 7196[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	10856[label="vuz317/Neg vuz3170",fontsize=10,color="white",style="solid",shape="box"];7186 -> 10856[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10856 -> 7197[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	7187[label="primQuotInt (primMulInt (Neg vuz3190) vuz317) (reduce2D (vuz316 * vuz317 + vuz318 * Neg vuz3190) (primMulInt (Neg vuz3190) vuz317))",fontsize=16,color="burlywood",shape="box"];10857[label="vuz317/Pos vuz3170",fontsize=10,color="white",style="solid",shape="box"];7187 -> 10857[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10857 -> 7198[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	10858[label="vuz317/Neg vuz3170",fontsize=10,color="white",style="solid",shape="box"];7187 -> 10858[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10858 -> 7199[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	7515[label="primMulNat (Succ vuz306100) (Succ vuz307100)",fontsize=16,color="black",shape="box"];7515 -> 7528[label="",style="solid", color="black", weight=3];
67.83/34.95	7516[label="primMulNat (Succ vuz306100) Zero",fontsize=16,color="black",shape="box"];7516 -> 7529[label="",style="solid", color="black", weight=3];
67.83/34.95	7517[label="primMulNat Zero (Succ vuz307100)",fontsize=16,color="black",shape="box"];7517 -> 7530[label="",style="solid", color="black", weight=3];
67.83/34.95	7518[label="primMulNat Zero Zero",fontsize=16,color="black",shape="box"];7518 -> 7531[label="",style="solid", color="black", weight=3];
67.83/34.95	7194[label="primQuotInt (primPlusInt (primMulInt (Pos vuz3160) vuz317) (vuz318 * vuz319)) (reduce2D (primPlusInt (primMulInt (Pos vuz3160) vuz317) (vuz318 * vuz319)) (vuz319 * vuz317))",fontsize=16,color="burlywood",shape="box"];10859[label="vuz317/Pos vuz3170",fontsize=10,color="white",style="solid",shape="box"];7194 -> 10859[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10859 -> 7206[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	10860[label="vuz317/Neg vuz3170",fontsize=10,color="white",style="solid",shape="box"];7194 -> 10860[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10860 -> 7207[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	7195[label="primQuotInt (primPlusInt (primMulInt (Neg vuz3160) vuz317) (vuz318 * vuz319)) (reduce2D (primPlusInt (primMulInt (Neg vuz3160) vuz317) (vuz318 * vuz319)) (vuz319 * vuz317))",fontsize=16,color="burlywood",shape="box"];10861[label="vuz317/Pos vuz3170",fontsize=10,color="white",style="solid",shape="box"];7195 -> 10861[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10861 -> 7208[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	10862[label="vuz317/Neg vuz3170",fontsize=10,color="white",style="solid",shape="box"];7195 -> 10862[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10862 -> 7209[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	7196[label="primQuotInt (primMulInt (Pos vuz3190) (Pos vuz3170)) (reduce2D (vuz316 * Pos vuz3170 + vuz318 * Pos vuz3190) (primMulInt (Pos vuz3190) (Pos vuz3170)))",fontsize=16,color="black",shape="box"];7196 -> 7210[label="",style="solid", color="black", weight=3];
67.83/34.95	7197[label="primQuotInt (primMulInt (Pos vuz3190) (Neg vuz3170)) (reduce2D (vuz316 * Neg vuz3170 + vuz318 * Pos vuz3190) (primMulInt (Pos vuz3190) (Neg vuz3170)))",fontsize=16,color="black",shape="box"];7197 -> 7211[label="",style="solid", color="black", weight=3];
67.83/34.95	7198[label="primQuotInt (primMulInt (Neg vuz3190) (Pos vuz3170)) (reduce2D (vuz316 * Pos vuz3170 + vuz318 * Neg vuz3190) (primMulInt (Neg vuz3190) (Pos vuz3170)))",fontsize=16,color="black",shape="box"];7198 -> 7212[label="",style="solid", color="black", weight=3];
67.83/34.95	7199[label="primQuotInt (primMulInt (Neg vuz3190) (Neg vuz3170)) (reduce2D (vuz316 * Neg vuz3170 + vuz318 * Neg vuz3190) (primMulInt (Neg vuz3190) (Neg vuz3170)))",fontsize=16,color="black",shape="box"];7199 -> 7213[label="",style="solid", color="black", weight=3];
67.83/34.95	7528 -> 7549[label="",style="dashed", color="red", weight=0];
67.83/34.95	7528[label="primPlusNat (primMulNat vuz306100 (Succ vuz307100)) (Succ vuz307100)",fontsize=16,color="magenta"];7528 -> 7550[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7529[label="Zero",fontsize=16,color="green",shape="box"];7530[label="Zero",fontsize=16,color="green",shape="box"];7531[label="Zero",fontsize=16,color="green",shape="box"];7206[label="primQuotInt (primPlusInt (primMulInt (Pos vuz3160) (Pos vuz3170)) (vuz318 * vuz319)) (reduce2D (primPlusInt (primMulInt (Pos vuz3160) (Pos vuz3170)) (vuz318 * vuz319)) (vuz319 * Pos vuz3170))",fontsize=16,color="black",shape="box"];7206 -> 7220[label="",style="solid", color="black", weight=3];
67.83/34.95	7207[label="primQuotInt (primPlusInt (primMulInt (Pos vuz3160) (Neg vuz3170)) (vuz318 * vuz319)) (reduce2D (primPlusInt (primMulInt (Pos vuz3160) (Neg vuz3170)) (vuz318 * vuz319)) (vuz319 * Neg vuz3170))",fontsize=16,color="black",shape="box"];7207 -> 7221[label="",style="solid", color="black", weight=3];
67.83/34.95	7208[label="primQuotInt (primPlusInt (primMulInt (Neg vuz3160) (Pos vuz3170)) (vuz318 * vuz319)) (reduce2D (primPlusInt (primMulInt (Neg vuz3160) (Pos vuz3170)) (vuz318 * vuz319)) (vuz319 * Pos vuz3170))",fontsize=16,color="black",shape="box"];7208 -> 7222[label="",style="solid", color="black", weight=3];
67.83/34.95	7209[label="primQuotInt (primPlusInt (primMulInt (Neg vuz3160) (Neg vuz3170)) (vuz318 * vuz319)) (reduce2D (primPlusInt (primMulInt (Neg vuz3160) (Neg vuz3170)) (vuz318 * vuz319)) (vuz319 * Neg vuz3170))",fontsize=16,color="black",shape="box"];7209 -> 7223[label="",style="solid", color="black", weight=3];
67.83/34.95	7210[label="primQuotInt (Pos (primMulNat vuz3190 vuz3170)) (reduce2D (vuz316 * Pos vuz3170 + vuz318 * Pos vuz3190) (Pos (primMulNat vuz3190 vuz3170)))",fontsize=16,color="black",shape="box"];7210 -> 7224[label="",style="solid", color="black", weight=3];
67.83/34.95	7211[label="primQuotInt (Neg (primMulNat vuz3190 vuz3170)) (reduce2D (vuz316 * Neg vuz3170 + vuz318 * Pos vuz3190) (Neg (primMulNat vuz3190 vuz3170)))",fontsize=16,color="black",shape="box"];7211 -> 7225[label="",style="solid", color="black", weight=3];
67.83/34.95	7212[label="primQuotInt (Neg (primMulNat vuz3190 vuz3170)) (reduce2D (vuz316 * Pos vuz3170 + vuz318 * Neg vuz3190) (Neg (primMulNat vuz3190 vuz3170)))",fontsize=16,color="black",shape="box"];7212 -> 7226[label="",style="solid", color="black", weight=3];
67.83/34.95	7213[label="primQuotInt (Pos (primMulNat vuz3190 vuz3170)) (reduce2D (vuz316 * Neg vuz3170 + vuz318 * Neg vuz3190) (Pos (primMulNat vuz3190 vuz3170)))",fontsize=16,color="black",shape="box"];7213 -> 7227[label="",style="solid", color="black", weight=3];
67.83/34.95	7550 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.95	7550[label="primMulNat vuz306100 (Succ vuz307100)",fontsize=16,color="magenta"];7550 -> 7551[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7550 -> 7552[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7549[label="primPlusNat vuz335 (Succ vuz307100)",fontsize=16,color="burlywood",shape="triangle"];10863[label="vuz335/Succ vuz3350",fontsize=10,color="white",style="solid",shape="box"];7549 -> 10863[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10863 -> 7553[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	10864[label="vuz335/Zero",fontsize=10,color="white",style="solid",shape="box"];7549 -> 10864[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10864 -> 7554[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	7220[label="primQuotInt (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (vuz318 * vuz319)) (reduce2D (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (vuz318 * vuz319)) (vuz319 * Pos vuz3170))",fontsize=16,color="black",shape="box"];7220 -> 7234[label="",style="solid", color="black", weight=3];
67.83/34.95	7221[label="primQuotInt (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (vuz318 * vuz319)) (reduce2D (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (vuz318 * vuz319)) (vuz319 * Neg vuz3170))",fontsize=16,color="black",shape="box"];7221 -> 7235[label="",style="solid", color="black", weight=3];
67.83/34.95	7222[label="primQuotInt (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (vuz318 * vuz319)) (reduce2D (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (vuz318 * vuz319)) (vuz319 * Pos vuz3170))",fontsize=16,color="black",shape="box"];7222 -> 7236[label="",style="solid", color="black", weight=3];
67.83/34.95	7223[label="primQuotInt (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (vuz318 * vuz319)) (reduce2D (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (vuz318 * vuz319)) (vuz319 * Neg vuz3170))",fontsize=16,color="black",shape="box"];7223 -> 7237[label="",style="solid", color="black", weight=3];
67.83/34.95	7224[label="primQuotInt (Pos (primMulNat vuz3190 vuz3170)) (gcd (vuz316 * Pos vuz3170 + vuz318 * Pos vuz3190) (Pos (primMulNat vuz3190 vuz3170)))",fontsize=16,color="black",shape="box"];7224 -> 7238[label="",style="solid", color="black", weight=3];
67.83/34.95	7225[label="primQuotInt (Neg (primMulNat vuz3190 vuz3170)) (gcd (vuz316 * Neg vuz3170 + vuz318 * Pos vuz3190) (Neg (primMulNat vuz3190 vuz3170)))",fontsize=16,color="black",shape="box"];7225 -> 7239[label="",style="solid", color="black", weight=3];
67.83/34.95	7226[label="primQuotInt (Neg (primMulNat vuz3190 vuz3170)) (gcd (vuz316 * Pos vuz3170 + vuz318 * Neg vuz3190) (Neg (primMulNat vuz3190 vuz3170)))",fontsize=16,color="black",shape="box"];7226 -> 7240[label="",style="solid", color="black", weight=3];
67.83/34.95	7227[label="primQuotInt (Pos (primMulNat vuz3190 vuz3170)) (gcd (vuz316 * Neg vuz3170 + vuz318 * Neg vuz3190) (Pos (primMulNat vuz3190 vuz3170)))",fontsize=16,color="black",shape="box"];7227 -> 7241[label="",style="solid", color="black", weight=3];
67.83/34.95	7551[label="vuz306100",fontsize=16,color="green",shape="box"];7552[label="Succ vuz307100",fontsize=16,color="green",shape="box"];7553[label="primPlusNat (Succ vuz3350) (Succ vuz307100)",fontsize=16,color="black",shape="box"];7553 -> 7564[label="",style="solid", color="black", weight=3];
67.83/34.95	7554[label="primPlusNat Zero (Succ vuz307100)",fontsize=16,color="black",shape="box"];7554 -> 7565[label="",style="solid", color="black", weight=3];
67.83/34.95	7234[label="primQuotInt (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (primMulInt vuz318 vuz319)) (reduce2D (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (primMulInt vuz318 vuz319)) (vuz319 * Pos vuz3170))",fontsize=16,color="burlywood",shape="box"];10865[label="vuz318/Pos vuz3180",fontsize=10,color="white",style="solid",shape="box"];7234 -> 10865[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10865 -> 7250[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	10866[label="vuz318/Neg vuz3180",fontsize=10,color="white",style="solid",shape="box"];7234 -> 10866[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10866 -> 7251[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	7235[label="primQuotInt (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (primMulInt vuz318 vuz319)) (reduce2D (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (primMulInt vuz318 vuz319)) (vuz319 * Neg vuz3170))",fontsize=16,color="burlywood",shape="box"];10867[label="vuz318/Pos vuz3180",fontsize=10,color="white",style="solid",shape="box"];7235 -> 10867[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10867 -> 7252[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	10868[label="vuz318/Neg vuz3180",fontsize=10,color="white",style="solid",shape="box"];7235 -> 10868[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10868 -> 7253[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	7236[label="primQuotInt (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (primMulInt vuz318 vuz319)) (reduce2D (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (primMulInt vuz318 vuz319)) (vuz319 * Pos vuz3170))",fontsize=16,color="burlywood",shape="box"];10869[label="vuz318/Pos vuz3180",fontsize=10,color="white",style="solid",shape="box"];7236 -> 10869[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10869 -> 7254[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	10870[label="vuz318/Neg vuz3180",fontsize=10,color="white",style="solid",shape="box"];7236 -> 10870[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10870 -> 7255[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	7237[label="primQuotInt (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (primMulInt vuz318 vuz319)) (reduce2D (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (primMulInt vuz318 vuz319)) (vuz319 * Neg vuz3170))",fontsize=16,color="burlywood",shape="box"];10871[label="vuz318/Pos vuz3180",fontsize=10,color="white",style="solid",shape="box"];7237 -> 10871[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10871 -> 7256[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	10872[label="vuz318/Neg vuz3180",fontsize=10,color="white",style="solid",shape="box"];7237 -> 10872[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10872 -> 7257[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	7238[label="primQuotInt (Pos (primMulNat vuz3190 vuz3170)) (gcd3 (vuz316 * Pos vuz3170 + vuz318 * Pos vuz3190) (Pos (primMulNat vuz3190 vuz3170)))",fontsize=16,color="black",shape="box"];7238 -> 7258[label="",style="solid", color="black", weight=3];
67.83/34.95	7239[label="primQuotInt (Neg (primMulNat vuz3190 vuz3170)) (gcd3 (vuz316 * Neg vuz3170 + vuz318 * Pos vuz3190) (Neg (primMulNat vuz3190 vuz3170)))",fontsize=16,color="black",shape="box"];7239 -> 7259[label="",style="solid", color="black", weight=3];
67.83/34.95	7240[label="primQuotInt (Neg (primMulNat vuz3190 vuz3170)) (gcd3 (vuz316 * Pos vuz3170 + vuz318 * Neg vuz3190) (Neg (primMulNat vuz3190 vuz3170)))",fontsize=16,color="black",shape="box"];7240 -> 7260[label="",style="solid", color="black", weight=3];
67.83/34.95	7241[label="primQuotInt (Pos (primMulNat vuz3190 vuz3170)) (gcd3 (vuz316 * Neg vuz3170 + vuz318 * Neg vuz3190) (Pos (primMulNat vuz3190 vuz3170)))",fontsize=16,color="black",shape="box"];7241 -> 7261[label="",style="solid", color="black", weight=3];
67.83/34.95	7564[label="Succ (Succ (primPlusNat vuz3350 vuz307100))",fontsize=16,color="green",shape="box"];7564 -> 7571[label="",style="dashed", color="green", weight=3];
67.83/34.95	7565[label="Succ vuz307100",fontsize=16,color="green",shape="box"];7250[label="primQuotInt (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (primMulInt (Pos vuz3180) vuz319)) (reduce2D (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (primMulInt (Pos vuz3180) vuz319)) (vuz319 * Pos vuz3170))",fontsize=16,color="burlywood",shape="box"];10873[label="vuz319/Pos vuz3190",fontsize=10,color="white",style="solid",shape="box"];7250 -> 10873[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10873 -> 7268[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	10874[label="vuz319/Neg vuz3190",fontsize=10,color="white",style="solid",shape="box"];7250 -> 10874[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10874 -> 7269[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	7251[label="primQuotInt (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (primMulInt (Neg vuz3180) vuz319)) (reduce2D (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (primMulInt (Neg vuz3180) vuz319)) (vuz319 * Pos vuz3170))",fontsize=16,color="burlywood",shape="box"];10875[label="vuz319/Pos vuz3190",fontsize=10,color="white",style="solid",shape="box"];7251 -> 10875[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10875 -> 7270[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	10876[label="vuz319/Neg vuz3190",fontsize=10,color="white",style="solid",shape="box"];7251 -> 10876[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10876 -> 7271[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	7252[label="primQuotInt (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (primMulInt (Pos vuz3180) vuz319)) (reduce2D (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (primMulInt (Pos vuz3180) vuz319)) (vuz319 * Neg vuz3170))",fontsize=16,color="burlywood",shape="box"];10877[label="vuz319/Pos vuz3190",fontsize=10,color="white",style="solid",shape="box"];7252 -> 10877[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10877 -> 7272[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	10878[label="vuz319/Neg vuz3190",fontsize=10,color="white",style="solid",shape="box"];7252 -> 10878[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10878 -> 7273[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	7253[label="primQuotInt (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (primMulInt (Neg vuz3180) vuz319)) (reduce2D (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (primMulInt (Neg vuz3180) vuz319)) (vuz319 * Neg vuz3170))",fontsize=16,color="burlywood",shape="box"];10879[label="vuz319/Pos vuz3190",fontsize=10,color="white",style="solid",shape="box"];7253 -> 10879[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10879 -> 7274[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	10880[label="vuz319/Neg vuz3190",fontsize=10,color="white",style="solid",shape="box"];7253 -> 10880[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10880 -> 7275[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	7254[label="primQuotInt (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (primMulInt (Pos vuz3180) vuz319)) (reduce2D (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (primMulInt (Pos vuz3180) vuz319)) (vuz319 * Pos vuz3170))",fontsize=16,color="burlywood",shape="box"];10881[label="vuz319/Pos vuz3190",fontsize=10,color="white",style="solid",shape="box"];7254 -> 10881[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10881 -> 7276[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	10882[label="vuz319/Neg vuz3190",fontsize=10,color="white",style="solid",shape="box"];7254 -> 10882[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10882 -> 7277[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	7255[label="primQuotInt (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (primMulInt (Neg vuz3180) vuz319)) (reduce2D (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (primMulInt (Neg vuz3180) vuz319)) (vuz319 * Pos vuz3170))",fontsize=16,color="burlywood",shape="box"];10883[label="vuz319/Pos vuz3190",fontsize=10,color="white",style="solid",shape="box"];7255 -> 10883[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10883 -> 7278[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	10884[label="vuz319/Neg vuz3190",fontsize=10,color="white",style="solid",shape="box"];7255 -> 10884[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10884 -> 7279[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	7256[label="primQuotInt (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (primMulInt (Pos vuz3180) vuz319)) (reduce2D (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (primMulInt (Pos vuz3180) vuz319)) (vuz319 * Neg vuz3170))",fontsize=16,color="burlywood",shape="box"];10885[label="vuz319/Pos vuz3190",fontsize=10,color="white",style="solid",shape="box"];7256 -> 10885[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10885 -> 7280[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	10886[label="vuz319/Neg vuz3190",fontsize=10,color="white",style="solid",shape="box"];7256 -> 10886[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10886 -> 7281[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	7257[label="primQuotInt (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (primMulInt (Neg vuz3180) vuz319)) (reduce2D (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (primMulInt (Neg vuz3180) vuz319)) (vuz319 * Neg vuz3170))",fontsize=16,color="burlywood",shape="box"];10887[label="vuz319/Pos vuz3190",fontsize=10,color="white",style="solid",shape="box"];7257 -> 10887[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10887 -> 7282[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	10888[label="vuz319/Neg vuz3190",fontsize=10,color="white",style="solid",shape="box"];7257 -> 10888[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10888 -> 7283[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	7258[label="primQuotInt (Pos (primMulNat vuz3190 vuz3170)) (gcd2 (vuz316 * Pos vuz3170 + vuz318 * Pos vuz3190 == fromInt (Pos Zero)) (vuz316 * Pos vuz3170 + vuz318 * Pos vuz3190) (Pos (primMulNat vuz3190 vuz3170)))",fontsize=16,color="black",shape="box"];7258 -> 7284[label="",style="solid", color="black", weight=3];
67.83/34.95	7259[label="primQuotInt (Neg (primMulNat vuz3190 vuz3170)) (gcd2 (vuz316 * Neg vuz3170 + vuz318 * Pos vuz3190 == fromInt (Pos Zero)) (vuz316 * Neg vuz3170 + vuz318 * Pos vuz3190) (Neg (primMulNat vuz3190 vuz3170)))",fontsize=16,color="black",shape="box"];7259 -> 7285[label="",style="solid", color="black", weight=3];
67.83/34.95	7260[label="primQuotInt (Neg (primMulNat vuz3190 vuz3170)) (gcd2 (vuz316 * Pos vuz3170 + vuz318 * Neg vuz3190 == fromInt (Pos Zero)) (vuz316 * Pos vuz3170 + vuz318 * Neg vuz3190) (Neg (primMulNat vuz3190 vuz3170)))",fontsize=16,color="black",shape="box"];7260 -> 7286[label="",style="solid", color="black", weight=3];
67.83/34.95	7261[label="primQuotInt (Pos (primMulNat vuz3190 vuz3170)) (gcd2 (vuz316 * Neg vuz3170 + vuz318 * Neg vuz3190 == fromInt (Pos Zero)) (vuz316 * Neg vuz3170 + vuz318 * Neg vuz3190) (Pos (primMulNat vuz3190 vuz3170)))",fontsize=16,color="black",shape="box"];7261 -> 7287[label="",style="solid", color="black", weight=3];
67.83/34.95	7571[label="primPlusNat vuz3350 vuz307100",fontsize=16,color="burlywood",shape="triangle"];10889[label="vuz3350/Succ vuz33500",fontsize=10,color="white",style="solid",shape="box"];7571 -> 10889[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10889 -> 7585[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	10890[label="vuz3350/Zero",fontsize=10,color="white",style="solid",shape="box"];7571 -> 10890[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10890 -> 7586[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	7268[label="primQuotInt (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (primMulInt (Pos vuz3180) (Pos vuz3190))) (reduce2D (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (primMulInt (Pos vuz3180) (Pos vuz3190))) (Pos vuz3190 * Pos vuz3170))",fontsize=16,color="black",shape="box"];7268 -> 7296[label="",style="solid", color="black", weight=3];
67.83/34.95	7269[label="primQuotInt (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (primMulInt (Pos vuz3180) (Neg vuz3190))) (reduce2D (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (primMulInt (Pos vuz3180) (Neg vuz3190))) (Neg vuz3190 * Pos vuz3170))",fontsize=16,color="black",shape="box"];7269 -> 7297[label="",style="solid", color="black", weight=3];
67.83/34.95	7270[label="primQuotInt (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (primMulInt (Neg vuz3180) (Pos vuz3190))) (reduce2D (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (primMulInt (Neg vuz3180) (Pos vuz3190))) (Pos vuz3190 * Pos vuz3170))",fontsize=16,color="black",shape="box"];7270 -> 7298[label="",style="solid", color="black", weight=3];
67.83/34.95	7271[label="primQuotInt (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (primMulInt (Neg vuz3180) (Neg vuz3190))) (reduce2D (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (primMulInt (Neg vuz3180) (Neg vuz3190))) (Neg vuz3190 * Pos vuz3170))",fontsize=16,color="black",shape="box"];7271 -> 7299[label="",style="solid", color="black", weight=3];
67.83/34.95	7272[label="primQuotInt (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (primMulInt (Pos vuz3180) (Pos vuz3190))) (reduce2D (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (primMulInt (Pos vuz3180) (Pos vuz3190))) (Pos vuz3190 * Neg vuz3170))",fontsize=16,color="black",shape="box"];7272 -> 7300[label="",style="solid", color="black", weight=3];
67.83/34.95	7273[label="primQuotInt (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (primMulInt (Pos vuz3180) (Neg vuz3190))) (reduce2D (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (primMulInt (Pos vuz3180) (Neg vuz3190))) (Neg vuz3190 * Neg vuz3170))",fontsize=16,color="black",shape="box"];7273 -> 7301[label="",style="solid", color="black", weight=3];
67.83/34.95	7274[label="primQuotInt (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (primMulInt (Neg vuz3180) (Pos vuz3190))) (reduce2D (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (primMulInt (Neg vuz3180) (Pos vuz3190))) (Pos vuz3190 * Neg vuz3170))",fontsize=16,color="black",shape="box"];7274 -> 7302[label="",style="solid", color="black", weight=3];
67.83/34.95	7275[label="primQuotInt (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (primMulInt (Neg vuz3180) (Neg vuz3190))) (reduce2D (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (primMulInt (Neg vuz3180) (Neg vuz3190))) (Neg vuz3190 * Neg vuz3170))",fontsize=16,color="black",shape="box"];7275 -> 7303[label="",style="solid", color="black", weight=3];
67.83/34.95	7276[label="primQuotInt (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (primMulInt (Pos vuz3180) (Pos vuz3190))) (reduce2D (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (primMulInt (Pos vuz3180) (Pos vuz3190))) (Pos vuz3190 * Pos vuz3170))",fontsize=16,color="black",shape="box"];7276 -> 7304[label="",style="solid", color="black", weight=3];
67.83/34.95	7277[label="primQuotInt (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (primMulInt (Pos vuz3180) (Neg vuz3190))) (reduce2D (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (primMulInt (Pos vuz3180) (Neg vuz3190))) (Neg vuz3190 * Pos vuz3170))",fontsize=16,color="black",shape="box"];7277 -> 7305[label="",style="solid", color="black", weight=3];
67.83/34.95	7278[label="primQuotInt (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (primMulInt (Neg vuz3180) (Pos vuz3190))) (reduce2D (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (primMulInt (Neg vuz3180) (Pos vuz3190))) (Pos vuz3190 * Pos vuz3170))",fontsize=16,color="black",shape="box"];7278 -> 7306[label="",style="solid", color="black", weight=3];
67.83/34.95	7279[label="primQuotInt (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (primMulInt (Neg vuz3180) (Neg vuz3190))) (reduce2D (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (primMulInt (Neg vuz3180) (Neg vuz3190))) (Neg vuz3190 * Pos vuz3170))",fontsize=16,color="black",shape="box"];7279 -> 7307[label="",style="solid", color="black", weight=3];
67.83/34.95	7280[label="primQuotInt (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (primMulInt (Pos vuz3180) (Pos vuz3190))) (reduce2D (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (primMulInt (Pos vuz3180) (Pos vuz3190))) (Pos vuz3190 * Neg vuz3170))",fontsize=16,color="black",shape="box"];7280 -> 7308[label="",style="solid", color="black", weight=3];
67.83/34.95	7281[label="primQuotInt (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (primMulInt (Pos vuz3180) (Neg vuz3190))) (reduce2D (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (primMulInt (Pos vuz3180) (Neg vuz3190))) (Neg vuz3190 * Neg vuz3170))",fontsize=16,color="black",shape="box"];7281 -> 7309[label="",style="solid", color="black", weight=3];
67.83/34.95	7282[label="primQuotInt (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (primMulInt (Neg vuz3180) (Pos vuz3190))) (reduce2D (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (primMulInt (Neg vuz3180) (Pos vuz3190))) (Pos vuz3190 * Neg vuz3170))",fontsize=16,color="black",shape="box"];7282 -> 7310[label="",style="solid", color="black", weight=3];
67.83/34.95	7283[label="primQuotInt (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (primMulInt (Neg vuz3180) (Neg vuz3190))) (reduce2D (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (primMulInt (Neg vuz3180) (Neg vuz3190))) (Neg vuz3190 * Neg vuz3170))",fontsize=16,color="black",shape="box"];7283 -> 7311[label="",style="solid", color="black", weight=3];
67.83/34.95	7284[label="primQuotInt (Pos (primMulNat vuz3190 vuz3170)) (gcd2 (primEqInt (vuz316 * Pos vuz3170 + vuz318 * Pos vuz3190) (fromInt (Pos Zero))) (vuz316 * Pos vuz3170 + vuz318 * Pos vuz3190) (Pos (primMulNat vuz3190 vuz3170)))",fontsize=16,color="black",shape="box"];7284 -> 7312[label="",style="solid", color="black", weight=3];
67.83/34.95	7285[label="primQuotInt (Neg (primMulNat vuz3190 vuz3170)) (gcd2 (primEqInt (vuz316 * Neg vuz3170 + vuz318 * Pos vuz3190) (fromInt (Pos Zero))) (vuz316 * Neg vuz3170 + vuz318 * Pos vuz3190) (Neg (primMulNat vuz3190 vuz3170)))",fontsize=16,color="black",shape="box"];7285 -> 7313[label="",style="solid", color="black", weight=3];
67.83/34.95	7286[label="primQuotInt (Neg (primMulNat vuz3190 vuz3170)) (gcd2 (primEqInt (vuz316 * Pos vuz3170 + vuz318 * Neg vuz3190) (fromInt (Pos Zero))) (vuz316 * Pos vuz3170 + vuz318 * Neg vuz3190) (Neg (primMulNat vuz3190 vuz3170)))",fontsize=16,color="black",shape="box"];7286 -> 7314[label="",style="solid", color="black", weight=3];
67.83/34.95	7287[label="primQuotInt (Pos (primMulNat vuz3190 vuz3170)) (gcd2 (primEqInt (vuz316 * Neg vuz3170 + vuz318 * Neg vuz3190) (fromInt (Pos Zero))) (vuz316 * Neg vuz3170 + vuz318 * Neg vuz3190) (Pos (primMulNat vuz3190 vuz3170)))",fontsize=16,color="black",shape="box"];7287 -> 7315[label="",style="solid", color="black", weight=3];
67.83/34.95	7585[label="primPlusNat (Succ vuz33500) vuz307100",fontsize=16,color="burlywood",shape="box"];10891[label="vuz307100/Succ vuz3071000",fontsize=10,color="white",style="solid",shape="box"];7585 -> 10891[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10891 -> 7590[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	10892[label="vuz307100/Zero",fontsize=10,color="white",style="solid",shape="box"];7585 -> 10892[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10892 -> 7591[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	7586[label="primPlusNat Zero vuz307100",fontsize=16,color="burlywood",shape="box"];10893[label="vuz307100/Succ vuz3071000",fontsize=10,color="white",style="solid",shape="box"];7586 -> 10893[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10893 -> 7592[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	10894[label="vuz307100/Zero",fontsize=10,color="white",style="solid",shape="box"];7586 -> 10894[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10894 -> 7593[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	7296[label="primQuotInt (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (Pos (primMulNat vuz3180 vuz3190))) (reduce2D (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (Pos (primMulNat vuz3180 vuz3190))) (Pos vuz3190 * Pos vuz3170))",fontsize=16,color="black",shape="box"];7296 -> 7324[label="",style="solid", color="black", weight=3];
67.83/34.95	7297[label="primQuotInt (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (Neg (primMulNat vuz3180 vuz3190))) (reduce2D (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (Neg (primMulNat vuz3180 vuz3190))) (Neg vuz3190 * Pos vuz3170))",fontsize=16,color="black",shape="box"];7297 -> 7325[label="",style="solid", color="black", weight=3];
67.83/34.95	7298[label="primQuotInt (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (Neg (primMulNat vuz3180 vuz3190))) (reduce2D (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (Neg (primMulNat vuz3180 vuz3190))) (Pos vuz3190 * Pos vuz3170))",fontsize=16,color="black",shape="box"];7298 -> 7326[label="",style="solid", color="black", weight=3];
67.83/34.95	7299[label="primQuotInt (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (Pos (primMulNat vuz3180 vuz3190))) (reduce2D (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (Pos (primMulNat vuz3180 vuz3190))) (Neg vuz3190 * Pos vuz3170))",fontsize=16,color="black",shape="box"];7299 -> 7327[label="",style="solid", color="black", weight=3];
67.83/34.95	7300[label="primQuotInt (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (Pos (primMulNat vuz3180 vuz3190))) (reduce2D (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (Pos (primMulNat vuz3180 vuz3190))) (Pos vuz3190 * Neg vuz3170))",fontsize=16,color="black",shape="box"];7300 -> 7328[label="",style="solid", color="black", weight=3];
67.83/34.95	7301[label="primQuotInt (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (Neg (primMulNat vuz3180 vuz3190))) (reduce2D (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (Neg (primMulNat vuz3180 vuz3190))) (Neg vuz3190 * Neg vuz3170))",fontsize=16,color="black",shape="box"];7301 -> 7329[label="",style="solid", color="black", weight=3];
67.83/34.95	7302[label="primQuotInt (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (Neg (primMulNat vuz3180 vuz3190))) (reduce2D (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (Neg (primMulNat vuz3180 vuz3190))) (Pos vuz3190 * Neg vuz3170))",fontsize=16,color="black",shape="box"];7302 -> 7330[label="",style="solid", color="black", weight=3];
67.83/34.95	7303[label="primQuotInt (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (Pos (primMulNat vuz3180 vuz3190))) (reduce2D (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (Pos (primMulNat vuz3180 vuz3190))) (Neg vuz3190 * Neg vuz3170))",fontsize=16,color="black",shape="box"];7303 -> 7331[label="",style="solid", color="black", weight=3];
67.83/34.95	7304[label="primQuotInt (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (Pos (primMulNat vuz3180 vuz3190))) (reduce2D (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (Pos (primMulNat vuz3180 vuz3190))) (Pos vuz3190 * Pos vuz3170))",fontsize=16,color="black",shape="box"];7304 -> 7332[label="",style="solid", color="black", weight=3];
67.83/34.95	7305[label="primQuotInt (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (Neg (primMulNat vuz3180 vuz3190))) (reduce2D (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (Neg (primMulNat vuz3180 vuz3190))) (Neg vuz3190 * Pos vuz3170))",fontsize=16,color="black",shape="box"];7305 -> 7333[label="",style="solid", color="black", weight=3];
67.83/34.95	7306[label="primQuotInt (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (Neg (primMulNat vuz3180 vuz3190))) (reduce2D (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (Neg (primMulNat vuz3180 vuz3190))) (Pos vuz3190 * Pos vuz3170))",fontsize=16,color="black",shape="box"];7306 -> 7334[label="",style="solid", color="black", weight=3];
67.83/34.95	7307[label="primQuotInt (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (Pos (primMulNat vuz3180 vuz3190))) (reduce2D (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (Pos (primMulNat vuz3180 vuz3190))) (Neg vuz3190 * Pos vuz3170))",fontsize=16,color="black",shape="box"];7307 -> 7335[label="",style="solid", color="black", weight=3];
67.83/34.95	7308[label="primQuotInt (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (Pos (primMulNat vuz3180 vuz3190))) (reduce2D (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (Pos (primMulNat vuz3180 vuz3190))) (Pos vuz3190 * Neg vuz3170))",fontsize=16,color="black",shape="box"];7308 -> 7336[label="",style="solid", color="black", weight=3];
67.83/34.95	7309[label="primQuotInt (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (Neg (primMulNat vuz3180 vuz3190))) (reduce2D (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (Neg (primMulNat vuz3180 vuz3190))) (Neg vuz3190 * Neg vuz3170))",fontsize=16,color="black",shape="box"];7309 -> 7337[label="",style="solid", color="black", weight=3];
67.83/34.95	7310[label="primQuotInt (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (Neg (primMulNat vuz3180 vuz3190))) (reduce2D (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (Neg (primMulNat vuz3180 vuz3190))) (Pos vuz3190 * Neg vuz3170))",fontsize=16,color="black",shape="box"];7310 -> 7338[label="",style="solid", color="black", weight=3];
67.83/34.95	7311[label="primQuotInt (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (Pos (primMulNat vuz3180 vuz3190))) (reduce2D (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (Pos (primMulNat vuz3180 vuz3190))) (Neg vuz3190 * Neg vuz3170))",fontsize=16,color="black",shape="box"];7311 -> 7339[label="",style="solid", color="black", weight=3];
67.83/34.95	7312[label="primQuotInt (Pos (primMulNat vuz3190 vuz3170)) (gcd2 (primEqInt (primPlusInt (vuz316 * Pos vuz3170) (vuz318 * Pos vuz3190)) (fromInt (Pos Zero))) (primPlusInt (vuz316 * Pos vuz3170) (vuz318 * Pos vuz3190)) (Pos (primMulNat vuz3190 vuz3170)))",fontsize=16,color="black",shape="box"];7312 -> 7340[label="",style="solid", color="black", weight=3];
67.83/34.95	7313[label="primQuotInt (Neg (primMulNat vuz3190 vuz3170)) (gcd2 (primEqInt (primPlusInt (vuz316 * Neg vuz3170) (vuz318 * Pos vuz3190)) (fromInt (Pos Zero))) (primPlusInt (vuz316 * Neg vuz3170) (vuz318 * Pos vuz3190)) (Neg (primMulNat vuz3190 vuz3170)))",fontsize=16,color="black",shape="box"];7313 -> 7341[label="",style="solid", color="black", weight=3];
67.83/34.95	7314[label="primQuotInt (Neg (primMulNat vuz3190 vuz3170)) (gcd2 (primEqInt (primPlusInt (vuz316 * Pos vuz3170) (vuz318 * Neg vuz3190)) (fromInt (Pos Zero))) (primPlusInt (vuz316 * Pos vuz3170) (vuz318 * Neg vuz3190)) (Neg (primMulNat vuz3190 vuz3170)))",fontsize=16,color="black",shape="box"];7314 -> 7342[label="",style="solid", color="black", weight=3];
67.83/34.95	7315[label="primQuotInt (Pos (primMulNat vuz3190 vuz3170)) (gcd2 (primEqInt (primPlusInt (vuz316 * Neg vuz3170) (vuz318 * Neg vuz3190)) (fromInt (Pos Zero))) (primPlusInt (vuz316 * Neg vuz3170) (vuz318 * Neg vuz3190)) (Pos (primMulNat vuz3190 vuz3170)))",fontsize=16,color="black",shape="box"];7315 -> 7343[label="",style="solid", color="black", weight=3];
67.83/34.95	7590[label="primPlusNat (Succ vuz33500) (Succ vuz3071000)",fontsize=16,color="black",shape="box"];7590 -> 7601[label="",style="solid", color="black", weight=3];
67.83/34.95	7591[label="primPlusNat (Succ vuz33500) Zero",fontsize=16,color="black",shape="box"];7591 -> 7602[label="",style="solid", color="black", weight=3];
67.83/34.95	7592[label="primPlusNat Zero (Succ vuz3071000)",fontsize=16,color="black",shape="box"];7592 -> 7603[label="",style="solid", color="black", weight=3];
67.83/34.95	7593[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="box"];7593 -> 7604[label="",style="solid", color="black", weight=3];
67.83/34.95	7324[label="primQuotInt (Pos (primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190))) (reduce2D (Pos (primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190))) (Pos vuz3190 * Pos vuz3170))",fontsize=16,color="black",shape="box"];7324 -> 7356[label="",style="solid", color="black", weight=3];
67.83/34.95	7325[label="primQuotInt (primMinusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190)) (reduce2D (primMinusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190)) (Neg vuz3190 * Pos vuz3170))",fontsize=16,color="burlywood",shape="box"];10895[label="vuz3160/Succ vuz31600",fontsize=10,color="white",style="solid",shape="box"];7325 -> 10895[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10895 -> 7357[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	10896[label="vuz3160/Zero",fontsize=10,color="white",style="solid",shape="box"];7325 -> 10896[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10896 -> 7358[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	7326[label="primQuotInt (primMinusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190)) (reduce2D (primMinusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190)) (Pos vuz3190 * Pos vuz3170))",fontsize=16,color="burlywood",shape="box"];10897[label="vuz3160/Succ vuz31600",fontsize=10,color="white",style="solid",shape="box"];7326 -> 10897[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10897 -> 7359[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	10898[label="vuz3160/Zero",fontsize=10,color="white",style="solid",shape="box"];7326 -> 10898[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10898 -> 7360[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	7327[label="primQuotInt (Pos (primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190))) (reduce2D (Pos (primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190))) (Neg vuz3190 * Pos vuz3170))",fontsize=16,color="black",shape="box"];7327 -> 7361[label="",style="solid", color="black", weight=3];
67.83/34.95	7328[label="primQuotInt (primMinusNat (primMulNat vuz3180 vuz3190) (primMulNat vuz3160 vuz3170)) (reduce2D (primMinusNat (primMulNat vuz3180 vuz3190) (primMulNat vuz3160 vuz3170)) (Pos vuz3190 * Neg vuz3170))",fontsize=16,color="burlywood",shape="box"];10899[label="vuz3180/Succ vuz31800",fontsize=10,color="white",style="solid",shape="box"];7328 -> 10899[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10899 -> 7362[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	10900[label="vuz3180/Zero",fontsize=10,color="white",style="solid",shape="box"];7328 -> 10900[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10900 -> 7363[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	7329[label="primQuotInt (Neg (primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190))) (reduce2D (Neg (primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190))) (Neg vuz3190 * Neg vuz3170))",fontsize=16,color="black",shape="box"];7329 -> 7364[label="",style="solid", color="black", weight=3];
67.83/34.95	7330[label="primQuotInt (Neg (primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190))) (reduce2D (Neg (primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190))) (Pos vuz3190 * Neg vuz3170))",fontsize=16,color="black",shape="box"];7330 -> 7365[label="",style="solid", color="black", weight=3];
67.83/34.95	7331[label="primQuotInt (primMinusNat (primMulNat vuz3180 vuz3190) (primMulNat vuz3160 vuz3170)) (reduce2D (primMinusNat (primMulNat vuz3180 vuz3190) (primMulNat vuz3160 vuz3170)) (Neg vuz3190 * Neg vuz3170))",fontsize=16,color="burlywood",shape="box"];10901[label="vuz3180/Succ vuz31800",fontsize=10,color="white",style="solid",shape="box"];7331 -> 10901[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10901 -> 7366[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	10902[label="vuz3180/Zero",fontsize=10,color="white",style="solid",shape="box"];7331 -> 10902[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10902 -> 7367[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	7332[label="primQuotInt (primMinusNat (primMulNat vuz3180 vuz3190) (primMulNat vuz3160 vuz3170)) (reduce2D (primMinusNat (primMulNat vuz3180 vuz3190) (primMulNat vuz3160 vuz3170)) (Pos vuz3190 * Pos vuz3170))",fontsize=16,color="burlywood",shape="box"];10903[label="vuz3180/Succ vuz31800",fontsize=10,color="white",style="solid",shape="box"];7332 -> 10903[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10903 -> 7368[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	10904[label="vuz3180/Zero",fontsize=10,color="white",style="solid",shape="box"];7332 -> 10904[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10904 -> 7369[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	7333[label="primQuotInt (Neg (primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190))) (reduce2D (Neg (primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190))) (Neg vuz3190 * Pos vuz3170))",fontsize=16,color="black",shape="box"];7333 -> 7370[label="",style="solid", color="black", weight=3];
67.83/34.95	7334[label="primQuotInt (Neg (primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190))) (reduce2D (Neg (primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190))) (Pos vuz3190 * Pos vuz3170))",fontsize=16,color="black",shape="box"];7334 -> 7371[label="",style="solid", color="black", weight=3];
67.83/34.95	7335[label="primQuotInt (primMinusNat (primMulNat vuz3180 vuz3190) (primMulNat vuz3160 vuz3170)) (reduce2D (primMinusNat (primMulNat vuz3180 vuz3190) (primMulNat vuz3160 vuz3170)) (Neg vuz3190 * Pos vuz3170))",fontsize=16,color="burlywood",shape="box"];10905[label="vuz3180/Succ vuz31800",fontsize=10,color="white",style="solid",shape="box"];7335 -> 10905[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10905 -> 7372[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	10906[label="vuz3180/Zero",fontsize=10,color="white",style="solid",shape="box"];7335 -> 10906[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10906 -> 7373[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	7336[label="primQuotInt (Pos (primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190))) (reduce2D (Pos (primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190))) (Pos vuz3190 * Neg vuz3170))",fontsize=16,color="black",shape="box"];7336 -> 7374[label="",style="solid", color="black", weight=3];
67.83/34.95	7337[label="primQuotInt (primMinusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190)) (reduce2D (primMinusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190)) (Neg vuz3190 * Neg vuz3170))",fontsize=16,color="burlywood",shape="box"];10907[label="vuz3160/Succ vuz31600",fontsize=10,color="white",style="solid",shape="box"];7337 -> 10907[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10907 -> 7375[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	10908[label="vuz3160/Zero",fontsize=10,color="white",style="solid",shape="box"];7337 -> 10908[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10908 -> 7376[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	7338[label="primQuotInt (primMinusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190)) (reduce2D (primMinusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190)) (Pos vuz3190 * Neg vuz3170))",fontsize=16,color="burlywood",shape="box"];10909[label="vuz3160/Succ vuz31600",fontsize=10,color="white",style="solid",shape="box"];7338 -> 10909[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10909 -> 7377[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	10910[label="vuz3160/Zero",fontsize=10,color="white",style="solid",shape="box"];7338 -> 10910[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10910 -> 7378[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	7339[label="primQuotInt (Pos (primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190))) (reduce2D (Pos (primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190))) (Neg vuz3190 * Neg vuz3170))",fontsize=16,color="black",shape="box"];7339 -> 7379[label="",style="solid", color="black", weight=3];
67.83/34.95	7340[label="primQuotInt (Pos (primMulNat vuz3190 vuz3170)) (gcd2 (primEqInt (primPlusInt (primMulInt vuz316 (Pos vuz3170)) (vuz318 * Pos vuz3190)) (fromInt (Pos Zero))) (primPlusInt (primMulInt vuz316 (Pos vuz3170)) (vuz318 * Pos vuz3190)) (Pos (primMulNat vuz3190 vuz3170)))",fontsize=16,color="burlywood",shape="box"];10911[label="vuz316/Pos vuz3160",fontsize=10,color="white",style="solid",shape="box"];7340 -> 10911[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10911 -> 7380[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	10912[label="vuz316/Neg vuz3160",fontsize=10,color="white",style="solid",shape="box"];7340 -> 10912[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10912 -> 7381[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	7341[label="primQuotInt (Neg (primMulNat vuz3190 vuz3170)) (gcd2 (primEqInt (primPlusInt (primMulInt vuz316 (Neg vuz3170)) (vuz318 * Pos vuz3190)) (fromInt (Pos Zero))) (primPlusInt (primMulInt vuz316 (Neg vuz3170)) (vuz318 * Pos vuz3190)) (Neg (primMulNat vuz3190 vuz3170)))",fontsize=16,color="burlywood",shape="box"];10913[label="vuz316/Pos vuz3160",fontsize=10,color="white",style="solid",shape="box"];7341 -> 10913[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10913 -> 7382[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	10914[label="vuz316/Neg vuz3160",fontsize=10,color="white",style="solid",shape="box"];7341 -> 10914[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10914 -> 7383[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	7342[label="primQuotInt (Neg (primMulNat vuz3190 vuz3170)) (gcd2 (primEqInt (primPlusInt (primMulInt vuz316 (Pos vuz3170)) (vuz318 * Neg vuz3190)) (fromInt (Pos Zero))) (primPlusInt (primMulInt vuz316 (Pos vuz3170)) (vuz318 * Neg vuz3190)) (Neg (primMulNat vuz3190 vuz3170)))",fontsize=16,color="burlywood",shape="box"];10915[label="vuz316/Pos vuz3160",fontsize=10,color="white",style="solid",shape="box"];7342 -> 10915[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10915 -> 7384[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	10916[label="vuz316/Neg vuz3160",fontsize=10,color="white",style="solid",shape="box"];7342 -> 10916[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10916 -> 7385[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	7343[label="primQuotInt (Pos (primMulNat vuz3190 vuz3170)) (gcd2 (primEqInt (primPlusInt (primMulInt vuz316 (Neg vuz3170)) (vuz318 * Neg vuz3190)) (fromInt (Pos Zero))) (primPlusInt (primMulInt vuz316 (Neg vuz3170)) (vuz318 * Neg vuz3190)) (Pos (primMulNat vuz3190 vuz3170)))",fontsize=16,color="burlywood",shape="box"];10917[label="vuz316/Pos vuz3160",fontsize=10,color="white",style="solid",shape="box"];7343 -> 10917[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10917 -> 7386[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	10918[label="vuz316/Neg vuz3160",fontsize=10,color="white",style="solid",shape="box"];7343 -> 10918[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10918 -> 7387[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	7601[label="Succ (Succ (primPlusNat vuz33500 vuz3071000))",fontsize=16,color="green",shape="box"];7601 -> 7616[label="",style="dashed", color="green", weight=3];
67.83/34.95	7602[label="Succ vuz33500",fontsize=16,color="green",shape="box"];7603[label="Succ vuz3071000",fontsize=16,color="green",shape="box"];7604[label="Zero",fontsize=16,color="green",shape="box"];7356[label="primQuotInt (Pos (primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190))) (gcd (Pos (primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190))) (Pos vuz3190 * Pos vuz3170))",fontsize=16,color="black",shape="box"];7356 -> 7427[label="",style="solid", color="black", weight=3];
67.83/34.95	7357[label="primQuotInt (primMinusNat (primMulNat (Succ vuz31600) vuz3170) (primMulNat vuz3180 vuz3190)) (reduce2D (primMinusNat (primMulNat (Succ vuz31600) vuz3170) (primMulNat vuz3180 vuz3190)) (Neg vuz3190 * Pos vuz3170))",fontsize=16,color="burlywood",shape="box"];10919[label="vuz3170/Succ vuz31700",fontsize=10,color="white",style="solid",shape="box"];7357 -> 10919[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10919 -> 7428[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	10920[label="vuz3170/Zero",fontsize=10,color="white",style="solid",shape="box"];7357 -> 10920[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10920 -> 7429[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	7358[label="primQuotInt (primMinusNat (primMulNat Zero vuz3170) (primMulNat vuz3180 vuz3190)) (reduce2D (primMinusNat (primMulNat Zero vuz3170) (primMulNat vuz3180 vuz3190)) (Neg vuz3190 * Pos vuz3170))",fontsize=16,color="burlywood",shape="box"];10921[label="vuz3170/Succ vuz31700",fontsize=10,color="white",style="solid",shape="box"];7358 -> 10921[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10921 -> 7430[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	10922[label="vuz3170/Zero",fontsize=10,color="white",style="solid",shape="box"];7358 -> 10922[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10922 -> 7431[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	7359[label="primQuotInt (primMinusNat (primMulNat (Succ vuz31600) vuz3170) (primMulNat vuz3180 vuz3190)) (reduce2D (primMinusNat (primMulNat (Succ vuz31600) vuz3170) (primMulNat vuz3180 vuz3190)) (Pos vuz3190 * Pos vuz3170))",fontsize=16,color="burlywood",shape="box"];10923[label="vuz3170/Succ vuz31700",fontsize=10,color="white",style="solid",shape="box"];7359 -> 10923[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10923 -> 7432[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	10924[label="vuz3170/Zero",fontsize=10,color="white",style="solid",shape="box"];7359 -> 10924[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10924 -> 7433[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	7360[label="primQuotInt (primMinusNat (primMulNat Zero vuz3170) (primMulNat vuz3180 vuz3190)) (reduce2D (primMinusNat (primMulNat Zero vuz3170) (primMulNat vuz3180 vuz3190)) (Pos vuz3190 * Pos vuz3170))",fontsize=16,color="burlywood",shape="box"];10925[label="vuz3170/Succ vuz31700",fontsize=10,color="white",style="solid",shape="box"];7360 -> 10925[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10925 -> 7434[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	10926[label="vuz3170/Zero",fontsize=10,color="white",style="solid",shape="box"];7360 -> 10926[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10926 -> 7435[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	7361[label="primQuotInt (Pos (primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190))) (gcd (Pos (primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190))) (Neg vuz3190 * Pos vuz3170))",fontsize=16,color="black",shape="box"];7361 -> 7436[label="",style="solid", color="black", weight=3];
67.83/34.95	7362[label="primQuotInt (primMinusNat (primMulNat (Succ vuz31800) vuz3190) (primMulNat vuz3160 vuz3170)) (reduce2D (primMinusNat (primMulNat (Succ vuz31800) vuz3190) (primMulNat vuz3160 vuz3170)) (Pos vuz3190 * Neg vuz3170))",fontsize=16,color="burlywood",shape="box"];10927[label="vuz3190/Succ vuz31900",fontsize=10,color="white",style="solid",shape="box"];7362 -> 10927[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10927 -> 7437[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	10928[label="vuz3190/Zero",fontsize=10,color="white",style="solid",shape="box"];7362 -> 10928[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10928 -> 7438[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	7363[label="primQuotInt (primMinusNat (primMulNat Zero vuz3190) (primMulNat vuz3160 vuz3170)) (reduce2D (primMinusNat (primMulNat Zero vuz3190) (primMulNat vuz3160 vuz3170)) (Pos vuz3190 * Neg vuz3170))",fontsize=16,color="burlywood",shape="box"];10929[label="vuz3190/Succ vuz31900",fontsize=10,color="white",style="solid",shape="box"];7363 -> 10929[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10929 -> 7439[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	10930[label="vuz3190/Zero",fontsize=10,color="white",style="solid",shape="box"];7363 -> 10930[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10930 -> 7440[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	7364[label="primQuotInt (Neg (primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190))) (gcd (Neg (primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190))) (Neg vuz3190 * Neg vuz3170))",fontsize=16,color="black",shape="box"];7364 -> 7441[label="",style="solid", color="black", weight=3];
67.83/34.95	7365[label="primQuotInt (Neg (primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190))) (gcd (Neg (primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190))) (Pos vuz3190 * Neg vuz3170))",fontsize=16,color="black",shape="box"];7365 -> 7442[label="",style="solid", color="black", weight=3];
67.83/34.95	7366[label="primQuotInt (primMinusNat (primMulNat (Succ vuz31800) vuz3190) (primMulNat vuz3160 vuz3170)) (reduce2D (primMinusNat (primMulNat (Succ vuz31800) vuz3190) (primMulNat vuz3160 vuz3170)) (Neg vuz3190 * Neg vuz3170))",fontsize=16,color="burlywood",shape="box"];10931[label="vuz3190/Succ vuz31900",fontsize=10,color="white",style="solid",shape="box"];7366 -> 10931[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10931 -> 7443[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	10932[label="vuz3190/Zero",fontsize=10,color="white",style="solid",shape="box"];7366 -> 10932[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10932 -> 7444[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	7367[label="primQuotInt (primMinusNat (primMulNat Zero vuz3190) (primMulNat vuz3160 vuz3170)) (reduce2D (primMinusNat (primMulNat Zero vuz3190) (primMulNat vuz3160 vuz3170)) (Neg vuz3190 * Neg vuz3170))",fontsize=16,color="burlywood",shape="box"];10933[label="vuz3190/Succ vuz31900",fontsize=10,color="white",style="solid",shape="box"];7367 -> 10933[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10933 -> 7445[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	10934[label="vuz3190/Zero",fontsize=10,color="white",style="solid",shape="box"];7367 -> 10934[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10934 -> 7446[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	7368[label="primQuotInt (primMinusNat (primMulNat (Succ vuz31800) vuz3190) (primMulNat vuz3160 vuz3170)) (reduce2D (primMinusNat (primMulNat (Succ vuz31800) vuz3190) (primMulNat vuz3160 vuz3170)) (Pos vuz3190 * Pos vuz3170))",fontsize=16,color="burlywood",shape="box"];10935[label="vuz3190/Succ vuz31900",fontsize=10,color="white",style="solid",shape="box"];7368 -> 10935[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10935 -> 7447[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	10936[label="vuz3190/Zero",fontsize=10,color="white",style="solid",shape="box"];7368 -> 10936[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10936 -> 7448[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	7369[label="primQuotInt (primMinusNat (primMulNat Zero vuz3190) (primMulNat vuz3160 vuz3170)) (reduce2D (primMinusNat (primMulNat Zero vuz3190) (primMulNat vuz3160 vuz3170)) (Pos vuz3190 * Pos vuz3170))",fontsize=16,color="burlywood",shape="box"];10937[label="vuz3190/Succ vuz31900",fontsize=10,color="white",style="solid",shape="box"];7369 -> 10937[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10937 -> 7449[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	10938[label="vuz3190/Zero",fontsize=10,color="white",style="solid",shape="box"];7369 -> 10938[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10938 -> 7450[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	7370[label="primQuotInt (Neg (primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190))) (gcd (Neg (primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190))) (Neg vuz3190 * Pos vuz3170))",fontsize=16,color="black",shape="box"];7370 -> 7451[label="",style="solid", color="black", weight=3];
67.83/34.95	7371[label="primQuotInt (Neg (primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190))) (gcd (Neg (primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190))) (Pos vuz3190 * Pos vuz3170))",fontsize=16,color="black",shape="box"];7371 -> 7452[label="",style="solid", color="black", weight=3];
67.83/34.95	7372[label="primQuotInt (primMinusNat (primMulNat (Succ vuz31800) vuz3190) (primMulNat vuz3160 vuz3170)) (reduce2D (primMinusNat (primMulNat (Succ vuz31800) vuz3190) (primMulNat vuz3160 vuz3170)) (Neg vuz3190 * Pos vuz3170))",fontsize=16,color="burlywood",shape="box"];10939[label="vuz3190/Succ vuz31900",fontsize=10,color="white",style="solid",shape="box"];7372 -> 10939[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10939 -> 7453[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	10940[label="vuz3190/Zero",fontsize=10,color="white",style="solid",shape="box"];7372 -> 10940[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10940 -> 7454[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	7373[label="primQuotInt (primMinusNat (primMulNat Zero vuz3190) (primMulNat vuz3160 vuz3170)) (reduce2D (primMinusNat (primMulNat Zero vuz3190) (primMulNat vuz3160 vuz3170)) (Neg vuz3190 * Pos vuz3170))",fontsize=16,color="burlywood",shape="box"];10941[label="vuz3190/Succ vuz31900",fontsize=10,color="white",style="solid",shape="box"];7373 -> 10941[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10941 -> 7455[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	10942[label="vuz3190/Zero",fontsize=10,color="white",style="solid",shape="box"];7373 -> 10942[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10942 -> 7456[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	7374[label="primQuotInt (Pos (primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190))) (gcd (Pos (primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190))) (Pos vuz3190 * Neg vuz3170))",fontsize=16,color="black",shape="box"];7374 -> 7457[label="",style="solid", color="black", weight=3];
67.83/34.95	7375[label="primQuotInt (primMinusNat (primMulNat (Succ vuz31600) vuz3170) (primMulNat vuz3180 vuz3190)) (reduce2D (primMinusNat (primMulNat (Succ vuz31600) vuz3170) (primMulNat vuz3180 vuz3190)) (Neg vuz3190 * Neg vuz3170))",fontsize=16,color="burlywood",shape="box"];10943[label="vuz3170/Succ vuz31700",fontsize=10,color="white",style="solid",shape="box"];7375 -> 10943[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10943 -> 7458[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	10944[label="vuz3170/Zero",fontsize=10,color="white",style="solid",shape="box"];7375 -> 10944[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10944 -> 7459[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	7376[label="primQuotInt (primMinusNat (primMulNat Zero vuz3170) (primMulNat vuz3180 vuz3190)) (reduce2D (primMinusNat (primMulNat Zero vuz3170) (primMulNat vuz3180 vuz3190)) (Neg vuz3190 * Neg vuz3170))",fontsize=16,color="burlywood",shape="box"];10945[label="vuz3170/Succ vuz31700",fontsize=10,color="white",style="solid",shape="box"];7376 -> 10945[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10945 -> 7460[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	10946[label="vuz3170/Zero",fontsize=10,color="white",style="solid",shape="box"];7376 -> 10946[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10946 -> 7461[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	7377[label="primQuotInt (primMinusNat (primMulNat (Succ vuz31600) vuz3170) (primMulNat vuz3180 vuz3190)) (reduce2D (primMinusNat (primMulNat (Succ vuz31600) vuz3170) (primMulNat vuz3180 vuz3190)) (Pos vuz3190 * Neg vuz3170))",fontsize=16,color="burlywood",shape="box"];10947[label="vuz3170/Succ vuz31700",fontsize=10,color="white",style="solid",shape="box"];7377 -> 10947[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10947 -> 7462[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	10948[label="vuz3170/Zero",fontsize=10,color="white",style="solid",shape="box"];7377 -> 10948[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10948 -> 7463[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	7378[label="primQuotInt (primMinusNat (primMulNat Zero vuz3170) (primMulNat vuz3180 vuz3190)) (reduce2D (primMinusNat (primMulNat Zero vuz3170) (primMulNat vuz3180 vuz3190)) (Pos vuz3190 * Neg vuz3170))",fontsize=16,color="burlywood",shape="box"];10949[label="vuz3170/Succ vuz31700",fontsize=10,color="white",style="solid",shape="box"];7378 -> 10949[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10949 -> 7464[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	10950[label="vuz3170/Zero",fontsize=10,color="white",style="solid",shape="box"];7378 -> 10950[label="",style="solid", color="burlywood", weight=9];
67.83/34.95	10950 -> 7465[label="",style="solid", color="burlywood", weight=3];
67.83/34.95	7379[label="primQuotInt (Pos (primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190))) (gcd (Pos (primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190))) (Neg vuz3190 * Neg vuz3170))",fontsize=16,color="black",shape="box"];7379 -> 7466[label="",style="solid", color="black", weight=3];
67.83/34.95	7380[label="primQuotInt (Pos (primMulNat vuz3190 vuz3170)) (gcd2 (primEqInt (primPlusInt (primMulInt (Pos vuz3160) (Pos vuz3170)) (vuz318 * Pos vuz3190)) (fromInt (Pos Zero))) (primPlusInt (primMulInt (Pos vuz3160) (Pos vuz3170)) (vuz318 * Pos vuz3190)) (Pos (primMulNat vuz3190 vuz3170)))",fontsize=16,color="black",shape="box"];7380 -> 7467[label="",style="solid", color="black", weight=3];
67.83/34.95	7381[label="primQuotInt (Pos (primMulNat vuz3190 vuz3170)) (gcd2 (primEqInt (primPlusInt (primMulInt (Neg vuz3160) (Pos vuz3170)) (vuz318 * Pos vuz3190)) (fromInt (Pos Zero))) (primPlusInt (primMulInt (Neg vuz3160) (Pos vuz3170)) (vuz318 * Pos vuz3190)) (Pos (primMulNat vuz3190 vuz3170)))",fontsize=16,color="black",shape="box"];7381 -> 7468[label="",style="solid", color="black", weight=3];
67.83/34.95	7382[label="primQuotInt (Neg (primMulNat vuz3190 vuz3170)) (gcd2 (primEqInt (primPlusInt (primMulInt (Pos vuz3160) (Neg vuz3170)) (vuz318 * Pos vuz3190)) (fromInt (Pos Zero))) (primPlusInt (primMulInt (Pos vuz3160) (Neg vuz3170)) (vuz318 * Pos vuz3190)) (Neg (primMulNat vuz3190 vuz3170)))",fontsize=16,color="black",shape="box"];7382 -> 7469[label="",style="solid", color="black", weight=3];
67.83/34.95	7383[label="primQuotInt (Neg (primMulNat vuz3190 vuz3170)) (gcd2 (primEqInt (primPlusInt (primMulInt (Neg vuz3160) (Neg vuz3170)) (vuz318 * Pos vuz3190)) (fromInt (Pos Zero))) (primPlusInt (primMulInt (Neg vuz3160) (Neg vuz3170)) (vuz318 * Pos vuz3190)) (Neg (primMulNat vuz3190 vuz3170)))",fontsize=16,color="black",shape="box"];7383 -> 7470[label="",style="solid", color="black", weight=3];
67.83/34.95	7384[label="primQuotInt (Neg (primMulNat vuz3190 vuz3170)) (gcd2 (primEqInt (primPlusInt (primMulInt (Pos vuz3160) (Pos vuz3170)) (vuz318 * Neg vuz3190)) (fromInt (Pos Zero))) (primPlusInt (primMulInt (Pos vuz3160) (Pos vuz3170)) (vuz318 * Neg vuz3190)) (Neg (primMulNat vuz3190 vuz3170)))",fontsize=16,color="black",shape="box"];7384 -> 7471[label="",style="solid", color="black", weight=3];
67.83/34.95	7385[label="primQuotInt (Neg (primMulNat vuz3190 vuz3170)) (gcd2 (primEqInt (primPlusInt (primMulInt (Neg vuz3160) (Pos vuz3170)) (vuz318 * Neg vuz3190)) (fromInt (Pos Zero))) (primPlusInt (primMulInt (Neg vuz3160) (Pos vuz3170)) (vuz318 * Neg vuz3190)) (Neg (primMulNat vuz3190 vuz3170)))",fontsize=16,color="black",shape="box"];7385 -> 7472[label="",style="solid", color="black", weight=3];
67.83/34.95	7386[label="primQuotInt (Pos (primMulNat vuz3190 vuz3170)) (gcd2 (primEqInt (primPlusInt (primMulInt (Pos vuz3160) (Neg vuz3170)) (vuz318 * Neg vuz3190)) (fromInt (Pos Zero))) (primPlusInt (primMulInt (Pos vuz3160) (Neg vuz3170)) (vuz318 * Neg vuz3190)) (Pos (primMulNat vuz3190 vuz3170)))",fontsize=16,color="black",shape="box"];7386 -> 7473[label="",style="solid", color="black", weight=3];
67.83/34.95	7387[label="primQuotInt (Pos (primMulNat vuz3190 vuz3170)) (gcd2 (primEqInt (primPlusInt (primMulInt (Neg vuz3160) (Neg vuz3170)) (vuz318 * Neg vuz3190)) (fromInt (Pos Zero))) (primPlusInt (primMulInt (Neg vuz3160) (Neg vuz3170)) (vuz318 * Neg vuz3190)) (Pos (primMulNat vuz3190 vuz3170)))",fontsize=16,color="black",shape="box"];7387 -> 7474[label="",style="solid", color="black", weight=3];
67.83/34.95	7616 -> 7571[label="",style="dashed", color="red", weight=0];
67.83/34.95	7616[label="primPlusNat vuz33500 vuz3071000",fontsize=16,color="magenta"];7616 -> 7622[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7616 -> 7623[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7427 -> 7667[label="",style="dashed", color="red", weight=0];
67.83/34.95	7427[label="primQuotInt (Pos (primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190))) (gcd3 (Pos (primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190))) (Pos vuz3190 * Pos vuz3170))",fontsize=16,color="magenta"];7427 -> 7668[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7427 -> 7669[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7428[label="primQuotInt (primMinusNat (primMulNat (Succ vuz31600) (Succ vuz31700)) (primMulNat vuz3180 vuz3190)) (reduce2D (primMinusNat (primMulNat (Succ vuz31600) (Succ vuz31700)) (primMulNat vuz3180 vuz3190)) (Neg vuz3190 * Pos (Succ vuz31700)))",fontsize=16,color="black",shape="box"];7428 -> 7534[label="",style="solid", color="black", weight=3];
67.83/34.95	7429[label="primQuotInt (primMinusNat (primMulNat (Succ vuz31600) Zero) (primMulNat vuz3180 vuz3190)) (reduce2D (primMinusNat (primMulNat (Succ vuz31600) Zero) (primMulNat vuz3180 vuz3190)) (Neg vuz3190 * Pos Zero))",fontsize=16,color="black",shape="box"];7429 -> 7535[label="",style="solid", color="black", weight=3];
67.83/34.95	7430[label="primQuotInt (primMinusNat (primMulNat Zero (Succ vuz31700)) (primMulNat vuz3180 vuz3190)) (reduce2D (primMinusNat (primMulNat Zero (Succ vuz31700)) (primMulNat vuz3180 vuz3190)) (Neg vuz3190 * Pos (Succ vuz31700)))",fontsize=16,color="black",shape="box"];7430 -> 7536[label="",style="solid", color="black", weight=3];
67.83/34.95	7431[label="primQuotInt (primMinusNat (primMulNat Zero Zero) (primMulNat vuz3180 vuz3190)) (reduce2D (primMinusNat (primMulNat Zero Zero) (primMulNat vuz3180 vuz3190)) (Neg vuz3190 * Pos Zero))",fontsize=16,color="black",shape="box"];7431 -> 7537[label="",style="solid", color="black", weight=3];
67.83/34.95	7432[label="primQuotInt (primMinusNat (primMulNat (Succ vuz31600) (Succ vuz31700)) (primMulNat vuz3180 vuz3190)) (reduce2D (primMinusNat (primMulNat (Succ vuz31600) (Succ vuz31700)) (primMulNat vuz3180 vuz3190)) (Pos vuz3190 * Pos (Succ vuz31700)))",fontsize=16,color="black",shape="box"];7432 -> 7538[label="",style="solid", color="black", weight=3];
67.83/34.95	7433[label="primQuotInt (primMinusNat (primMulNat (Succ vuz31600) Zero) (primMulNat vuz3180 vuz3190)) (reduce2D (primMinusNat (primMulNat (Succ vuz31600) Zero) (primMulNat vuz3180 vuz3190)) (Pos vuz3190 * Pos Zero))",fontsize=16,color="black",shape="box"];7433 -> 7539[label="",style="solid", color="black", weight=3];
67.83/34.95	7434[label="primQuotInt (primMinusNat (primMulNat Zero (Succ vuz31700)) (primMulNat vuz3180 vuz3190)) (reduce2D (primMinusNat (primMulNat Zero (Succ vuz31700)) (primMulNat vuz3180 vuz3190)) (Pos vuz3190 * Pos (Succ vuz31700)))",fontsize=16,color="black",shape="box"];7434 -> 7540[label="",style="solid", color="black", weight=3];
67.83/34.95	7435[label="primQuotInt (primMinusNat (primMulNat Zero Zero) (primMulNat vuz3180 vuz3190)) (reduce2D (primMinusNat (primMulNat Zero Zero) (primMulNat vuz3180 vuz3190)) (Pos vuz3190 * Pos Zero))",fontsize=16,color="black",shape="box"];7435 -> 7541[label="",style="solid", color="black", weight=3];
67.83/34.95	7436 -> 7713[label="",style="dashed", color="red", weight=0];
67.83/34.95	7436[label="primQuotInt (Pos (primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190))) (gcd3 (Pos (primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190))) (Neg vuz3190 * Pos vuz3170))",fontsize=16,color="magenta"];7436 -> 7714[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7436 -> 7715[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7437[label="primQuotInt (primMinusNat (primMulNat (Succ vuz31800) (Succ vuz31900)) (primMulNat vuz3160 vuz3170)) (reduce2D (primMinusNat (primMulNat (Succ vuz31800) (Succ vuz31900)) (primMulNat vuz3160 vuz3170)) (Pos (Succ vuz31900) * Neg vuz3170))",fontsize=16,color="black",shape="box"];7437 -> 7555[label="",style="solid", color="black", weight=3];
67.83/34.95	7438[label="primQuotInt (primMinusNat (primMulNat (Succ vuz31800) Zero) (primMulNat vuz3160 vuz3170)) (reduce2D (primMinusNat (primMulNat (Succ vuz31800) Zero) (primMulNat vuz3160 vuz3170)) (Pos Zero * Neg vuz3170))",fontsize=16,color="black",shape="box"];7438 -> 7556[label="",style="solid", color="black", weight=3];
67.83/34.95	7439[label="primQuotInt (primMinusNat (primMulNat Zero (Succ vuz31900)) (primMulNat vuz3160 vuz3170)) (reduce2D (primMinusNat (primMulNat Zero (Succ vuz31900)) (primMulNat vuz3160 vuz3170)) (Pos (Succ vuz31900) * Neg vuz3170))",fontsize=16,color="black",shape="box"];7439 -> 7557[label="",style="solid", color="black", weight=3];
67.83/34.95	7440[label="primQuotInt (primMinusNat (primMulNat Zero Zero) (primMulNat vuz3160 vuz3170)) (reduce2D (primMinusNat (primMulNat Zero Zero) (primMulNat vuz3160 vuz3170)) (Pos Zero * Neg vuz3170))",fontsize=16,color="black",shape="box"];7440 -> 7558[label="",style="solid", color="black", weight=3];
67.83/34.95	7441 -> 7745[label="",style="dashed", color="red", weight=0];
67.83/34.95	7441[label="primQuotInt (Neg (primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190))) (gcd3 (Neg (primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190))) (Neg vuz3190 * Neg vuz3170))",fontsize=16,color="magenta"];7441 -> 7746[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7441 -> 7747[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7442 -> 7763[label="",style="dashed", color="red", weight=0];
67.83/34.95	7442[label="primQuotInt (Neg (primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190))) (gcd3 (Neg (primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190))) (Pos vuz3190 * Neg vuz3170))",fontsize=16,color="magenta"];7442 -> 7764[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7442 -> 7765[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7443[label="primQuotInt (primMinusNat (primMulNat (Succ vuz31800) (Succ vuz31900)) (primMulNat vuz3160 vuz3170)) (reduce2D (primMinusNat (primMulNat (Succ vuz31800) (Succ vuz31900)) (primMulNat vuz3160 vuz3170)) (Neg (Succ vuz31900) * Neg vuz3170))",fontsize=16,color="black",shape="box"];7443 -> 7572[label="",style="solid", color="black", weight=3];
67.83/34.95	7444[label="primQuotInt (primMinusNat (primMulNat (Succ vuz31800) Zero) (primMulNat vuz3160 vuz3170)) (reduce2D (primMinusNat (primMulNat (Succ vuz31800) Zero) (primMulNat vuz3160 vuz3170)) (Neg Zero * Neg vuz3170))",fontsize=16,color="black",shape="box"];7444 -> 7573[label="",style="solid", color="black", weight=3];
67.83/34.95	7445[label="primQuotInt (primMinusNat (primMulNat Zero (Succ vuz31900)) (primMulNat vuz3160 vuz3170)) (reduce2D (primMinusNat (primMulNat Zero (Succ vuz31900)) (primMulNat vuz3160 vuz3170)) (Neg (Succ vuz31900) * Neg vuz3170))",fontsize=16,color="black",shape="box"];7445 -> 7574[label="",style="solid", color="black", weight=3];
67.83/34.95	7446[label="primQuotInt (primMinusNat (primMulNat Zero Zero) (primMulNat vuz3160 vuz3170)) (reduce2D (primMinusNat (primMulNat Zero Zero) (primMulNat vuz3160 vuz3170)) (Neg Zero * Neg vuz3170))",fontsize=16,color="black",shape="box"];7446 -> 7575[label="",style="solid", color="black", weight=3];
67.83/34.95	7447[label="primQuotInt (primMinusNat (primMulNat (Succ vuz31800) (Succ vuz31900)) (primMulNat vuz3160 vuz3170)) (reduce2D (primMinusNat (primMulNat (Succ vuz31800) (Succ vuz31900)) (primMulNat vuz3160 vuz3170)) (Pos (Succ vuz31900) * Pos vuz3170))",fontsize=16,color="black",shape="box"];7447 -> 7576[label="",style="solid", color="black", weight=3];
67.83/34.95	7448[label="primQuotInt (primMinusNat (primMulNat (Succ vuz31800) Zero) (primMulNat vuz3160 vuz3170)) (reduce2D (primMinusNat (primMulNat (Succ vuz31800) Zero) (primMulNat vuz3160 vuz3170)) (Pos Zero * Pos vuz3170))",fontsize=16,color="black",shape="box"];7448 -> 7577[label="",style="solid", color="black", weight=3];
67.83/34.95	7449[label="primQuotInt (primMinusNat (primMulNat Zero (Succ vuz31900)) (primMulNat vuz3160 vuz3170)) (reduce2D (primMinusNat (primMulNat Zero (Succ vuz31900)) (primMulNat vuz3160 vuz3170)) (Pos (Succ vuz31900) * Pos vuz3170))",fontsize=16,color="black",shape="box"];7449 -> 7578[label="",style="solid", color="black", weight=3];
67.83/34.95	7450[label="primQuotInt (primMinusNat (primMulNat Zero Zero) (primMulNat vuz3160 vuz3170)) (reduce2D (primMinusNat (primMulNat Zero Zero) (primMulNat vuz3160 vuz3170)) (Pos Zero * Pos vuz3170))",fontsize=16,color="black",shape="box"];7450 -> 7579[label="",style="solid", color="black", weight=3];
67.83/34.95	7451 -> 7809[label="",style="dashed", color="red", weight=0];
67.83/34.95	7451[label="primQuotInt (Neg (primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190))) (gcd3 (Neg (primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190))) (Neg vuz3190 * Pos vuz3170))",fontsize=16,color="magenta"];7451 -> 7810[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7451 -> 7811[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7452 -> 7587[label="",style="dashed", color="red", weight=0];
67.83/34.95	7452[label="primQuotInt (Neg (primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190))) (gcd3 (Neg (primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190))) (Pos vuz3190 * Pos vuz3170))",fontsize=16,color="magenta"];7452 -> 7588[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7452 -> 7589[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7453[label="primQuotInt (primMinusNat (primMulNat (Succ vuz31800) (Succ vuz31900)) (primMulNat vuz3160 vuz3170)) (reduce2D (primMinusNat (primMulNat (Succ vuz31800) (Succ vuz31900)) (primMulNat vuz3160 vuz3170)) (Neg (Succ vuz31900) * Pos vuz3170))",fontsize=16,color="black",shape="box"];7453 -> 7594[label="",style="solid", color="black", weight=3];
67.83/34.95	7454[label="primQuotInt (primMinusNat (primMulNat (Succ vuz31800) Zero) (primMulNat vuz3160 vuz3170)) (reduce2D (primMinusNat (primMulNat (Succ vuz31800) Zero) (primMulNat vuz3160 vuz3170)) (Neg Zero * Pos vuz3170))",fontsize=16,color="black",shape="box"];7454 -> 7595[label="",style="solid", color="black", weight=3];
67.83/34.95	7455[label="primQuotInt (primMinusNat (primMulNat Zero (Succ vuz31900)) (primMulNat vuz3160 vuz3170)) (reduce2D (primMinusNat (primMulNat Zero (Succ vuz31900)) (primMulNat vuz3160 vuz3170)) (Neg (Succ vuz31900) * Pos vuz3170))",fontsize=16,color="black",shape="box"];7455 -> 7596[label="",style="solid", color="black", weight=3];
67.83/34.95	7456[label="primQuotInt (primMinusNat (primMulNat Zero Zero) (primMulNat vuz3160 vuz3170)) (reduce2D (primMinusNat (primMulNat Zero Zero) (primMulNat vuz3160 vuz3170)) (Neg Zero * Pos vuz3170))",fontsize=16,color="black",shape="box"];7456 -> 7597[label="",style="solid", color="black", weight=3];
67.83/34.95	7457 -> 7598[label="",style="dashed", color="red", weight=0];
67.83/34.95	7457[label="primQuotInt (Pos (primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190))) (gcd3 (Pos (primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190))) (Pos vuz3190 * Neg vuz3170))",fontsize=16,color="magenta"];7457 -> 7599[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7457 -> 7600[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7458[label="primQuotInt (primMinusNat (primMulNat (Succ vuz31600) (Succ vuz31700)) (primMulNat vuz3180 vuz3190)) (reduce2D (primMinusNat (primMulNat (Succ vuz31600) (Succ vuz31700)) (primMulNat vuz3180 vuz3190)) (Neg vuz3190 * Neg (Succ vuz31700)))",fontsize=16,color="black",shape="box"];7458 -> 7605[label="",style="solid", color="black", weight=3];
67.83/34.95	7459[label="primQuotInt (primMinusNat (primMulNat (Succ vuz31600) Zero) (primMulNat vuz3180 vuz3190)) (reduce2D (primMinusNat (primMulNat (Succ vuz31600) Zero) (primMulNat vuz3180 vuz3190)) (Neg vuz3190 * Neg Zero))",fontsize=16,color="black",shape="box"];7459 -> 7606[label="",style="solid", color="black", weight=3];
67.83/34.95	7460[label="primQuotInt (primMinusNat (primMulNat Zero (Succ vuz31700)) (primMulNat vuz3180 vuz3190)) (reduce2D (primMinusNat (primMulNat Zero (Succ vuz31700)) (primMulNat vuz3180 vuz3190)) (Neg vuz3190 * Neg (Succ vuz31700)))",fontsize=16,color="black",shape="box"];7460 -> 7607[label="",style="solid", color="black", weight=3];
67.83/34.95	7461[label="primQuotInt (primMinusNat (primMulNat Zero Zero) (primMulNat vuz3180 vuz3190)) (reduce2D (primMinusNat (primMulNat Zero Zero) (primMulNat vuz3180 vuz3190)) (Neg vuz3190 * Neg Zero))",fontsize=16,color="black",shape="box"];7461 -> 7608[label="",style="solid", color="black", weight=3];
67.83/34.95	7462[label="primQuotInt (primMinusNat (primMulNat (Succ vuz31600) (Succ vuz31700)) (primMulNat vuz3180 vuz3190)) (reduce2D (primMinusNat (primMulNat (Succ vuz31600) (Succ vuz31700)) (primMulNat vuz3180 vuz3190)) (Pos vuz3190 * Neg (Succ vuz31700)))",fontsize=16,color="black",shape="box"];7462 -> 7609[label="",style="solid", color="black", weight=3];
67.83/34.95	7463[label="primQuotInt (primMinusNat (primMulNat (Succ vuz31600) Zero) (primMulNat vuz3180 vuz3190)) (reduce2D (primMinusNat (primMulNat (Succ vuz31600) Zero) (primMulNat vuz3180 vuz3190)) (Pos vuz3190 * Neg Zero))",fontsize=16,color="black",shape="box"];7463 -> 7610[label="",style="solid", color="black", weight=3];
67.83/34.95	7464[label="primQuotInt (primMinusNat (primMulNat Zero (Succ vuz31700)) (primMulNat vuz3180 vuz3190)) (reduce2D (primMinusNat (primMulNat Zero (Succ vuz31700)) (primMulNat vuz3180 vuz3190)) (Pos vuz3190 * Neg (Succ vuz31700)))",fontsize=16,color="black",shape="box"];7464 -> 7611[label="",style="solid", color="black", weight=3];
67.83/34.95	7465[label="primQuotInt (primMinusNat (primMulNat Zero Zero) (primMulNat vuz3180 vuz3190)) (reduce2D (primMinusNat (primMulNat Zero Zero) (primMulNat vuz3180 vuz3190)) (Pos vuz3190 * Neg Zero))",fontsize=16,color="black",shape="box"];7465 -> 7612[label="",style="solid", color="black", weight=3];
67.83/34.95	7466 -> 7613[label="",style="dashed", color="red", weight=0];
67.83/34.95	7466[label="primQuotInt (Pos (primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190))) (gcd3 (Pos (primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190))) (Neg vuz3190 * Neg vuz3170))",fontsize=16,color="magenta"];7466 -> 7614[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7466 -> 7615[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7467 -> 7617[label="",style="dashed", color="red", weight=0];
67.83/34.95	7467[label="primQuotInt (Pos (primMulNat vuz3190 vuz3170)) (gcd2 (primEqInt (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (vuz318 * Pos vuz3190)) (fromInt (Pos Zero))) (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (vuz318 * Pos vuz3190)) (Pos (primMulNat vuz3190 vuz3170)))",fontsize=16,color="magenta"];7467 -> 7618[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7467 -> 7619[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7467 -> 7620[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7467 -> 7621[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7468 -> 7624[label="",style="dashed", color="red", weight=0];
67.83/34.95	7468[label="primQuotInt (Pos (primMulNat vuz3190 vuz3170)) (gcd2 (primEqInt (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (vuz318 * Pos vuz3190)) (fromInt (Pos Zero))) (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (vuz318 * Pos vuz3190)) (Pos (primMulNat vuz3190 vuz3170)))",fontsize=16,color="magenta"];7468 -> 7625[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7468 -> 7626[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7468 -> 7627[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7468 -> 7628[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7469 -> 7629[label="",style="dashed", color="red", weight=0];
67.83/34.95	7469[label="primQuotInt (Neg (primMulNat vuz3190 vuz3170)) (gcd2 (primEqInt (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (vuz318 * Pos vuz3190)) (fromInt (Pos Zero))) (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (vuz318 * Pos vuz3190)) (Neg (primMulNat vuz3190 vuz3170)))",fontsize=16,color="magenta"];7469 -> 7630[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7469 -> 7631[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7469 -> 7632[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7469 -> 7633[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7470 -> 7634[label="",style="dashed", color="red", weight=0];
67.83/34.95	7470[label="primQuotInt (Neg (primMulNat vuz3190 vuz3170)) (gcd2 (primEqInt (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (vuz318 * Pos vuz3190)) (fromInt (Pos Zero))) (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (vuz318 * Pos vuz3190)) (Neg (primMulNat vuz3190 vuz3170)))",fontsize=16,color="magenta"];7470 -> 7635[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7470 -> 7636[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7470 -> 7637[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7470 -> 7638[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7471 -> 7639[label="",style="dashed", color="red", weight=0];
67.83/34.95	7471[label="primQuotInt (Neg (primMulNat vuz3190 vuz3170)) (gcd2 (primEqInt (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (vuz318 * Neg vuz3190)) (fromInt (Pos Zero))) (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (vuz318 * Neg vuz3190)) (Neg (primMulNat vuz3190 vuz3170)))",fontsize=16,color="magenta"];7471 -> 7640[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7471 -> 7641[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7471 -> 7642[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7471 -> 7643[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7472 -> 7644[label="",style="dashed", color="red", weight=0];
67.83/34.95	7472[label="primQuotInt (Neg (primMulNat vuz3190 vuz3170)) (gcd2 (primEqInt (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (vuz318 * Neg vuz3190)) (fromInt (Pos Zero))) (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (vuz318 * Neg vuz3190)) (Neg (primMulNat vuz3190 vuz3170)))",fontsize=16,color="magenta"];7472 -> 7645[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7472 -> 7646[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7472 -> 7647[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7472 -> 7648[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7473 -> 7649[label="",style="dashed", color="red", weight=0];
67.83/34.95	7473[label="primQuotInt (Pos (primMulNat vuz3190 vuz3170)) (gcd2 (primEqInt (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (vuz318 * Neg vuz3190)) (fromInt (Pos Zero))) (primPlusInt (Neg (primMulNat vuz3160 vuz3170)) (vuz318 * Neg vuz3190)) (Pos (primMulNat vuz3190 vuz3170)))",fontsize=16,color="magenta"];7473 -> 7650[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7473 -> 7651[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7473 -> 7652[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7473 -> 7653[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7474 -> 7654[label="",style="dashed", color="red", weight=0];
67.83/34.95	7474[label="primQuotInt (Pos (primMulNat vuz3190 vuz3170)) (gcd2 (primEqInt (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (vuz318 * Neg vuz3190)) (fromInt (Pos Zero))) (primPlusInt (Pos (primMulNat vuz3160 vuz3170)) (vuz318 * Neg vuz3190)) (Pos (primMulNat vuz3190 vuz3170)))",fontsize=16,color="magenta"];7474 -> 7655[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7474 -> 7656[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7474 -> 7657[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7474 -> 7658[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7622[label="vuz33500",fontsize=16,color="green",shape="box"];7623[label="vuz3071000",fontsize=16,color="green",shape="box"];7668 -> 7571[label="",style="dashed", color="red", weight=0];
67.83/34.95	7668[label="primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190)",fontsize=16,color="magenta"];7668 -> 7672[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7668 -> 7673[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7669 -> 7571[label="",style="dashed", color="red", weight=0];
67.83/34.95	7669[label="primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190)",fontsize=16,color="magenta"];7669 -> 7674[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7669 -> 7675[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7667[label="primQuotInt (Pos vuz398) (gcd3 (Pos vuz399) (Pos vuz3190 * Pos vuz3170))",fontsize=16,color="black",shape="triangle"];7667 -> 7676[label="",style="solid", color="black", weight=3];
67.83/34.95	7534 -> 7677[label="",style="dashed", color="red", weight=0];
67.83/34.95	7534[label="primQuotInt (primMinusNat (primPlusNat (primMulNat vuz31600 (Succ vuz31700)) (Succ vuz31700)) (primMulNat vuz3180 vuz3190)) (reduce2D (primMinusNat (primPlusNat (primMulNat vuz31600 (Succ vuz31700)) (Succ vuz31700)) (primMulNat vuz3180 vuz3190)) (Neg vuz3190 * Pos (Succ vuz31700)))",fontsize=16,color="magenta"];7534 -> 7678[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7534 -> 7679[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7534 -> 7680[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7534 -> 7681[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7535 -> 7686[label="",style="dashed", color="red", weight=0];
67.83/34.95	7535[label="primQuotInt (primMinusNat Zero (primMulNat vuz3180 vuz3190)) (reduce2D (primMinusNat Zero (primMulNat vuz3180 vuz3190)) (Neg vuz3190 * Pos Zero))",fontsize=16,color="magenta"];7535 -> 7687[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7535 -> 7688[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7536 -> 7677[label="",style="dashed", color="red", weight=0];
67.83/34.95	7536[label="primQuotInt (primMinusNat Zero (primMulNat vuz3180 vuz3190)) (reduce2D (primMinusNat Zero (primMulNat vuz3180 vuz3190)) (Neg vuz3190 * Pos (Succ vuz31700)))",fontsize=16,color="magenta"];7536 -> 7682[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7536 -> 7683[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7536 -> 7684[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7536 -> 7685[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7537 -> 7686[label="",style="dashed", color="red", weight=0];
67.83/34.95	7537[label="primQuotInt (primMinusNat Zero (primMulNat vuz3180 vuz3190)) (reduce2D (primMinusNat Zero (primMulNat vuz3180 vuz3190)) (Neg vuz3190 * Pos Zero))",fontsize=16,color="magenta"];7537 -> 7689[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7537 -> 7690[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7538 -> 7691[label="",style="dashed", color="red", weight=0];
67.83/34.95	7538[label="primQuotInt (primMinusNat (primPlusNat (primMulNat vuz31600 (Succ vuz31700)) (Succ vuz31700)) (primMulNat vuz3180 vuz3190)) (reduce2D (primMinusNat (primPlusNat (primMulNat vuz31600 (Succ vuz31700)) (Succ vuz31700)) (primMulNat vuz3180 vuz3190)) (Pos vuz3190 * Pos (Succ vuz31700)))",fontsize=16,color="magenta"];7538 -> 7692[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7538 -> 7693[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7538 -> 7694[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7538 -> 7695[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7539 -> 7700[label="",style="dashed", color="red", weight=0];
67.83/34.95	7539[label="primQuotInt (primMinusNat Zero (primMulNat vuz3180 vuz3190)) (reduce2D (primMinusNat Zero (primMulNat vuz3180 vuz3190)) (Pos vuz3190 * Pos Zero))",fontsize=16,color="magenta"];7539 -> 7701[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7539 -> 7702[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7540 -> 7691[label="",style="dashed", color="red", weight=0];
67.83/34.95	7540[label="primQuotInt (primMinusNat Zero (primMulNat vuz3180 vuz3190)) (reduce2D (primMinusNat Zero (primMulNat vuz3180 vuz3190)) (Pos vuz3190 * Pos (Succ vuz31700)))",fontsize=16,color="magenta"];7540 -> 7696[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7540 -> 7697[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7540 -> 7698[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7540 -> 7699[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7541 -> 7700[label="",style="dashed", color="red", weight=0];
67.83/34.95	7541[label="primQuotInt (primMinusNat Zero (primMulNat vuz3180 vuz3190)) (reduce2D (primMinusNat Zero (primMulNat vuz3180 vuz3190)) (Pos vuz3190 * Pos Zero))",fontsize=16,color="magenta"];7541 -> 7703[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7541 -> 7704[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7714 -> 7571[label="",style="dashed", color="red", weight=0];
67.83/34.95	7714[label="primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190)",fontsize=16,color="magenta"];7714 -> 7718[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7714 -> 7719[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7715 -> 7571[label="",style="dashed", color="red", weight=0];
67.83/34.95	7715[label="primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190)",fontsize=16,color="magenta"];7715 -> 7720[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7715 -> 7721[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7713[label="primQuotInt (Pos vuz416) (gcd3 (Pos vuz417) (Neg vuz3190 * Pos vuz3170))",fontsize=16,color="black",shape="triangle"];7713 -> 7722[label="",style="solid", color="black", weight=3];
67.83/34.95	7555 -> 7723[label="",style="dashed", color="red", weight=0];
67.83/34.95	7555[label="primQuotInt (primMinusNat (primPlusNat (primMulNat vuz31800 (Succ vuz31900)) (Succ vuz31900)) (primMulNat vuz3160 vuz3170)) (reduce2D (primMinusNat (primPlusNat (primMulNat vuz31800 (Succ vuz31900)) (Succ vuz31900)) (primMulNat vuz3160 vuz3170)) (Pos (Succ vuz31900) * Neg vuz3170))",fontsize=16,color="magenta"];7555 -> 7724[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7555 -> 7725[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7555 -> 7726[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7555 -> 7727[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7556 -> 7732[label="",style="dashed", color="red", weight=0];
67.83/34.95	7556[label="primQuotInt (primMinusNat Zero (primMulNat vuz3160 vuz3170)) (reduce2D (primMinusNat Zero (primMulNat vuz3160 vuz3170)) (Pos Zero * Neg vuz3170))",fontsize=16,color="magenta"];7556 -> 7733[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7556 -> 7734[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7557 -> 7723[label="",style="dashed", color="red", weight=0];
67.83/34.95	7557[label="primQuotInt (primMinusNat Zero (primMulNat vuz3160 vuz3170)) (reduce2D (primMinusNat Zero (primMulNat vuz3160 vuz3170)) (Pos (Succ vuz31900) * Neg vuz3170))",fontsize=16,color="magenta"];7557 -> 7728[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7557 -> 7729[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7557 -> 7730[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7557 -> 7731[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7558 -> 7732[label="",style="dashed", color="red", weight=0];
67.83/34.95	7558[label="primQuotInt (primMinusNat Zero (primMulNat vuz3160 vuz3170)) (reduce2D (primMinusNat Zero (primMulNat vuz3160 vuz3170)) (Pos Zero * Neg vuz3170))",fontsize=16,color="magenta"];7558 -> 7735[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7558 -> 7736[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7746 -> 7571[label="",style="dashed", color="red", weight=0];
67.83/34.95	7746[label="primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190)",fontsize=16,color="magenta"];7746 -> 7750[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7746 -> 7751[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7747 -> 7571[label="",style="dashed", color="red", weight=0];
67.83/34.95	7747[label="primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190)",fontsize=16,color="magenta"];7747 -> 7752[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7747 -> 7753[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7745[label="primQuotInt (Neg vuz426) (gcd3 (Neg vuz427) (Neg vuz3190 * Neg vuz3170))",fontsize=16,color="black",shape="triangle"];7745 -> 7754[label="",style="solid", color="black", weight=3];
67.83/34.95	7764 -> 7571[label="",style="dashed", color="red", weight=0];
67.83/34.95	7764[label="primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190)",fontsize=16,color="magenta"];7764 -> 7768[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7764 -> 7769[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7765 -> 7571[label="",style="dashed", color="red", weight=0];
67.83/34.95	7765[label="primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190)",fontsize=16,color="magenta"];7765 -> 7770[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7765 -> 7771[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7763[label="primQuotInt (Neg vuz428) (gcd3 (Neg vuz429) (Pos vuz3190 * Neg vuz3170))",fontsize=16,color="black",shape="triangle"];7763 -> 7772[label="",style="solid", color="black", weight=3];
67.83/34.95	7572 -> 7773[label="",style="dashed", color="red", weight=0];
67.83/34.95	7572[label="primQuotInt (primMinusNat (primPlusNat (primMulNat vuz31800 (Succ vuz31900)) (Succ vuz31900)) (primMulNat vuz3160 vuz3170)) (reduce2D (primMinusNat (primPlusNat (primMulNat vuz31800 (Succ vuz31900)) (Succ vuz31900)) (primMulNat vuz3160 vuz3170)) (Neg (Succ vuz31900) * Neg vuz3170))",fontsize=16,color="magenta"];7572 -> 7774[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7572 -> 7775[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7572 -> 7776[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7572 -> 7777[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7573 -> 7782[label="",style="dashed", color="red", weight=0];
67.83/34.95	7573[label="primQuotInt (primMinusNat Zero (primMulNat vuz3160 vuz3170)) (reduce2D (primMinusNat Zero (primMulNat vuz3160 vuz3170)) (Neg Zero * Neg vuz3170))",fontsize=16,color="magenta"];7573 -> 7783[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7573 -> 7784[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7574 -> 7773[label="",style="dashed", color="red", weight=0];
67.83/34.95	7574[label="primQuotInt (primMinusNat Zero (primMulNat vuz3160 vuz3170)) (reduce2D (primMinusNat Zero (primMulNat vuz3160 vuz3170)) (Neg (Succ vuz31900) * Neg vuz3170))",fontsize=16,color="magenta"];7574 -> 7778[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7574 -> 7779[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7574 -> 7780[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7574 -> 7781[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7575 -> 7782[label="",style="dashed", color="red", weight=0];
67.83/34.95	7575[label="primQuotInt (primMinusNat Zero (primMulNat vuz3160 vuz3170)) (reduce2D (primMinusNat Zero (primMulNat vuz3160 vuz3170)) (Neg Zero * Neg vuz3170))",fontsize=16,color="magenta"];7575 -> 7785[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7575 -> 7786[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7576 -> 7787[label="",style="dashed", color="red", weight=0];
67.83/34.95	7576[label="primQuotInt (primMinusNat (primPlusNat (primMulNat vuz31800 (Succ vuz31900)) (Succ vuz31900)) (primMulNat vuz3160 vuz3170)) (reduce2D (primMinusNat (primPlusNat (primMulNat vuz31800 (Succ vuz31900)) (Succ vuz31900)) (primMulNat vuz3160 vuz3170)) (Pos (Succ vuz31900) * Pos vuz3170))",fontsize=16,color="magenta"];7576 -> 7788[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7576 -> 7789[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7576 -> 7790[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7576 -> 7791[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7577 -> 7796[label="",style="dashed", color="red", weight=0];
67.83/34.95	7577[label="primQuotInt (primMinusNat Zero (primMulNat vuz3160 vuz3170)) (reduce2D (primMinusNat Zero (primMulNat vuz3160 vuz3170)) (Pos Zero * Pos vuz3170))",fontsize=16,color="magenta"];7577 -> 7797[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7577 -> 7798[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7578 -> 7787[label="",style="dashed", color="red", weight=0];
67.83/34.95	7578[label="primQuotInt (primMinusNat Zero (primMulNat vuz3160 vuz3170)) (reduce2D (primMinusNat Zero (primMulNat vuz3160 vuz3170)) (Pos (Succ vuz31900) * Pos vuz3170))",fontsize=16,color="magenta"];7578 -> 7792[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7578 -> 7793[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7578 -> 7794[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7578 -> 7795[label="",style="dashed", color="magenta", weight=3];
67.83/34.95	7579 -> 7796[label="",style="dashed", color="red", weight=0];
67.83/34.96	7579[label="primQuotInt (primMinusNat Zero (primMulNat vuz3160 vuz3170)) (reduce2D (primMinusNat Zero (primMulNat vuz3160 vuz3170)) (Pos Zero * Pos vuz3170))",fontsize=16,color="magenta"];7579 -> 7799[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7579 -> 7800[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7810 -> 7571[label="",style="dashed", color="red", weight=0];
67.83/34.96	7810[label="primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190)",fontsize=16,color="magenta"];7810 -> 7814[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7810 -> 7815[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7811 -> 7571[label="",style="dashed", color="red", weight=0];
67.83/34.96	7811[label="primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190)",fontsize=16,color="magenta"];7811 -> 7816[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7811 -> 7817[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7809[label="primQuotInt (Neg vuz446) (gcd3 (Neg vuz447) (Neg vuz3190 * Pos vuz3170))",fontsize=16,color="black",shape="triangle"];7809 -> 7818[label="",style="solid", color="black", weight=3];
67.83/34.96	7588 -> 7571[label="",style="dashed", color="red", weight=0];
67.83/34.96	7588[label="primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190)",fontsize=16,color="magenta"];7588 -> 7819[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7588 -> 7820[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7589 -> 7571[label="",style="dashed", color="red", weight=0];
67.83/34.96	7589[label="primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190)",fontsize=16,color="magenta"];7589 -> 7821[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7589 -> 7822[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7587[label="primQuotInt (Neg vuz348) (gcd3 (Neg vuz349) (Pos vuz3190 * Pos vuz3170))",fontsize=16,color="black",shape="triangle"];7587 -> 7823[label="",style="solid", color="black", weight=3];
67.83/34.96	7594 -> 7824[label="",style="dashed", color="red", weight=0];
67.83/34.96	7594[label="primQuotInt (primMinusNat (primPlusNat (primMulNat vuz31800 (Succ vuz31900)) (Succ vuz31900)) (primMulNat vuz3160 vuz3170)) (reduce2D (primMinusNat (primPlusNat (primMulNat vuz31800 (Succ vuz31900)) (Succ vuz31900)) (primMulNat vuz3160 vuz3170)) (Neg (Succ vuz31900) * Pos vuz3170))",fontsize=16,color="magenta"];7594 -> 7825[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7594 -> 7826[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7594 -> 7827[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7594 -> 7828[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7595 -> 7833[label="",style="dashed", color="red", weight=0];
67.83/34.96	7595[label="primQuotInt (primMinusNat Zero (primMulNat vuz3160 vuz3170)) (reduce2D (primMinusNat Zero (primMulNat vuz3160 vuz3170)) (Neg Zero * Pos vuz3170))",fontsize=16,color="magenta"];7595 -> 7834[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7595 -> 7835[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7596 -> 7824[label="",style="dashed", color="red", weight=0];
67.83/34.96	7596[label="primQuotInt (primMinusNat Zero (primMulNat vuz3160 vuz3170)) (reduce2D (primMinusNat Zero (primMulNat vuz3160 vuz3170)) (Neg (Succ vuz31900) * Pos vuz3170))",fontsize=16,color="magenta"];7596 -> 7829[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7596 -> 7830[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7596 -> 7831[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7596 -> 7832[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7597 -> 7833[label="",style="dashed", color="red", weight=0];
67.83/34.96	7597[label="primQuotInt (primMinusNat Zero (primMulNat vuz3160 vuz3170)) (reduce2D (primMinusNat Zero (primMulNat vuz3160 vuz3170)) (Neg Zero * Pos vuz3170))",fontsize=16,color="magenta"];7597 -> 7836[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7597 -> 7837[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7599 -> 7571[label="",style="dashed", color="red", weight=0];
67.83/34.96	7599[label="primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190)",fontsize=16,color="magenta"];7599 -> 7838[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7599 -> 7839[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7600 -> 7571[label="",style="dashed", color="red", weight=0];
67.83/34.96	7600[label="primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190)",fontsize=16,color="magenta"];7600 -> 7840[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7600 -> 7841[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7598[label="primQuotInt (Pos vuz354) (gcd3 (Pos vuz355) (Pos vuz3190 * Neg vuz3170))",fontsize=16,color="black",shape="triangle"];7598 -> 7842[label="",style="solid", color="black", weight=3];
67.83/34.96	7605 -> 7843[label="",style="dashed", color="red", weight=0];
67.83/34.96	7605[label="primQuotInt (primMinusNat (primPlusNat (primMulNat vuz31600 (Succ vuz31700)) (Succ vuz31700)) (primMulNat vuz3180 vuz3190)) (reduce2D (primMinusNat (primPlusNat (primMulNat vuz31600 (Succ vuz31700)) (Succ vuz31700)) (primMulNat vuz3180 vuz3190)) (Neg vuz3190 * Neg (Succ vuz31700)))",fontsize=16,color="magenta"];7605 -> 7844[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7605 -> 7845[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7605 -> 7846[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7605 -> 7847[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7606 -> 7852[label="",style="dashed", color="red", weight=0];
67.83/34.96	7606[label="primQuotInt (primMinusNat Zero (primMulNat vuz3180 vuz3190)) (reduce2D (primMinusNat Zero (primMulNat vuz3180 vuz3190)) (Neg vuz3190 * Neg Zero))",fontsize=16,color="magenta"];7606 -> 7853[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7606 -> 7854[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7607 -> 7843[label="",style="dashed", color="red", weight=0];
67.83/34.96	7607[label="primQuotInt (primMinusNat Zero (primMulNat vuz3180 vuz3190)) (reduce2D (primMinusNat Zero (primMulNat vuz3180 vuz3190)) (Neg vuz3190 * Neg (Succ vuz31700)))",fontsize=16,color="magenta"];7607 -> 7848[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7607 -> 7849[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7607 -> 7850[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7607 -> 7851[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7608 -> 7852[label="",style="dashed", color="red", weight=0];
67.83/34.96	7608[label="primQuotInt (primMinusNat Zero (primMulNat vuz3180 vuz3190)) (reduce2D (primMinusNat Zero (primMulNat vuz3180 vuz3190)) (Neg vuz3190 * Neg Zero))",fontsize=16,color="magenta"];7608 -> 7855[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7608 -> 7856[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7609 -> 7857[label="",style="dashed", color="red", weight=0];
67.83/34.96	7609[label="primQuotInt (primMinusNat (primPlusNat (primMulNat vuz31600 (Succ vuz31700)) (Succ vuz31700)) (primMulNat vuz3180 vuz3190)) (reduce2D (primMinusNat (primPlusNat (primMulNat vuz31600 (Succ vuz31700)) (Succ vuz31700)) (primMulNat vuz3180 vuz3190)) (Pos vuz3190 * Neg (Succ vuz31700)))",fontsize=16,color="magenta"];7609 -> 7858[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7609 -> 7859[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7609 -> 7860[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7609 -> 7861[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7610 -> 7866[label="",style="dashed", color="red", weight=0];
67.83/34.96	7610[label="primQuotInt (primMinusNat Zero (primMulNat vuz3180 vuz3190)) (reduce2D (primMinusNat Zero (primMulNat vuz3180 vuz3190)) (Pos vuz3190 * Neg Zero))",fontsize=16,color="magenta"];7610 -> 7867[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7610 -> 7868[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7611 -> 7857[label="",style="dashed", color="red", weight=0];
67.83/34.96	7611[label="primQuotInt (primMinusNat Zero (primMulNat vuz3180 vuz3190)) (reduce2D (primMinusNat Zero (primMulNat vuz3180 vuz3190)) (Pos vuz3190 * Neg (Succ vuz31700)))",fontsize=16,color="magenta"];7611 -> 7862[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7611 -> 7863[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7611 -> 7864[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7611 -> 7865[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7612 -> 7866[label="",style="dashed", color="red", weight=0];
67.83/34.96	7612[label="primQuotInt (primMinusNat Zero (primMulNat vuz3180 vuz3190)) (reduce2D (primMinusNat Zero (primMulNat vuz3180 vuz3190)) (Pos vuz3190 * Neg Zero))",fontsize=16,color="magenta"];7612 -> 7869[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7612 -> 7870[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7614 -> 7571[label="",style="dashed", color="red", weight=0];
67.83/34.96	7614[label="primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190)",fontsize=16,color="magenta"];7614 -> 7871[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7614 -> 7872[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7615 -> 7571[label="",style="dashed", color="red", weight=0];
67.83/34.96	7615[label="primPlusNat (primMulNat vuz3160 vuz3170) (primMulNat vuz3180 vuz3190)",fontsize=16,color="magenta"];7615 -> 7873[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7615 -> 7874[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7613[label="primQuotInt (Pos vuz360) (gcd3 (Pos vuz361) (Neg vuz3190 * Neg vuz3170))",fontsize=16,color="black",shape="triangle"];7613 -> 7875[label="",style="solid", color="black", weight=3];
67.83/34.96	7618 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.96	7618[label="primMulNat vuz3190 vuz3170",fontsize=16,color="magenta"];7618 -> 7876[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7618 -> 7877[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7619 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.96	7619[label="primMulNat vuz3160 vuz3170",fontsize=16,color="magenta"];7619 -> 7878[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7619 -> 7879[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7620 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.96	7620[label="primMulNat vuz3160 vuz3170",fontsize=16,color="magenta"];7620 -> 7880[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7620 -> 7881[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7621 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.96	7621[label="primMulNat vuz3190 vuz3170",fontsize=16,color="magenta"];7621 -> 7882[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7621 -> 7883[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7617[label="primQuotInt (Pos vuz366) (gcd2 (primEqInt (primPlusInt (Pos vuz369) (vuz318 * Pos vuz3190)) (fromInt (Pos Zero))) (primPlusInt (Pos vuz368) (vuz318 * Pos vuz3190)) (Pos vuz367))",fontsize=16,color="black",shape="triangle"];7617 -> 7884[label="",style="solid", color="black", weight=3];
67.83/34.96	7625 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.96	7625[label="primMulNat vuz3160 vuz3170",fontsize=16,color="magenta"];7625 -> 7885[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7625 -> 7886[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7626 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.96	7626[label="primMulNat vuz3160 vuz3170",fontsize=16,color="magenta"];7626 -> 7887[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7626 -> 7888[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7627 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.96	7627[label="primMulNat vuz3190 vuz3170",fontsize=16,color="magenta"];7627 -> 7889[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7627 -> 7890[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7628 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.96	7628[label="primMulNat vuz3190 vuz3170",fontsize=16,color="magenta"];7628 -> 7891[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7628 -> 7892[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7624[label="primQuotInt (Pos vuz370) (gcd2 (primEqInt (primPlusInt (Neg vuz373) (vuz318 * Pos vuz3190)) (fromInt (Pos Zero))) (primPlusInt (Neg vuz372) (vuz318 * Pos vuz3190)) (Pos vuz371))",fontsize=16,color="black",shape="triangle"];7624 -> 7893[label="",style="solid", color="black", weight=3];
67.83/34.96	7630 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.96	7630[label="primMulNat vuz3190 vuz3170",fontsize=16,color="magenta"];7630 -> 7894[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7630 -> 7895[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7631 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.96	7631[label="primMulNat vuz3160 vuz3170",fontsize=16,color="magenta"];7631 -> 7896[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7631 -> 7897[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7632 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.96	7632[label="primMulNat vuz3190 vuz3170",fontsize=16,color="magenta"];7632 -> 7898[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7632 -> 7899[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7633 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.96	7633[label="primMulNat vuz3160 vuz3170",fontsize=16,color="magenta"];7633 -> 7900[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7633 -> 7901[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7629[label="primQuotInt (Neg vuz374) (gcd2 (primEqInt (primPlusInt (Neg vuz377) (vuz318 * Pos vuz3190)) (fromInt (Pos Zero))) (primPlusInt (Neg vuz376) (vuz318 * Pos vuz3190)) (Neg vuz375))",fontsize=16,color="black",shape="triangle"];7629 -> 7902[label="",style="solid", color="black", weight=3];
67.83/34.96	7635 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.96	7635[label="primMulNat vuz3190 vuz3170",fontsize=16,color="magenta"];7635 -> 7903[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7635 -> 7904[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7636 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.96	7636[label="primMulNat vuz3160 vuz3170",fontsize=16,color="magenta"];7636 -> 7905[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7636 -> 7906[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7637 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.96	7637[label="primMulNat vuz3160 vuz3170",fontsize=16,color="magenta"];7637 -> 7907[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7637 -> 7908[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7638 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.96	7638[label="primMulNat vuz3190 vuz3170",fontsize=16,color="magenta"];7638 -> 7909[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7638 -> 7910[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7634[label="primQuotInt (Neg vuz378) (gcd2 (primEqInt (primPlusInt (Pos vuz381) (vuz318 * Pos vuz3190)) (fromInt (Pos Zero))) (primPlusInt (Pos vuz380) (vuz318 * Pos vuz3190)) (Neg vuz379))",fontsize=16,color="black",shape="triangle"];7634 -> 7911[label="",style="solid", color="black", weight=3];
67.83/34.96	7640 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.96	7640[label="primMulNat vuz3190 vuz3170",fontsize=16,color="magenta"];7640 -> 7912[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7640 -> 7913[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7641 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.96	7641[label="primMulNat vuz3190 vuz3170",fontsize=16,color="magenta"];7641 -> 7914[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7641 -> 7915[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7642 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.96	7642[label="primMulNat vuz3160 vuz3170",fontsize=16,color="magenta"];7642 -> 7916[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7642 -> 7917[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7643 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.96	7643[label="primMulNat vuz3160 vuz3170",fontsize=16,color="magenta"];7643 -> 7918[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7643 -> 7919[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7639[label="primQuotInt (Neg vuz382) (gcd2 (primEqInt (primPlusInt (Pos vuz385) (vuz318 * Neg vuz3190)) (fromInt (Pos Zero))) (primPlusInt (Pos vuz384) (vuz318 * Neg vuz3190)) (Neg vuz383))",fontsize=16,color="black",shape="triangle"];7639 -> 7920[label="",style="solid", color="black", weight=3];
67.83/34.96	7645 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.96	7645[label="primMulNat vuz3190 vuz3170",fontsize=16,color="magenta"];7645 -> 7921[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7645 -> 7922[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7646 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.96	7646[label="primMulNat vuz3160 vuz3170",fontsize=16,color="magenta"];7646 -> 7923[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7646 -> 7924[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7647 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.96	7647[label="primMulNat vuz3160 vuz3170",fontsize=16,color="magenta"];7647 -> 7925[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7647 -> 7926[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7648 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.96	7648[label="primMulNat vuz3190 vuz3170",fontsize=16,color="magenta"];7648 -> 7927[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7648 -> 7928[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7644[label="primQuotInt (Neg vuz386) (gcd2 (primEqInt (primPlusInt (Neg vuz389) (vuz318 * Neg vuz3190)) (fromInt (Pos Zero))) (primPlusInt (Neg vuz388) (vuz318 * Neg vuz3190)) (Neg vuz387))",fontsize=16,color="black",shape="triangle"];7644 -> 7929[label="",style="solid", color="black", weight=3];
67.83/34.96	7650 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.96	7650[label="primMulNat vuz3190 vuz3170",fontsize=16,color="magenta"];7650 -> 7930[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7650 -> 7931[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7651 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.96	7651[label="primMulNat vuz3160 vuz3170",fontsize=16,color="magenta"];7651 -> 7932[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7651 -> 7933[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7652 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.96	7652[label="primMulNat vuz3160 vuz3170",fontsize=16,color="magenta"];7652 -> 7934[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7652 -> 7935[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7653 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.96	7653[label="primMulNat vuz3190 vuz3170",fontsize=16,color="magenta"];7653 -> 7936[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7653 -> 7937[label="",style="dashed", color="magenta", weight=3];
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67.83/34.96	7679 -> 7571[label="",style="dashed", color="red", weight=0];
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67.83/34.96	7680 -> 7571[label="",style="dashed", color="red", weight=0];
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67.83/34.96	7680 -> 7962[label="",style="dashed", color="magenta", weight=3];
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67.83/34.96	7682 -> 7480[label="",style="dashed", color="red", weight=0];
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67.83/34.96	7685[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];7685 -> 7975[label="",style="dashed", color="magenta", weight=3];
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67.83/34.96	7692 -> 7571[label="",style="dashed", color="red", weight=0];
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67.83/34.96	7692 -> 7982[label="",style="dashed", color="magenta", weight=3];
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67.83/34.96	7694 -> 7571[label="",style="dashed", color="red", weight=0];
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67.83/34.96	7694 -> 7986[label="",style="dashed", color="magenta", weight=3];
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67.83/34.96	10956[label="vuz409/Zero",fontsize=10,color="white",style="solid",shape="box"];7691 -> 10956[label="",style="solid", color="burlywood", weight=9];
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67.83/34.96	7701 -> 7480[label="",style="dashed", color="red", weight=0];
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67.83/34.96	7702 -> 7480[label="",style="dashed", color="red", weight=0];
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67.83/34.96	10957 -> 7995[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	10958[label="vuz414/Zero",fontsize=10,color="white",style="solid",shape="box"];7700 -> 10958[label="",style="solid", color="burlywood", weight=9];
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67.83/34.96	7703 -> 7480[label="",style="dashed", color="red", weight=0];
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67.83/34.96	7719[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];7719 -> 8007[label="",style="dashed", color="magenta", weight=3];
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67.83/34.96	7722 -> 8254[label="",style="dashed", color="red", weight=0];
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67.83/34.96	7725 -> 7571[label="",style="dashed", color="red", weight=0];
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67.83/34.96	7725 -> 8017[label="",style="dashed", color="magenta", weight=3];
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67.83/34.96	7726[label="primMulNat vuz3160 vuz3170",fontsize=16,color="magenta"];7726 -> 8018[label="",style="dashed", color="magenta", weight=3];
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67.83/34.96	7727 -> 7571[label="",style="dashed", color="red", weight=0];
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67.83/34.96	7734 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.96	7734[label="primMulNat vuz3160 vuz3170",fontsize=16,color="magenta"];7734 -> 8026[label="",style="dashed", color="magenta", weight=3];
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67.83/34.96	10962[label="vuz424/Zero",fontsize=10,color="white",style="solid",shape="box"];7732 -> 10962[label="",style="solid", color="burlywood", weight=9];
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67.83/34.96	7728 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.96	7728[label="primMulNat vuz3160 vuz3170",fontsize=16,color="magenta"];7728 -> 8030[label="",style="dashed", color="magenta", weight=3];
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67.83/34.96	7729[label="Zero",fontsize=16,color="green",shape="box"];7730 -> 7480[label="",style="dashed", color="red", weight=0];
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67.83/34.96	7731[label="Zero",fontsize=16,color="green",shape="box"];7735 -> 7480[label="",style="dashed", color="red", weight=0];
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67.83/34.96	7844 -> 7571[label="",style="dashed", color="red", weight=0];
67.83/34.96	7844[label="primPlusNat (primMulNat vuz31600 (Succ vuz31700)) (Succ vuz31700)",fontsize=16,color="magenta"];7844 -> 8155[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7844 -> 8156[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7845 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.96	7845[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];7845 -> 8157[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7845 -> 8158[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7846 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.96	7846[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];7846 -> 8159[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7846 -> 8160[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7847 -> 7571[label="",style="dashed", color="red", weight=0];
67.83/34.96	7847[label="primPlusNat (primMulNat vuz31600 (Succ vuz31700)) (Succ vuz31700)",fontsize=16,color="magenta"];7847 -> 8161[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7847 -> 8162[label="",style="dashed", color="magenta", weight=3];
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67.83/34.96	10975 -> 8163[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	10976[label="vuz457/Zero",fontsize=10,color="white",style="solid",shape="box"];7843 -> 10976[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	10976 -> 8164[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	7853 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.96	7853[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];7853 -> 8165[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7853 -> 8166[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7854 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.96	7854[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];7854 -> 8167[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7854 -> 8168[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7852[label="primQuotInt (primMinusNat Zero vuz462) (reduce2D (primMinusNat Zero vuz463) (Neg vuz3190 * Neg Zero))",fontsize=16,color="burlywood",shape="triangle"];10977[label="vuz462/Succ vuz4620",fontsize=10,color="white",style="solid",shape="box"];7852 -> 10977[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	10977 -> 8169[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	10978[label="vuz462/Zero",fontsize=10,color="white",style="solid",shape="box"];7852 -> 10978[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	10978 -> 8170[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	7848[label="Zero",fontsize=16,color="green",shape="box"];7849 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.96	7849[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];7849 -> 8171[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7849 -> 8172[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7850 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.96	7850[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];7850 -> 8173[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7850 -> 8174[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7851[label="Zero",fontsize=16,color="green",shape="box"];7855 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.96	7855[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];7855 -> 8175[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7855 -> 8176[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7856 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.96	7856[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];7856 -> 8177[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7856 -> 8178[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7858 -> 7571[label="",style="dashed", color="red", weight=0];
67.83/34.96	7858[label="primPlusNat (primMulNat vuz31600 (Succ vuz31700)) (Succ vuz31700)",fontsize=16,color="magenta"];7858 -> 8179[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7858 -> 8180[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7859 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.96	7859[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];7859 -> 8181[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7859 -> 8182[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7860 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.96	7860[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];7860 -> 8183[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7860 -> 8184[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7861 -> 7571[label="",style="dashed", color="red", weight=0];
67.83/34.96	7861[label="primPlusNat (primMulNat vuz31600 (Succ vuz31700)) (Succ vuz31700)",fontsize=16,color="magenta"];7861 -> 8185[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7861 -> 8186[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7857[label="primQuotInt (primMinusNat vuz465 vuz464) (reduce2D (primMinusNat vuz467 vuz466) (Pos vuz3190 * Neg (Succ vuz31700)))",fontsize=16,color="burlywood",shape="triangle"];10979[label="vuz465/Succ vuz4650",fontsize=10,color="white",style="solid",shape="box"];7857 -> 10979[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	10979 -> 8187[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	10980[label="vuz465/Zero",fontsize=10,color="white",style="solid",shape="box"];7857 -> 10980[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	10980 -> 8188[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	7867 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.96	7867[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];7867 -> 8189[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7867 -> 8190[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7868 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.96	7868[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];7868 -> 8191[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7868 -> 8192[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7866[label="primQuotInt (primMinusNat Zero vuz470) (reduce2D (primMinusNat Zero vuz471) (Pos vuz3190 * Neg Zero))",fontsize=16,color="burlywood",shape="triangle"];10981[label="vuz470/Succ vuz4700",fontsize=10,color="white",style="solid",shape="box"];7866 -> 10981[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	10981 -> 8193[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	10982[label="vuz470/Zero",fontsize=10,color="white",style="solid",shape="box"];7866 -> 10982[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	10982 -> 8194[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	7862[label="Zero",fontsize=16,color="green",shape="box"];7863 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.96	7863[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];7863 -> 8195[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7863 -> 8196[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7864 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.96	7864[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];7864 -> 8197[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7864 -> 8198[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7865[label="Zero",fontsize=16,color="green",shape="box"];7869 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.96	7869[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];7869 -> 8199[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7869 -> 8200[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7870 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.96	7870[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];7870 -> 8201[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7870 -> 8202[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7871 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.96	7871[label="primMulNat vuz3160 vuz3170",fontsize=16,color="magenta"];7871 -> 8203[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7871 -> 8204[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7872 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.96	7872[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];7872 -> 8205[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7872 -> 8206[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7873 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.96	7873[label="primMulNat vuz3160 vuz3170",fontsize=16,color="magenta"];7873 -> 8207[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7873 -> 8208[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7874 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.96	7874[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];7874 -> 8209[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7874 -> 8210[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7875 -> 8350[label="",style="dashed", color="red", weight=0];
67.83/34.96	7875[label="primQuotInt (Pos vuz360) (gcd2 (Pos vuz361 == fromInt (Pos Zero)) (Pos vuz361) (Neg vuz3190 * Neg vuz3170))",fontsize=16,color="magenta"];7875 -> 8351[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7876[label="vuz3190",fontsize=16,color="green",shape="box"];7877[label="vuz3170",fontsize=16,color="green",shape="box"];7878[label="vuz3160",fontsize=16,color="green",shape="box"];7879[label="vuz3170",fontsize=16,color="green",shape="box"];7880[label="vuz3160",fontsize=16,color="green",shape="box"];7881[label="vuz3170",fontsize=16,color="green",shape="box"];7882[label="vuz3190",fontsize=16,color="green",shape="box"];7883[label="vuz3170",fontsize=16,color="green",shape="box"];7884[label="primQuotInt (Pos vuz366) (gcd2 (primEqInt (primPlusInt (Pos vuz369) (primMulInt vuz318 (Pos vuz3190))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz368) (primMulInt vuz318 (Pos vuz3190))) (Pos vuz367))",fontsize=16,color="burlywood",shape="box"];10983[label="vuz318/Pos vuz3180",fontsize=10,color="white",style="solid",shape="box"];7884 -> 10983[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	10983 -> 8212[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	10984[label="vuz318/Neg vuz3180",fontsize=10,color="white",style="solid",shape="box"];7884 -> 10984[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	10984 -> 8213[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	7885[label="vuz3160",fontsize=16,color="green",shape="box"];7886[label="vuz3170",fontsize=16,color="green",shape="box"];7887[label="vuz3160",fontsize=16,color="green",shape="box"];7888[label="vuz3170",fontsize=16,color="green",shape="box"];7889[label="vuz3190",fontsize=16,color="green",shape="box"];7890[label="vuz3170",fontsize=16,color="green",shape="box"];7891[label="vuz3190",fontsize=16,color="green",shape="box"];7892[label="vuz3170",fontsize=16,color="green",shape="box"];7893[label="primQuotInt (Pos vuz370) (gcd2 (primEqInt (primPlusInt (Neg vuz373) (primMulInt vuz318 (Pos vuz3190))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz372) (primMulInt vuz318 (Pos vuz3190))) (Pos vuz371))",fontsize=16,color="burlywood",shape="box"];10985[label="vuz318/Pos vuz3180",fontsize=10,color="white",style="solid",shape="box"];7893 -> 10985[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	10985 -> 8214[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	10986[label="vuz318/Neg vuz3180",fontsize=10,color="white",style="solid",shape="box"];7893 -> 10986[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	10986 -> 8215[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	7894[label="vuz3190",fontsize=16,color="green",shape="box"];7895[label="vuz3170",fontsize=16,color="green",shape="box"];7896[label="vuz3160",fontsize=16,color="green",shape="box"];7897[label="vuz3170",fontsize=16,color="green",shape="box"];7898[label="vuz3190",fontsize=16,color="green",shape="box"];7899[label="vuz3170",fontsize=16,color="green",shape="box"];7900[label="vuz3160",fontsize=16,color="green",shape="box"];7901[label="vuz3170",fontsize=16,color="green",shape="box"];7902[label="primQuotInt (Neg vuz374) (gcd2 (primEqInt (primPlusInt (Neg vuz377) (primMulInt vuz318 (Pos vuz3190))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz376) (primMulInt vuz318 (Pos vuz3190))) (Neg vuz375))",fontsize=16,color="burlywood",shape="box"];10987[label="vuz318/Pos vuz3180",fontsize=10,color="white",style="solid",shape="box"];7902 -> 10987[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	10987 -> 8216[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	10988[label="vuz318/Neg vuz3180",fontsize=10,color="white",style="solid",shape="box"];7902 -> 10988[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	10988 -> 8217[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	7903[label="vuz3190",fontsize=16,color="green",shape="box"];7904[label="vuz3170",fontsize=16,color="green",shape="box"];7905[label="vuz3160",fontsize=16,color="green",shape="box"];7906[label="vuz3170",fontsize=16,color="green",shape="box"];7907[label="vuz3160",fontsize=16,color="green",shape="box"];7908[label="vuz3170",fontsize=16,color="green",shape="box"];7909[label="vuz3190",fontsize=16,color="green",shape="box"];7910[label="vuz3170",fontsize=16,color="green",shape="box"];7911[label="primQuotInt (Neg vuz378) (gcd2 (primEqInt (primPlusInt (Pos vuz381) (primMulInt vuz318 (Pos vuz3190))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz380) (primMulInt vuz318 (Pos vuz3190))) (Neg vuz379))",fontsize=16,color="burlywood",shape="box"];10989[label="vuz318/Pos vuz3180",fontsize=10,color="white",style="solid",shape="box"];7911 -> 10989[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	10989 -> 8218[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	10990[label="vuz318/Neg vuz3180",fontsize=10,color="white",style="solid",shape="box"];7911 -> 10990[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	10990 -> 8219[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	7912[label="vuz3190",fontsize=16,color="green",shape="box"];7913[label="vuz3170",fontsize=16,color="green",shape="box"];7914[label="vuz3190",fontsize=16,color="green",shape="box"];7915[label="vuz3170",fontsize=16,color="green",shape="box"];7916[label="vuz3160",fontsize=16,color="green",shape="box"];7917[label="vuz3170",fontsize=16,color="green",shape="box"];7918[label="vuz3160",fontsize=16,color="green",shape="box"];7919[label="vuz3170",fontsize=16,color="green",shape="box"];7920[label="primQuotInt (Neg vuz382) (gcd2 (primEqInt (primPlusInt (Pos vuz385) (primMulInt vuz318 (Neg vuz3190))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz384) (primMulInt vuz318 (Neg vuz3190))) (Neg vuz383))",fontsize=16,color="burlywood",shape="box"];10991[label="vuz318/Pos vuz3180",fontsize=10,color="white",style="solid",shape="box"];7920 -> 10991[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	10991 -> 8220[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	10992[label="vuz318/Neg vuz3180",fontsize=10,color="white",style="solid",shape="box"];7920 -> 10992[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	10992 -> 8221[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	7921[label="vuz3190",fontsize=16,color="green",shape="box"];7922[label="vuz3170",fontsize=16,color="green",shape="box"];7923[label="vuz3160",fontsize=16,color="green",shape="box"];7924[label="vuz3170",fontsize=16,color="green",shape="box"];7925[label="vuz3160",fontsize=16,color="green",shape="box"];7926[label="vuz3170",fontsize=16,color="green",shape="box"];7927[label="vuz3190",fontsize=16,color="green",shape="box"];7928[label="vuz3170",fontsize=16,color="green",shape="box"];7929[label="primQuotInt (Neg vuz386) (gcd2 (primEqInt (primPlusInt (Neg vuz389) (primMulInt vuz318 (Neg vuz3190))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz388) (primMulInt vuz318 (Neg vuz3190))) (Neg vuz387))",fontsize=16,color="burlywood",shape="box"];10993[label="vuz318/Pos vuz3180",fontsize=10,color="white",style="solid",shape="box"];7929 -> 10993[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	10993 -> 8222[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	10994[label="vuz318/Neg vuz3180",fontsize=10,color="white",style="solid",shape="box"];7929 -> 10994[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	10994 -> 8223[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	7930[label="vuz3190",fontsize=16,color="green",shape="box"];7931[label="vuz3170",fontsize=16,color="green",shape="box"];7932[label="vuz3160",fontsize=16,color="green",shape="box"];7933[label="vuz3170",fontsize=16,color="green",shape="box"];7934[label="vuz3160",fontsize=16,color="green",shape="box"];7935[label="vuz3170",fontsize=16,color="green",shape="box"];7936[label="vuz3190",fontsize=16,color="green",shape="box"];7937[label="vuz3170",fontsize=16,color="green",shape="box"];7938[label="primQuotInt (Pos vuz390) (gcd2 (primEqInt (primPlusInt (Neg vuz393) (primMulInt vuz318 (Neg vuz3190))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz392) (primMulInt vuz318 (Neg vuz3190))) (Pos vuz391))",fontsize=16,color="burlywood",shape="box"];10995[label="vuz318/Pos vuz3180",fontsize=10,color="white",style="solid",shape="box"];7938 -> 10995[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	10995 -> 8224[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	10996[label="vuz318/Neg vuz3180",fontsize=10,color="white",style="solid",shape="box"];7938 -> 10996[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	10996 -> 8225[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	7939[label="vuz3190",fontsize=16,color="green",shape="box"];7940[label="vuz3170",fontsize=16,color="green",shape="box"];7941[label="vuz3160",fontsize=16,color="green",shape="box"];7942[label="vuz3170",fontsize=16,color="green",shape="box"];7943[label="vuz3190",fontsize=16,color="green",shape="box"];7944[label="vuz3170",fontsize=16,color="green",shape="box"];7945[label="vuz3160",fontsize=16,color="green",shape="box"];7946[label="vuz3170",fontsize=16,color="green",shape="box"];7947[label="primQuotInt (Pos vuz394) (gcd2 (primEqInt (primPlusInt (Pos vuz397) (primMulInt vuz318 (Neg vuz3190))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz396) (primMulInt vuz318 (Neg vuz3190))) (Pos vuz395))",fontsize=16,color="burlywood",shape="box"];10997[label="vuz318/Pos vuz3180",fontsize=10,color="white",style="solid",shape="box"];7947 -> 10997[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	10997 -> 8226[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	10998[label="vuz318/Neg vuz3180",fontsize=10,color="white",style="solid",shape="box"];7947 -> 10998[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	10998 -> 8227[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	7948[label="vuz3160",fontsize=16,color="green",shape="box"];7949[label="vuz3170",fontsize=16,color="green",shape="box"];7950[label="vuz3180",fontsize=16,color="green",shape="box"];7951[label="vuz3190",fontsize=16,color="green",shape="box"];7952[label="vuz3160",fontsize=16,color="green",shape="box"];7953[label="vuz3170",fontsize=16,color="green",shape="box"];7954[label="vuz3180",fontsize=16,color="green",shape="box"];7955[label="vuz3190",fontsize=16,color="green",shape="box"];8229 -> 9987[label="",style="dashed", color="red", weight=0];
67.83/34.96	8229[label="Pos vuz399 == fromInt (Pos Zero)",fontsize=16,color="magenta"];8229 -> 9989[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8228[label="primQuotInt (Pos vuz398) (gcd2 vuz472 (Pos vuz399) (Pos vuz3190 * Pos vuz3170))",fontsize=16,color="burlywood",shape="triangle"];10999[label="vuz472/False",fontsize=10,color="white",style="solid",shape="box"];8228 -> 10999[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	10999 -> 8232[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	11000[label="vuz472/True",fontsize=10,color="white",style="solid",shape="box"];8228 -> 11000[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	11000 -> 8233[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	7957[label="vuz3180",fontsize=16,color="green",shape="box"];7958[label="vuz3190",fontsize=16,color="green",shape="box"];7959 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.96	7959[label="primMulNat vuz31600 (Succ vuz31700)",fontsize=16,color="magenta"];7959 -> 8234[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7959 -> 8235[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7960[label="Succ vuz31700",fontsize=16,color="green",shape="box"];7961 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.96	7961[label="primMulNat vuz31600 (Succ vuz31700)",fontsize=16,color="magenta"];7961 -> 8236[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7961 -> 8237[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7962[label="Succ vuz31700",fontsize=16,color="green",shape="box"];7963[label="vuz3180",fontsize=16,color="green",shape="box"];7964[label="vuz3190",fontsize=16,color="green",shape="box"];7965[label="primQuotInt (primMinusNat (Succ vuz4010) vuz400) (reduce2D (primMinusNat vuz403 vuz402) (Neg vuz3190 * Pos (Succ vuz31700)))",fontsize=16,color="burlywood",shape="box"];11001[label="vuz400/Succ vuz4000",fontsize=10,color="white",style="solid",shape="box"];7965 -> 11001[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	11001 -> 8238[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	11002[label="vuz400/Zero",fontsize=10,color="white",style="solid",shape="box"];7965 -> 11002[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	11002 -> 8239[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	7966[label="primQuotInt (primMinusNat Zero vuz400) (reduce2D (primMinusNat vuz403 vuz402) (Neg vuz3190 * Pos (Succ vuz31700)))",fontsize=16,color="burlywood",shape="box"];11003[label="vuz400/Succ vuz4000",fontsize=10,color="white",style="solid",shape="box"];7966 -> 11003[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	11003 -> 8240[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	11004[label="vuz400/Zero",fontsize=10,color="white",style="solid",shape="box"];7966 -> 11004[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	11004 -> 8241[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	7967[label="vuz3180",fontsize=16,color="green",shape="box"];7968[label="vuz3190",fontsize=16,color="green",shape="box"];7969[label="vuz3180",fontsize=16,color="green",shape="box"];7970[label="vuz3190",fontsize=16,color="green",shape="box"];7971[label="primQuotInt (primMinusNat Zero (Succ vuz4060)) (reduce2D (primMinusNat Zero vuz407) (Neg vuz3190 * Pos Zero))",fontsize=16,color="black",shape="box"];7971 -> 8242[label="",style="solid", color="black", weight=3];
67.83/34.96	7972[label="primQuotInt (primMinusNat Zero Zero) (reduce2D (primMinusNat Zero vuz407) (Neg vuz3190 * Pos Zero))",fontsize=16,color="black",shape="box"];7972 -> 8243[label="",style="solid", color="black", weight=3];
67.83/34.96	7973[label="vuz3180",fontsize=16,color="green",shape="box"];7974[label="vuz3190",fontsize=16,color="green",shape="box"];7975[label="vuz3180",fontsize=16,color="green",shape="box"];7976[label="vuz3190",fontsize=16,color="green",shape="box"];7977[label="vuz3180",fontsize=16,color="green",shape="box"];7978[label="vuz3190",fontsize=16,color="green",shape="box"];7979[label="vuz3180",fontsize=16,color="green",shape="box"];7980[label="vuz3190",fontsize=16,color="green",shape="box"];7981 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.96	7981[label="primMulNat vuz31600 (Succ vuz31700)",fontsize=16,color="magenta"];7981 -> 8244[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7981 -> 8245[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7982[label="Succ vuz31700",fontsize=16,color="green",shape="box"];7983[label="vuz3180",fontsize=16,color="green",shape="box"];7984[label="vuz3190",fontsize=16,color="green",shape="box"];7985 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.96	7985[label="primMulNat vuz31600 (Succ vuz31700)",fontsize=16,color="magenta"];7985 -> 8246[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7985 -> 8247[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7986[label="Succ vuz31700",fontsize=16,color="green",shape="box"];7987[label="vuz3180",fontsize=16,color="green",shape="box"];7988[label="vuz3190",fontsize=16,color="green",shape="box"];7989[label="primQuotInt (primMinusNat (Succ vuz4090) vuz408) (reduce2D (primMinusNat vuz411 vuz410) (Pos vuz3190 * Pos (Succ vuz31700)))",fontsize=16,color="burlywood",shape="box"];11005[label="vuz408/Succ vuz4080",fontsize=10,color="white",style="solid",shape="box"];7989 -> 11005[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	11005 -> 8248[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	11006[label="vuz408/Zero",fontsize=10,color="white",style="solid",shape="box"];7989 -> 11006[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	11006 -> 8249[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	7990[label="primQuotInt (primMinusNat Zero vuz408) (reduce2D (primMinusNat vuz411 vuz410) (Pos vuz3190 * Pos (Succ vuz31700)))",fontsize=16,color="burlywood",shape="box"];11007[label="vuz408/Succ vuz4080",fontsize=10,color="white",style="solid",shape="box"];7990 -> 11007[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	11007 -> 8250[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	11008[label="vuz408/Zero",fontsize=10,color="white",style="solid",shape="box"];7990 -> 11008[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	11008 -> 8251[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	7991[label="vuz3180",fontsize=16,color="green",shape="box"];7992[label="vuz3190",fontsize=16,color="green",shape="box"];7993[label="vuz3180",fontsize=16,color="green",shape="box"];7994[label="vuz3190",fontsize=16,color="green",shape="box"];7995[label="primQuotInt (primMinusNat Zero (Succ vuz4140)) (reduce2D (primMinusNat Zero vuz415) (Pos vuz3190 * Pos Zero))",fontsize=16,color="black",shape="box"];7995 -> 8252[label="",style="solid", color="black", weight=3];
67.83/34.96	7996[label="primQuotInt (primMinusNat Zero Zero) (reduce2D (primMinusNat Zero vuz415) (Pos vuz3190 * Pos Zero))",fontsize=16,color="black",shape="box"];7996 -> 8253[label="",style="solid", color="black", weight=3];
67.83/34.96	7997[label="vuz3180",fontsize=16,color="green",shape="box"];7998[label="vuz3190",fontsize=16,color="green",shape="box"];7999[label="vuz3180",fontsize=16,color="green",shape="box"];8000[label="vuz3190",fontsize=16,color="green",shape="box"];8001[label="vuz3180",fontsize=16,color="green",shape="box"];8002[label="vuz3190",fontsize=16,color="green",shape="box"];8003[label="vuz3180",fontsize=16,color="green",shape="box"];8004[label="vuz3190",fontsize=16,color="green",shape="box"];8005[label="vuz3160",fontsize=16,color="green",shape="box"];8006[label="vuz3170",fontsize=16,color="green",shape="box"];8007[label="vuz3180",fontsize=16,color="green",shape="box"];8008[label="vuz3190",fontsize=16,color="green",shape="box"];8009[label="vuz3160",fontsize=16,color="green",shape="box"];8010[label="vuz3170",fontsize=16,color="green",shape="box"];8011[label="vuz3180",fontsize=16,color="green",shape="box"];8012[label="vuz3190",fontsize=16,color="green",shape="box"];8255 -> 9987[label="",style="dashed", color="red", weight=0];
67.83/34.96	8255[label="Pos vuz417 == fromInt (Pos Zero)",fontsize=16,color="magenta"];8255 -> 9990[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8254[label="primQuotInt (Pos vuz416) (gcd2 vuz473 (Pos vuz417) (Neg vuz3190 * Pos vuz3170))",fontsize=16,color="burlywood",shape="triangle"];11009[label="vuz473/False",fontsize=10,color="white",style="solid",shape="box"];8254 -> 11009[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	11009 -> 8258[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	11010[label="vuz473/True",fontsize=10,color="white",style="solid",shape="box"];8254 -> 11010[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	11010 -> 8259[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	8014[label="vuz3160",fontsize=16,color="green",shape="box"];8015[label="vuz3170",fontsize=16,color="green",shape="box"];8016 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.96	8016[label="primMulNat vuz31800 (Succ vuz31900)",fontsize=16,color="magenta"];8016 -> 8260[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8016 -> 8261[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8017[label="Succ vuz31900",fontsize=16,color="green",shape="box"];8018[label="vuz3160",fontsize=16,color="green",shape="box"];8019[label="vuz3170",fontsize=16,color="green",shape="box"];8020 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.96	8020[label="primMulNat vuz31800 (Succ vuz31900)",fontsize=16,color="magenta"];8020 -> 8262[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8020 -> 8263[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8021[label="Succ vuz31900",fontsize=16,color="green",shape="box"];8022[label="primQuotInt (primMinusNat (Succ vuz4190) vuz418) (reduce2D (primMinusNat vuz421 vuz420) (Pos (Succ vuz31900) * Neg vuz3170))",fontsize=16,color="burlywood",shape="box"];11011[label="vuz418/Succ vuz4180",fontsize=10,color="white",style="solid",shape="box"];8022 -> 11011[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	11011 -> 8264[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	11012[label="vuz418/Zero",fontsize=10,color="white",style="solid",shape="box"];8022 -> 11012[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	11012 -> 8265[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	8023[label="primQuotInt (primMinusNat Zero vuz418) (reduce2D (primMinusNat vuz421 vuz420) (Pos (Succ vuz31900) * Neg vuz3170))",fontsize=16,color="burlywood",shape="box"];11013[label="vuz418/Succ vuz4180",fontsize=10,color="white",style="solid",shape="box"];8023 -> 11013[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	11013 -> 8266[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	11014[label="vuz418/Zero",fontsize=10,color="white",style="solid",shape="box"];8023 -> 11014[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	11014 -> 8267[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	8024[label="vuz3160",fontsize=16,color="green",shape="box"];8025[label="vuz3170",fontsize=16,color="green",shape="box"];8026[label="vuz3160",fontsize=16,color="green",shape="box"];8027[label="vuz3170",fontsize=16,color="green",shape="box"];8028[label="primQuotInt (primMinusNat Zero (Succ vuz4240)) (reduce2D (primMinusNat Zero vuz425) (Pos Zero * Neg vuz3170))",fontsize=16,color="black",shape="box"];8028 -> 8268[label="",style="solid", color="black", weight=3];
67.83/34.96	8029[label="primQuotInt (primMinusNat Zero Zero) (reduce2D (primMinusNat Zero vuz425) (Pos Zero * Neg vuz3170))",fontsize=16,color="black",shape="box"];8029 -> 8269[label="",style="solid", color="black", weight=3];
67.83/34.96	8030[label="vuz3160",fontsize=16,color="green",shape="box"];8031[label="vuz3170",fontsize=16,color="green",shape="box"];8032[label="vuz3160",fontsize=16,color="green",shape="box"];8033[label="vuz3170",fontsize=16,color="green",shape="box"];8034[label="vuz3160",fontsize=16,color="green",shape="box"];8035[label="vuz3170",fontsize=16,color="green",shape="box"];8036[label="vuz3160",fontsize=16,color="green",shape="box"];8037[label="vuz3170",fontsize=16,color="green",shape="box"];8038[label="vuz3160",fontsize=16,color="green",shape="box"];8039[label="vuz3170",fontsize=16,color="green",shape="box"];8040[label="vuz3180",fontsize=16,color="green",shape="box"];8041[label="vuz3190",fontsize=16,color="green",shape="box"];8042[label="vuz3160",fontsize=16,color="green",shape="box"];8043[label="vuz3170",fontsize=16,color="green",shape="box"];8044[label="vuz3180",fontsize=16,color="green",shape="box"];8045[label="vuz3190",fontsize=16,color="green",shape="box"];8271 -> 9987[label="",style="dashed", color="red", weight=0];
67.83/34.96	8271[label="Neg vuz427 == fromInt (Pos Zero)",fontsize=16,color="magenta"];8271 -> 9991[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8270[label="primQuotInt (Neg vuz426) (gcd2 vuz474 (Neg vuz427) (Neg vuz3190 * Neg vuz3170))",fontsize=16,color="burlywood",shape="triangle"];11015[label="vuz474/False",fontsize=10,color="white",style="solid",shape="box"];8270 -> 11015[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	11015 -> 8274[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	11016[label="vuz474/True",fontsize=10,color="white",style="solid",shape="box"];8270 -> 11016[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	11016 -> 8275[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	8047[label="vuz3160",fontsize=16,color="green",shape="box"];8048[label="vuz3170",fontsize=16,color="green",shape="box"];8049[label="vuz3180",fontsize=16,color="green",shape="box"];8050[label="vuz3190",fontsize=16,color="green",shape="box"];8051[label="vuz3160",fontsize=16,color="green",shape="box"];8052[label="vuz3170",fontsize=16,color="green",shape="box"];8053[label="vuz3180",fontsize=16,color="green",shape="box"];8054[label="vuz3190",fontsize=16,color="green",shape="box"];8277 -> 9987[label="",style="dashed", color="red", weight=0];
67.83/34.96	8277[label="Neg vuz429 == fromInt (Pos Zero)",fontsize=16,color="magenta"];8277 -> 9992[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8276[label="primQuotInt (Neg vuz428) (gcd2 vuz475 (Neg vuz429) (Pos vuz3190 * Neg vuz3170))",fontsize=16,color="burlywood",shape="triangle"];11017[label="vuz475/False",fontsize=10,color="white",style="solid",shape="box"];8276 -> 11017[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	11017 -> 8280[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	11018[label="vuz475/True",fontsize=10,color="white",style="solid",shape="box"];8276 -> 11018[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	11018 -> 8281[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	8056 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.96	8056[label="primMulNat vuz31800 (Succ vuz31900)",fontsize=16,color="magenta"];8056 -> 8282[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8056 -> 8283[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8057[label="Succ vuz31900",fontsize=16,color="green",shape="box"];8058[label="vuz3160",fontsize=16,color="green",shape="box"];8059[label="vuz3170",fontsize=16,color="green",shape="box"];8060[label="vuz3160",fontsize=16,color="green",shape="box"];8061[label="vuz3170",fontsize=16,color="green",shape="box"];8062 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.96	8062[label="primMulNat vuz31800 (Succ vuz31900)",fontsize=16,color="magenta"];8062 -> 8284[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8062 -> 8285[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8063[label="Succ vuz31900",fontsize=16,color="green",shape="box"];8064[label="primQuotInt (primMinusNat (Succ vuz4310) vuz430) (reduce2D (primMinusNat vuz433 vuz432) (Neg (Succ vuz31900) * Neg vuz3170))",fontsize=16,color="burlywood",shape="box"];11019[label="vuz430/Succ vuz4300",fontsize=10,color="white",style="solid",shape="box"];8064 -> 11019[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	11019 -> 8286[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	11020[label="vuz430/Zero",fontsize=10,color="white",style="solid",shape="box"];8064 -> 11020[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	11020 -> 8287[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	8065[label="primQuotInt (primMinusNat Zero vuz430) (reduce2D (primMinusNat vuz433 vuz432) (Neg (Succ vuz31900) * Neg vuz3170))",fontsize=16,color="burlywood",shape="box"];11021[label="vuz430/Succ vuz4300",fontsize=10,color="white",style="solid",shape="box"];8065 -> 11021[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	11021 -> 8288[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	11022[label="vuz430/Zero",fontsize=10,color="white",style="solid",shape="box"];8065 -> 11022[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	11022 -> 8289[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	8066[label="vuz3160",fontsize=16,color="green",shape="box"];8067[label="vuz3170",fontsize=16,color="green",shape="box"];8068[label="vuz3160",fontsize=16,color="green",shape="box"];8069[label="vuz3170",fontsize=16,color="green",shape="box"];8070[label="primQuotInt (primMinusNat Zero (Succ vuz4360)) (reduce2D (primMinusNat Zero vuz437) (Neg Zero * Neg vuz3170))",fontsize=16,color="black",shape="box"];8070 -> 8290[label="",style="solid", color="black", weight=3];
67.83/34.96	8071[label="primQuotInt (primMinusNat Zero Zero) (reduce2D (primMinusNat Zero vuz437) (Neg Zero * Neg vuz3170))",fontsize=16,color="black",shape="box"];8071 -> 8291[label="",style="solid", color="black", weight=3];
67.83/34.96	8072[label="vuz3160",fontsize=16,color="green",shape="box"];8073[label="vuz3170",fontsize=16,color="green",shape="box"];8074[label="vuz3160",fontsize=16,color="green",shape="box"];8075[label="vuz3170",fontsize=16,color="green",shape="box"];8076[label="vuz3160",fontsize=16,color="green",shape="box"];8077[label="vuz3170",fontsize=16,color="green",shape="box"];8078[label="vuz3160",fontsize=16,color="green",shape="box"];8079[label="vuz3170",fontsize=16,color="green",shape="box"];8080 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.96	8080[label="primMulNat vuz31800 (Succ vuz31900)",fontsize=16,color="magenta"];8080 -> 8292[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8080 -> 8293[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8081[label="Succ vuz31900",fontsize=16,color="green",shape="box"];8082[label="vuz3160",fontsize=16,color="green",shape="box"];8083[label="vuz3170",fontsize=16,color="green",shape="box"];8084[label="vuz3160",fontsize=16,color="green",shape="box"];8085[label="vuz3170",fontsize=16,color="green",shape="box"];8086 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.96	8086[label="primMulNat vuz31800 (Succ vuz31900)",fontsize=16,color="magenta"];8086 -> 8294[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8086 -> 8295[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8087[label="Succ vuz31900",fontsize=16,color="green",shape="box"];8088[label="primQuotInt (primMinusNat (Succ vuz4390) vuz438) (reduce2D (primMinusNat vuz441 vuz440) (Pos (Succ vuz31900) * Pos vuz3170))",fontsize=16,color="burlywood",shape="box"];11023[label="vuz438/Succ vuz4380",fontsize=10,color="white",style="solid",shape="box"];8088 -> 11023[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	11023 -> 8296[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	11024[label="vuz438/Zero",fontsize=10,color="white",style="solid",shape="box"];8088 -> 11024[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	11024 -> 8297[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	8089[label="primQuotInt (primMinusNat Zero vuz438) (reduce2D (primMinusNat vuz441 vuz440) (Pos (Succ vuz31900) * Pos vuz3170))",fontsize=16,color="burlywood",shape="box"];11025[label="vuz438/Succ vuz4380",fontsize=10,color="white",style="solid",shape="box"];8089 -> 11025[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	11025 -> 8298[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	11026[label="vuz438/Zero",fontsize=10,color="white",style="solid",shape="box"];8089 -> 11026[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	11026 -> 8299[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	8090[label="vuz3160",fontsize=16,color="green",shape="box"];8091[label="vuz3170",fontsize=16,color="green",shape="box"];8092[label="vuz3160",fontsize=16,color="green",shape="box"];8093[label="vuz3170",fontsize=16,color="green",shape="box"];8094[label="primQuotInt (primMinusNat Zero (Succ vuz4440)) (reduce2D (primMinusNat Zero vuz445) (Pos Zero * Pos vuz3170))",fontsize=16,color="black",shape="box"];8094 -> 8300[label="",style="solid", color="black", weight=3];
67.83/34.96	8095[label="primQuotInt (primMinusNat Zero Zero) (reduce2D (primMinusNat Zero vuz445) (Pos Zero * Pos vuz3170))",fontsize=16,color="black",shape="box"];8095 -> 8301[label="",style="solid", color="black", weight=3];
67.83/34.96	8096[label="vuz3160",fontsize=16,color="green",shape="box"];8097[label="vuz3170",fontsize=16,color="green",shape="box"];8098[label="vuz3160",fontsize=16,color="green",shape="box"];8099[label="vuz3170",fontsize=16,color="green",shape="box"];8100[label="vuz3160",fontsize=16,color="green",shape="box"];8101[label="vuz3170",fontsize=16,color="green",shape="box"];8102[label="vuz3160",fontsize=16,color="green",shape="box"];8103[label="vuz3170",fontsize=16,color="green",shape="box"];8104[label="vuz3160",fontsize=16,color="green",shape="box"];8105[label="vuz3170",fontsize=16,color="green",shape="box"];8106[label="vuz3180",fontsize=16,color="green",shape="box"];8107[label="vuz3190",fontsize=16,color="green",shape="box"];8108[label="vuz3160",fontsize=16,color="green",shape="box"];8109[label="vuz3170",fontsize=16,color="green",shape="box"];8110[label="vuz3180",fontsize=16,color="green",shape="box"];8111[label="vuz3190",fontsize=16,color="green",shape="box"];8303 -> 9987[label="",style="dashed", color="red", weight=0];
67.83/34.96	8303[label="Neg vuz447 == fromInt (Pos Zero)",fontsize=16,color="magenta"];8303 -> 9993[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8302[label="primQuotInt (Neg vuz446) (gcd2 vuz476 (Neg vuz447) (Neg vuz3190 * Pos vuz3170))",fontsize=16,color="burlywood",shape="triangle"];11027[label="vuz476/False",fontsize=10,color="white",style="solid",shape="box"];8302 -> 11027[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	11027 -> 8306[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	11028[label="vuz476/True",fontsize=10,color="white",style="solid",shape="box"];8302 -> 11028[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	11028 -> 8307[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	8113[label="vuz3160",fontsize=16,color="green",shape="box"];8114[label="vuz3170",fontsize=16,color="green",shape="box"];8115[label="vuz3180",fontsize=16,color="green",shape="box"];8116[label="vuz3190",fontsize=16,color="green",shape="box"];8117[label="vuz3160",fontsize=16,color="green",shape="box"];8118[label="vuz3170",fontsize=16,color="green",shape="box"];8119[label="vuz3180",fontsize=16,color="green",shape="box"];8120[label="vuz3190",fontsize=16,color="green",shape="box"];8309 -> 9987[label="",style="dashed", color="red", weight=0];
67.83/34.96	8309[label="Neg vuz349 == fromInt (Pos Zero)",fontsize=16,color="magenta"];8309 -> 9994[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8308[label="primQuotInt (Neg vuz348) (gcd2 vuz477 (Neg vuz349) (Pos vuz3190 * Pos vuz3170))",fontsize=16,color="burlywood",shape="triangle"];11029[label="vuz477/False",fontsize=10,color="white",style="solid",shape="box"];8308 -> 11029[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	11029 -> 8312[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	11030[label="vuz477/True",fontsize=10,color="white",style="solid",shape="box"];8308 -> 11030[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	11030 -> 8313[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	8122 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.96	8122[label="primMulNat vuz31800 (Succ vuz31900)",fontsize=16,color="magenta"];8122 -> 8314[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8122 -> 8315[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8123[label="Succ vuz31900",fontsize=16,color="green",shape="box"];8124 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.96	8124[label="primMulNat vuz31800 (Succ vuz31900)",fontsize=16,color="magenta"];8124 -> 8316[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8124 -> 8317[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8125[label="Succ vuz31900",fontsize=16,color="green",shape="box"];8126[label="vuz3160",fontsize=16,color="green",shape="box"];8127[label="vuz3170",fontsize=16,color="green",shape="box"];8128[label="vuz3160",fontsize=16,color="green",shape="box"];8129[label="vuz3170",fontsize=16,color="green",shape="box"];8130[label="primQuotInt (primMinusNat (Succ vuz4490) vuz448) (reduce2D (primMinusNat vuz451 vuz450) (Neg (Succ vuz31900) * Pos vuz3170))",fontsize=16,color="burlywood",shape="box"];11031[label="vuz448/Succ vuz4480",fontsize=10,color="white",style="solid",shape="box"];8130 -> 11031[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	11031 -> 8318[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	11032[label="vuz448/Zero",fontsize=10,color="white",style="solid",shape="box"];8130 -> 11032[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	11032 -> 8319[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	8131[label="primQuotInt (primMinusNat Zero vuz448) (reduce2D (primMinusNat vuz451 vuz450) (Neg (Succ vuz31900) * Pos vuz3170))",fontsize=16,color="burlywood",shape="box"];11033[label="vuz448/Succ vuz4480",fontsize=10,color="white",style="solid",shape="box"];8131 -> 11033[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	11033 -> 8320[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	11034[label="vuz448/Zero",fontsize=10,color="white",style="solid",shape="box"];8131 -> 11034[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	11034 -> 8321[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	8132[label="vuz3160",fontsize=16,color="green",shape="box"];8133[label="vuz3170",fontsize=16,color="green",shape="box"];8134[label="vuz3160",fontsize=16,color="green",shape="box"];8135[label="vuz3170",fontsize=16,color="green",shape="box"];8136[label="primQuotInt (primMinusNat Zero (Succ vuz4540)) (reduce2D (primMinusNat Zero vuz455) (Neg Zero * Pos vuz3170))",fontsize=16,color="black",shape="box"];8136 -> 8322[label="",style="solid", color="black", weight=3];
67.83/34.96	8137[label="primQuotInt (primMinusNat Zero Zero) (reduce2D (primMinusNat Zero vuz455) (Neg Zero * Pos vuz3170))",fontsize=16,color="black",shape="box"];8137 -> 8323[label="",style="solid", color="black", weight=3];
67.83/34.96	8138[label="vuz3160",fontsize=16,color="green",shape="box"];8139[label="vuz3170",fontsize=16,color="green",shape="box"];8140[label="vuz3160",fontsize=16,color="green",shape="box"];8141[label="vuz3170",fontsize=16,color="green",shape="box"];8142[label="vuz3160",fontsize=16,color="green",shape="box"];8143[label="vuz3170",fontsize=16,color="green",shape="box"];8144[label="vuz3160",fontsize=16,color="green",shape="box"];8145[label="vuz3170",fontsize=16,color="green",shape="box"];8146[label="vuz3160",fontsize=16,color="green",shape="box"];8147[label="vuz3170",fontsize=16,color="green",shape="box"];8148[label="vuz3180",fontsize=16,color="green",shape="box"];8149[label="vuz3190",fontsize=16,color="green",shape="box"];8150[label="vuz3160",fontsize=16,color="green",shape="box"];8151[label="vuz3170",fontsize=16,color="green",shape="box"];8152[label="vuz3180",fontsize=16,color="green",shape="box"];8153[label="vuz3190",fontsize=16,color="green",shape="box"];8325 -> 9987[label="",style="dashed", color="red", weight=0];
67.83/34.96	8325[label="Pos vuz355 == fromInt (Pos Zero)",fontsize=16,color="magenta"];8325 -> 9995[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8324[label="primQuotInt (Pos vuz354) (gcd2 vuz478 (Pos vuz355) (Pos vuz3190 * Neg vuz3170))",fontsize=16,color="burlywood",shape="triangle"];11035[label="vuz478/False",fontsize=10,color="white",style="solid",shape="box"];8324 -> 11035[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	11035 -> 8328[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	11036[label="vuz478/True",fontsize=10,color="white",style="solid",shape="box"];8324 -> 11036[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	11036 -> 8329[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	8155 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.96	8155[label="primMulNat vuz31600 (Succ vuz31700)",fontsize=16,color="magenta"];8155 -> 8330[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8155 -> 8331[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8156[label="Succ vuz31700",fontsize=16,color="green",shape="box"];8157[label="vuz3180",fontsize=16,color="green",shape="box"];8158[label="vuz3190",fontsize=16,color="green",shape="box"];8159[label="vuz3180",fontsize=16,color="green",shape="box"];8160[label="vuz3190",fontsize=16,color="green",shape="box"];8161 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.96	8161[label="primMulNat vuz31600 (Succ vuz31700)",fontsize=16,color="magenta"];8161 -> 8332[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8161 -> 8333[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8162[label="Succ vuz31700",fontsize=16,color="green",shape="box"];8163[label="primQuotInt (primMinusNat (Succ vuz4570) vuz456) (reduce2D (primMinusNat vuz459 vuz458) (Neg vuz3190 * Neg (Succ vuz31700)))",fontsize=16,color="burlywood",shape="box"];11037[label="vuz456/Succ vuz4560",fontsize=10,color="white",style="solid",shape="box"];8163 -> 11037[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	11037 -> 8334[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	11038[label="vuz456/Zero",fontsize=10,color="white",style="solid",shape="box"];8163 -> 11038[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	11038 -> 8335[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	8164[label="primQuotInt (primMinusNat Zero vuz456) (reduce2D (primMinusNat vuz459 vuz458) (Neg vuz3190 * Neg (Succ vuz31700)))",fontsize=16,color="burlywood",shape="box"];11039[label="vuz456/Succ vuz4560",fontsize=10,color="white",style="solid",shape="box"];8164 -> 11039[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	11039 -> 8336[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	11040[label="vuz456/Zero",fontsize=10,color="white",style="solid",shape="box"];8164 -> 11040[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	11040 -> 8337[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	8165[label="vuz3180",fontsize=16,color="green",shape="box"];8166[label="vuz3190",fontsize=16,color="green",shape="box"];8167[label="vuz3180",fontsize=16,color="green",shape="box"];8168[label="vuz3190",fontsize=16,color="green",shape="box"];8169[label="primQuotInt (primMinusNat Zero (Succ vuz4620)) (reduce2D (primMinusNat Zero vuz463) (Neg vuz3190 * Neg Zero))",fontsize=16,color="black",shape="box"];8169 -> 8338[label="",style="solid", color="black", weight=3];
67.83/34.96	8170[label="primQuotInt (primMinusNat Zero Zero) (reduce2D (primMinusNat Zero vuz463) (Neg vuz3190 * Neg Zero))",fontsize=16,color="black",shape="box"];8170 -> 8339[label="",style="solid", color="black", weight=3];
67.83/34.96	8171[label="vuz3180",fontsize=16,color="green",shape="box"];8172[label="vuz3190",fontsize=16,color="green",shape="box"];8173[label="vuz3180",fontsize=16,color="green",shape="box"];8174[label="vuz3190",fontsize=16,color="green",shape="box"];8175[label="vuz3180",fontsize=16,color="green",shape="box"];8176[label="vuz3190",fontsize=16,color="green",shape="box"];8177[label="vuz3180",fontsize=16,color="green",shape="box"];8178[label="vuz3190",fontsize=16,color="green",shape="box"];8179 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.96	8179[label="primMulNat vuz31600 (Succ vuz31700)",fontsize=16,color="magenta"];8179 -> 8340[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8179 -> 8341[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8180[label="Succ vuz31700",fontsize=16,color="green",shape="box"];8181[label="vuz3180",fontsize=16,color="green",shape="box"];8182[label="vuz3190",fontsize=16,color="green",shape="box"];8183[label="vuz3180",fontsize=16,color="green",shape="box"];8184[label="vuz3190",fontsize=16,color="green",shape="box"];8185 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.96	8185[label="primMulNat vuz31600 (Succ vuz31700)",fontsize=16,color="magenta"];8185 -> 8342[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8185 -> 8343[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8186[label="Succ vuz31700",fontsize=16,color="green",shape="box"];8187[label="primQuotInt (primMinusNat (Succ vuz4650) vuz464) (reduce2D (primMinusNat vuz467 vuz466) (Pos vuz3190 * Neg (Succ vuz31700)))",fontsize=16,color="burlywood",shape="box"];11041[label="vuz464/Succ vuz4640",fontsize=10,color="white",style="solid",shape="box"];8187 -> 11041[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	11041 -> 8344[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	11042[label="vuz464/Zero",fontsize=10,color="white",style="solid",shape="box"];8187 -> 11042[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	11042 -> 8345[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	8188[label="primQuotInt (primMinusNat Zero vuz464) (reduce2D (primMinusNat vuz467 vuz466) (Pos vuz3190 * Neg (Succ vuz31700)))",fontsize=16,color="burlywood",shape="box"];11043[label="vuz464/Succ vuz4640",fontsize=10,color="white",style="solid",shape="box"];8188 -> 11043[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	11043 -> 8346[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	11044[label="vuz464/Zero",fontsize=10,color="white",style="solid",shape="box"];8188 -> 11044[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	11044 -> 8347[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	8189[label="vuz3180",fontsize=16,color="green",shape="box"];8190[label="vuz3190",fontsize=16,color="green",shape="box"];8191[label="vuz3180",fontsize=16,color="green",shape="box"];8192[label="vuz3190",fontsize=16,color="green",shape="box"];8193[label="primQuotInt (primMinusNat Zero (Succ vuz4700)) (reduce2D (primMinusNat Zero vuz471) (Pos vuz3190 * Neg Zero))",fontsize=16,color="black",shape="box"];8193 -> 8348[label="",style="solid", color="black", weight=3];
67.83/34.96	8194[label="primQuotInt (primMinusNat Zero Zero) (reduce2D (primMinusNat Zero vuz471) (Pos vuz3190 * Neg Zero))",fontsize=16,color="black",shape="box"];8194 -> 8349[label="",style="solid", color="black", weight=3];
67.83/34.96	8195[label="vuz3180",fontsize=16,color="green",shape="box"];8196[label="vuz3190",fontsize=16,color="green",shape="box"];8197[label="vuz3180",fontsize=16,color="green",shape="box"];8198[label="vuz3190",fontsize=16,color="green",shape="box"];8199[label="vuz3180",fontsize=16,color="green",shape="box"];8200[label="vuz3190",fontsize=16,color="green",shape="box"];8201[label="vuz3180",fontsize=16,color="green",shape="box"];8202[label="vuz3190",fontsize=16,color="green",shape="box"];8203[label="vuz3160",fontsize=16,color="green",shape="box"];8204[label="vuz3170",fontsize=16,color="green",shape="box"];8205[label="vuz3180",fontsize=16,color="green",shape="box"];8206[label="vuz3190",fontsize=16,color="green",shape="box"];8207[label="vuz3160",fontsize=16,color="green",shape="box"];8208[label="vuz3170",fontsize=16,color="green",shape="box"];8209[label="vuz3180",fontsize=16,color="green",shape="box"];8210[label="vuz3190",fontsize=16,color="green",shape="box"];8351 -> 9987[label="",style="dashed", color="red", weight=0];
67.83/34.96	8351[label="Pos vuz361 == fromInt (Pos Zero)",fontsize=16,color="magenta"];8351 -> 9996[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8350[label="primQuotInt (Pos vuz360) (gcd2 vuz479 (Pos vuz361) (Neg vuz3190 * Neg vuz3170))",fontsize=16,color="burlywood",shape="triangle"];11045[label="vuz479/False",fontsize=10,color="white",style="solid",shape="box"];8350 -> 11045[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	11045 -> 8354[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	11046[label="vuz479/True",fontsize=10,color="white",style="solid",shape="box"];8350 -> 11046[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	11046 -> 8355[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	8212[label="primQuotInt (Pos vuz366) (gcd2 (primEqInt (primPlusInt (Pos vuz369) (primMulInt (Pos vuz3180) (Pos vuz3190))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz368) (primMulInt (Pos vuz3180) (Pos vuz3190))) (Pos vuz367))",fontsize=16,color="black",shape="box"];8212 -> 8356[label="",style="solid", color="black", weight=3];
67.83/34.96	8213[label="primQuotInt (Pos vuz366) (gcd2 (primEqInt (primPlusInt (Pos vuz369) (primMulInt (Neg vuz3180) (Pos vuz3190))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz368) (primMulInt (Neg vuz3180) (Pos vuz3190))) (Pos vuz367))",fontsize=16,color="black",shape="box"];8213 -> 8357[label="",style="solid", color="black", weight=3];
67.83/34.96	8214[label="primQuotInt (Pos vuz370) (gcd2 (primEqInt (primPlusInt (Neg vuz373) (primMulInt (Pos vuz3180) (Pos vuz3190))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz372) (primMulInt (Pos vuz3180) (Pos vuz3190))) (Pos vuz371))",fontsize=16,color="black",shape="box"];8214 -> 8358[label="",style="solid", color="black", weight=3];
67.83/34.96	8215[label="primQuotInt (Pos vuz370) (gcd2 (primEqInt (primPlusInt (Neg vuz373) (primMulInt (Neg vuz3180) (Pos vuz3190))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz372) (primMulInt (Neg vuz3180) (Pos vuz3190))) (Pos vuz371))",fontsize=16,color="black",shape="box"];8215 -> 8359[label="",style="solid", color="black", weight=3];
67.83/34.96	8216[label="primQuotInt (Neg vuz374) (gcd2 (primEqInt (primPlusInt (Neg vuz377) (primMulInt (Pos vuz3180) (Pos vuz3190))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz376) (primMulInt (Pos vuz3180) (Pos vuz3190))) (Neg vuz375))",fontsize=16,color="black",shape="box"];8216 -> 8360[label="",style="solid", color="black", weight=3];
67.83/34.96	8217[label="primQuotInt (Neg vuz374) (gcd2 (primEqInt (primPlusInt (Neg vuz377) (primMulInt (Neg vuz3180) (Pos vuz3190))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz376) (primMulInt (Neg vuz3180) (Pos vuz3190))) (Neg vuz375))",fontsize=16,color="black",shape="box"];8217 -> 8361[label="",style="solid", color="black", weight=3];
67.83/34.96	8218[label="primQuotInt (Neg vuz378) (gcd2 (primEqInt (primPlusInt (Pos vuz381) (primMulInt (Pos vuz3180) (Pos vuz3190))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz380) (primMulInt (Pos vuz3180) (Pos vuz3190))) (Neg vuz379))",fontsize=16,color="black",shape="box"];8218 -> 8362[label="",style="solid", color="black", weight=3];
67.83/34.96	8219[label="primQuotInt (Neg vuz378) (gcd2 (primEqInt (primPlusInt (Pos vuz381) (primMulInt (Neg vuz3180) (Pos vuz3190))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz380) (primMulInt (Neg vuz3180) (Pos vuz3190))) (Neg vuz379))",fontsize=16,color="black",shape="box"];8219 -> 8363[label="",style="solid", color="black", weight=3];
67.83/34.96	8220[label="primQuotInt (Neg vuz382) (gcd2 (primEqInt (primPlusInt (Pos vuz385) (primMulInt (Pos vuz3180) (Neg vuz3190))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz384) (primMulInt (Pos vuz3180) (Neg vuz3190))) (Neg vuz383))",fontsize=16,color="black",shape="box"];8220 -> 8364[label="",style="solid", color="black", weight=3];
67.83/34.96	8221[label="primQuotInt (Neg vuz382) (gcd2 (primEqInt (primPlusInt (Pos vuz385) (primMulInt (Neg vuz3180) (Neg vuz3190))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz384) (primMulInt (Neg vuz3180) (Neg vuz3190))) (Neg vuz383))",fontsize=16,color="black",shape="box"];8221 -> 8365[label="",style="solid", color="black", weight=3];
67.83/34.96	8222[label="primQuotInt (Neg vuz386) (gcd2 (primEqInt (primPlusInt (Neg vuz389) (primMulInt (Pos vuz3180) (Neg vuz3190))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz388) (primMulInt (Pos vuz3180) (Neg vuz3190))) (Neg vuz387))",fontsize=16,color="black",shape="box"];8222 -> 8366[label="",style="solid", color="black", weight=3];
67.83/34.96	8223[label="primQuotInt (Neg vuz386) (gcd2 (primEqInt (primPlusInt (Neg vuz389) (primMulInt (Neg vuz3180) (Neg vuz3190))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz388) (primMulInt (Neg vuz3180) (Neg vuz3190))) (Neg vuz387))",fontsize=16,color="black",shape="box"];8223 -> 8367[label="",style="solid", color="black", weight=3];
67.83/34.96	8224[label="primQuotInt (Pos vuz390) (gcd2 (primEqInt (primPlusInt (Neg vuz393) (primMulInt (Pos vuz3180) (Neg vuz3190))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz392) (primMulInt (Pos vuz3180) (Neg vuz3190))) (Pos vuz391))",fontsize=16,color="black",shape="box"];8224 -> 8368[label="",style="solid", color="black", weight=3];
67.83/34.96	8225[label="primQuotInt (Pos vuz390) (gcd2 (primEqInt (primPlusInt (Neg vuz393) (primMulInt (Neg vuz3180) (Neg vuz3190))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz392) (primMulInt (Neg vuz3180) (Neg vuz3190))) (Pos vuz391))",fontsize=16,color="black",shape="box"];8225 -> 8369[label="",style="solid", color="black", weight=3];
67.83/34.96	8226[label="primQuotInt (Pos vuz394) (gcd2 (primEqInt (primPlusInt (Pos vuz397) (primMulInt (Pos vuz3180) (Neg vuz3190))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz396) (primMulInt (Pos vuz3180) (Neg vuz3190))) (Pos vuz395))",fontsize=16,color="black",shape="box"];8226 -> 8370[label="",style="solid", color="black", weight=3];
67.83/34.96	8227[label="primQuotInt (Pos vuz394) (gcd2 (primEqInt (primPlusInt (Pos vuz397) (primMulInt (Neg vuz3180) (Neg vuz3190))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz396) (primMulInt (Neg vuz3180) (Neg vuz3190))) (Pos vuz395))",fontsize=16,color="black",shape="box"];8227 -> 8371[label="",style="solid", color="black", weight=3];
67.83/34.96	9989[label="Pos vuz399",fontsize=16,color="green",shape="box"];8232[label="primQuotInt (Pos vuz398) (gcd2 False (Pos vuz399) (Pos vuz3190 * Pos vuz3170))",fontsize=16,color="black",shape="box"];8232 -> 8373[label="",style="solid", color="black", weight=3];
67.83/34.96	8233[label="primQuotInt (Pos vuz398) (gcd2 True (Pos vuz399) (Pos vuz3190 * Pos vuz3170))",fontsize=16,color="black",shape="box"];8233 -> 8374[label="",style="solid", color="black", weight=3];
67.83/34.96	8234[label="vuz31600",fontsize=16,color="green",shape="box"];8235[label="Succ vuz31700",fontsize=16,color="green",shape="box"];8236[label="vuz31600",fontsize=16,color="green",shape="box"];8237[label="Succ vuz31700",fontsize=16,color="green",shape="box"];8238[label="primQuotInt (primMinusNat (Succ vuz4010) (Succ vuz4000)) (reduce2D (primMinusNat vuz403 vuz402) (Neg vuz3190 * Pos (Succ vuz31700)))",fontsize=16,color="black",shape="box"];8238 -> 8375[label="",style="solid", color="black", weight=3];
67.83/34.96	8239[label="primQuotInt (primMinusNat (Succ vuz4010) Zero) (reduce2D (primMinusNat vuz403 vuz402) (Neg vuz3190 * Pos (Succ vuz31700)))",fontsize=16,color="black",shape="box"];8239 -> 8376[label="",style="solid", color="black", weight=3];
67.83/34.96	8240[label="primQuotInt (primMinusNat Zero (Succ vuz4000)) (reduce2D (primMinusNat vuz403 vuz402) (Neg vuz3190 * Pos (Succ vuz31700)))",fontsize=16,color="black",shape="box"];8240 -> 8377[label="",style="solid", color="black", weight=3];
67.83/34.96	8241[label="primQuotInt (primMinusNat Zero Zero) (reduce2D (primMinusNat vuz403 vuz402) (Neg vuz3190 * Pos (Succ vuz31700)))",fontsize=16,color="black",shape="box"];8241 -> 8378[label="",style="solid", color="black", weight=3];
67.83/34.96	8242[label="primQuotInt (Neg (Succ vuz4060)) (reduce2D (Neg (Succ vuz4060)) (Neg vuz3190 * Pos Zero))",fontsize=16,color="black",shape="box"];8242 -> 8379[label="",style="solid", color="black", weight=3];
67.83/34.96	8243[label="primQuotInt (Pos Zero) (reduce2D (Pos Zero) (Neg vuz3190 * Pos Zero))",fontsize=16,color="black",shape="box"];8243 -> 8380[label="",style="solid", color="black", weight=3];
67.83/34.96	8244[label="vuz31600",fontsize=16,color="green",shape="box"];8245[label="Succ vuz31700",fontsize=16,color="green",shape="box"];8246[label="vuz31600",fontsize=16,color="green",shape="box"];8247[label="Succ vuz31700",fontsize=16,color="green",shape="box"];8248[label="primQuotInt (primMinusNat (Succ vuz4090) (Succ vuz4080)) (reduce2D (primMinusNat vuz411 vuz410) (Pos vuz3190 * Pos (Succ vuz31700)))",fontsize=16,color="black",shape="box"];8248 -> 8381[label="",style="solid", color="black", weight=3];
67.83/34.96	8249[label="primQuotInt (primMinusNat (Succ vuz4090) Zero) (reduce2D (primMinusNat vuz411 vuz410) (Pos vuz3190 * Pos (Succ vuz31700)))",fontsize=16,color="black",shape="box"];8249 -> 8382[label="",style="solid", color="black", weight=3];
67.83/34.96	8250[label="primQuotInt (primMinusNat Zero (Succ vuz4080)) (reduce2D (primMinusNat vuz411 vuz410) (Pos vuz3190 * Pos (Succ vuz31700)))",fontsize=16,color="black",shape="box"];8250 -> 8383[label="",style="solid", color="black", weight=3];
67.83/34.96	8251[label="primQuotInt (primMinusNat Zero Zero) (reduce2D (primMinusNat vuz411 vuz410) (Pos vuz3190 * Pos (Succ vuz31700)))",fontsize=16,color="black",shape="box"];8251 -> 8384[label="",style="solid", color="black", weight=3];
67.83/34.96	8252[label="primQuotInt (Neg (Succ vuz4140)) (reduce2D (Neg (Succ vuz4140)) (Pos vuz3190 * Pos Zero))",fontsize=16,color="black",shape="box"];8252 -> 8385[label="",style="solid", color="black", weight=3];
67.83/34.96	8253[label="primQuotInt (Pos Zero) (reduce2D (Pos Zero) (Pos vuz3190 * Pos Zero))",fontsize=16,color="black",shape="box"];8253 -> 8386[label="",style="solid", color="black", weight=3];
67.83/34.96	9990[label="Pos vuz417",fontsize=16,color="green",shape="box"];8258[label="primQuotInt (Pos vuz416) (gcd2 False (Pos vuz417) (Neg vuz3190 * Pos vuz3170))",fontsize=16,color="black",shape="box"];8258 -> 8387[label="",style="solid", color="black", weight=3];
67.83/34.96	8259[label="primQuotInt (Pos vuz416) (gcd2 True (Pos vuz417) (Neg vuz3190 * Pos vuz3170))",fontsize=16,color="black",shape="box"];8259 -> 8388[label="",style="solid", color="black", weight=3];
67.83/34.96	8260[label="vuz31800",fontsize=16,color="green",shape="box"];8261[label="Succ vuz31900",fontsize=16,color="green",shape="box"];8262[label="vuz31800",fontsize=16,color="green",shape="box"];8263[label="Succ vuz31900",fontsize=16,color="green",shape="box"];8264[label="primQuotInt (primMinusNat (Succ vuz4190) (Succ vuz4180)) (reduce2D (primMinusNat vuz421 vuz420) (Pos (Succ vuz31900) * Neg vuz3170))",fontsize=16,color="black",shape="box"];8264 -> 8389[label="",style="solid", color="black", weight=3];
67.83/34.96	8265[label="primQuotInt (primMinusNat (Succ vuz4190) Zero) (reduce2D (primMinusNat vuz421 vuz420) (Pos (Succ vuz31900) * Neg vuz3170))",fontsize=16,color="black",shape="box"];8265 -> 8390[label="",style="solid", color="black", weight=3];
67.83/34.96	8266[label="primQuotInt (primMinusNat Zero (Succ vuz4180)) (reduce2D (primMinusNat vuz421 vuz420) (Pos (Succ vuz31900) * Neg vuz3170))",fontsize=16,color="black",shape="box"];8266 -> 8391[label="",style="solid", color="black", weight=3];
67.83/34.96	8267[label="primQuotInt (primMinusNat Zero Zero) (reduce2D (primMinusNat vuz421 vuz420) (Pos (Succ vuz31900) * Neg vuz3170))",fontsize=16,color="black",shape="box"];8267 -> 8392[label="",style="solid", color="black", weight=3];
67.83/34.96	8268[label="primQuotInt (Neg (Succ vuz4240)) (reduce2D (Neg (Succ vuz4240)) (Pos Zero * Neg vuz3170))",fontsize=16,color="black",shape="box"];8268 -> 8393[label="",style="solid", color="black", weight=3];
67.83/34.96	8269[label="primQuotInt (Pos Zero) (reduce2D (Pos Zero) (Pos Zero * Neg vuz3170))",fontsize=16,color="black",shape="box"];8269 -> 8394[label="",style="solid", color="black", weight=3];
67.83/34.96	9991[label="Neg vuz427",fontsize=16,color="green",shape="box"];8274[label="primQuotInt (Neg vuz426) (gcd2 False (Neg vuz427) (Neg vuz3190 * Neg vuz3170))",fontsize=16,color="black",shape="box"];8274 -> 8396[label="",style="solid", color="black", weight=3];
67.83/34.96	8275[label="primQuotInt (Neg vuz426) (gcd2 True (Neg vuz427) (Neg vuz3190 * Neg vuz3170))",fontsize=16,color="black",shape="box"];8275 -> 8397[label="",style="solid", color="black", weight=3];
67.83/34.96	9992[label="Neg vuz429",fontsize=16,color="green",shape="box"];8280[label="primQuotInt (Neg vuz428) (gcd2 False (Neg vuz429) (Pos vuz3190 * Neg vuz3170))",fontsize=16,color="black",shape="box"];8280 -> 8398[label="",style="solid", color="black", weight=3];
67.83/34.96	8281[label="primQuotInt (Neg vuz428) (gcd2 True (Neg vuz429) (Pos vuz3190 * Neg vuz3170))",fontsize=16,color="black",shape="box"];8281 -> 8399[label="",style="solid", color="black", weight=3];
67.83/34.96	8282[label="vuz31800",fontsize=16,color="green",shape="box"];8283[label="Succ vuz31900",fontsize=16,color="green",shape="box"];8284[label="vuz31800",fontsize=16,color="green",shape="box"];8285[label="Succ vuz31900",fontsize=16,color="green",shape="box"];8286[label="primQuotInt (primMinusNat (Succ vuz4310) (Succ vuz4300)) (reduce2D (primMinusNat vuz433 vuz432) (Neg (Succ vuz31900) * Neg vuz3170))",fontsize=16,color="black",shape="box"];8286 -> 8400[label="",style="solid", color="black", weight=3];
67.83/34.96	8287[label="primQuotInt (primMinusNat (Succ vuz4310) Zero) (reduce2D (primMinusNat vuz433 vuz432) (Neg (Succ vuz31900) * Neg vuz3170))",fontsize=16,color="black",shape="box"];8287 -> 8401[label="",style="solid", color="black", weight=3];
67.83/34.96	8288[label="primQuotInt (primMinusNat Zero (Succ vuz4300)) (reduce2D (primMinusNat vuz433 vuz432) (Neg (Succ vuz31900) * Neg vuz3170))",fontsize=16,color="black",shape="box"];8288 -> 8402[label="",style="solid", color="black", weight=3];
67.83/34.96	8289[label="primQuotInt (primMinusNat Zero Zero) (reduce2D (primMinusNat vuz433 vuz432) (Neg (Succ vuz31900) * Neg vuz3170))",fontsize=16,color="black",shape="box"];8289 -> 8403[label="",style="solid", color="black", weight=3];
67.83/34.96	8290[label="primQuotInt (Neg (Succ vuz4360)) (reduce2D (Neg (Succ vuz4360)) (Neg Zero * Neg vuz3170))",fontsize=16,color="black",shape="box"];8290 -> 8404[label="",style="solid", color="black", weight=3];
67.83/34.96	8291[label="primQuotInt (Pos Zero) (reduce2D (Pos Zero) (Neg Zero * Neg vuz3170))",fontsize=16,color="black",shape="box"];8291 -> 8405[label="",style="solid", color="black", weight=3];
67.83/34.96	8292[label="vuz31800",fontsize=16,color="green",shape="box"];8293[label="Succ vuz31900",fontsize=16,color="green",shape="box"];8294[label="vuz31800",fontsize=16,color="green",shape="box"];8295[label="Succ vuz31900",fontsize=16,color="green",shape="box"];8296[label="primQuotInt (primMinusNat (Succ vuz4390) (Succ vuz4380)) (reduce2D (primMinusNat vuz441 vuz440) (Pos (Succ vuz31900) * Pos vuz3170))",fontsize=16,color="black",shape="box"];8296 -> 8406[label="",style="solid", color="black", weight=3];
67.83/34.96	8297[label="primQuotInt (primMinusNat (Succ vuz4390) Zero) (reduce2D (primMinusNat vuz441 vuz440) (Pos (Succ vuz31900) * Pos vuz3170))",fontsize=16,color="black",shape="box"];8297 -> 8407[label="",style="solid", color="black", weight=3];
67.83/34.96	8298[label="primQuotInt (primMinusNat Zero (Succ vuz4380)) (reduce2D (primMinusNat vuz441 vuz440) (Pos (Succ vuz31900) * Pos vuz3170))",fontsize=16,color="black",shape="box"];8298 -> 8408[label="",style="solid", color="black", weight=3];
67.83/34.96	8299[label="primQuotInt (primMinusNat Zero Zero) (reduce2D (primMinusNat vuz441 vuz440) (Pos (Succ vuz31900) * Pos vuz3170))",fontsize=16,color="black",shape="box"];8299 -> 8409[label="",style="solid", color="black", weight=3];
67.83/34.96	8300[label="primQuotInt (Neg (Succ vuz4440)) (reduce2D (Neg (Succ vuz4440)) (Pos Zero * Pos vuz3170))",fontsize=16,color="black",shape="box"];8300 -> 8410[label="",style="solid", color="black", weight=3];
67.83/34.96	8301[label="primQuotInt (Pos Zero) (reduce2D (Pos Zero) (Pos Zero * Pos vuz3170))",fontsize=16,color="black",shape="box"];8301 -> 8411[label="",style="solid", color="black", weight=3];
67.83/34.96	9993[label="Neg vuz447",fontsize=16,color="green",shape="box"];8306[label="primQuotInt (Neg vuz446) (gcd2 False (Neg vuz447) (Neg vuz3190 * Pos vuz3170))",fontsize=16,color="black",shape="box"];8306 -> 8412[label="",style="solid", color="black", weight=3];
67.83/34.96	8307[label="primQuotInt (Neg vuz446) (gcd2 True (Neg vuz447) (Neg vuz3190 * Pos vuz3170))",fontsize=16,color="black",shape="box"];8307 -> 8413[label="",style="solid", color="black", weight=3];
67.83/34.96	9994[label="Neg vuz349",fontsize=16,color="green",shape="box"];8312[label="primQuotInt (Neg vuz348) (gcd2 False (Neg vuz349) (Pos vuz3190 * Pos vuz3170))",fontsize=16,color="black",shape="box"];8312 -> 8414[label="",style="solid", color="black", weight=3];
67.83/34.96	8313[label="primQuotInt (Neg vuz348) (gcd2 True (Neg vuz349) (Pos vuz3190 * Pos vuz3170))",fontsize=16,color="black",shape="box"];8313 -> 8415[label="",style="solid", color="black", weight=3];
67.83/34.96	8314[label="vuz31800",fontsize=16,color="green",shape="box"];8315[label="Succ vuz31900",fontsize=16,color="green",shape="box"];8316[label="vuz31800",fontsize=16,color="green",shape="box"];8317[label="Succ vuz31900",fontsize=16,color="green",shape="box"];8318[label="primQuotInt (primMinusNat (Succ vuz4490) (Succ vuz4480)) (reduce2D (primMinusNat vuz451 vuz450) (Neg (Succ vuz31900) * Pos vuz3170))",fontsize=16,color="black",shape="box"];8318 -> 8416[label="",style="solid", color="black", weight=3];
67.83/34.96	8319[label="primQuotInt (primMinusNat (Succ vuz4490) Zero) (reduce2D (primMinusNat vuz451 vuz450) (Neg (Succ vuz31900) * Pos vuz3170))",fontsize=16,color="black",shape="box"];8319 -> 8417[label="",style="solid", color="black", weight=3];
67.83/34.96	8320[label="primQuotInt (primMinusNat Zero (Succ vuz4480)) (reduce2D (primMinusNat vuz451 vuz450) (Neg (Succ vuz31900) * Pos vuz3170))",fontsize=16,color="black",shape="box"];8320 -> 8418[label="",style="solid", color="black", weight=3];
67.83/34.96	8321[label="primQuotInt (primMinusNat Zero Zero) (reduce2D (primMinusNat vuz451 vuz450) (Neg (Succ vuz31900) * Pos vuz3170))",fontsize=16,color="black",shape="box"];8321 -> 8419[label="",style="solid", color="black", weight=3];
67.83/34.96	8322[label="primQuotInt (Neg (Succ vuz4540)) (reduce2D (Neg (Succ vuz4540)) (Neg Zero * Pos vuz3170))",fontsize=16,color="black",shape="box"];8322 -> 8420[label="",style="solid", color="black", weight=3];
67.83/34.96	8323[label="primQuotInt (Pos Zero) (reduce2D (Pos Zero) (Neg Zero * Pos vuz3170))",fontsize=16,color="black",shape="box"];8323 -> 8421[label="",style="solid", color="black", weight=3];
67.83/34.96	9995[label="Pos vuz355",fontsize=16,color="green",shape="box"];8328[label="primQuotInt (Pos vuz354) (gcd2 False (Pos vuz355) (Pos vuz3190 * Neg vuz3170))",fontsize=16,color="black",shape="box"];8328 -> 8422[label="",style="solid", color="black", weight=3];
67.83/34.96	8329[label="primQuotInt (Pos vuz354) (gcd2 True (Pos vuz355) (Pos vuz3190 * Neg vuz3170))",fontsize=16,color="black",shape="box"];8329 -> 8423[label="",style="solid", color="black", weight=3];
67.83/34.96	8330[label="vuz31600",fontsize=16,color="green",shape="box"];8331[label="Succ vuz31700",fontsize=16,color="green",shape="box"];8332[label="vuz31600",fontsize=16,color="green",shape="box"];8333[label="Succ vuz31700",fontsize=16,color="green",shape="box"];8334[label="primQuotInt (primMinusNat (Succ vuz4570) (Succ vuz4560)) (reduce2D (primMinusNat vuz459 vuz458) (Neg vuz3190 * Neg (Succ vuz31700)))",fontsize=16,color="black",shape="box"];8334 -> 8424[label="",style="solid", color="black", weight=3];
67.83/34.96	8335[label="primQuotInt (primMinusNat (Succ vuz4570) Zero) (reduce2D (primMinusNat vuz459 vuz458) (Neg vuz3190 * Neg (Succ vuz31700)))",fontsize=16,color="black",shape="box"];8335 -> 8425[label="",style="solid", color="black", weight=3];
67.83/34.96	8336[label="primQuotInt (primMinusNat Zero (Succ vuz4560)) (reduce2D (primMinusNat vuz459 vuz458) (Neg vuz3190 * Neg (Succ vuz31700)))",fontsize=16,color="black",shape="box"];8336 -> 8426[label="",style="solid", color="black", weight=3];
67.83/34.96	8337[label="primQuotInt (primMinusNat Zero Zero) (reduce2D (primMinusNat vuz459 vuz458) (Neg vuz3190 * Neg (Succ vuz31700)))",fontsize=16,color="black",shape="box"];8337 -> 8427[label="",style="solid", color="black", weight=3];
67.83/34.96	8338[label="primQuotInt (Neg (Succ vuz4620)) (reduce2D (Neg (Succ vuz4620)) (Neg vuz3190 * Neg Zero))",fontsize=16,color="black",shape="box"];8338 -> 8428[label="",style="solid", color="black", weight=3];
67.83/34.96	8339[label="primQuotInt (Pos Zero) (reduce2D (Pos Zero) (Neg vuz3190 * Neg Zero))",fontsize=16,color="black",shape="box"];8339 -> 8429[label="",style="solid", color="black", weight=3];
67.83/34.96	8340[label="vuz31600",fontsize=16,color="green",shape="box"];8341[label="Succ vuz31700",fontsize=16,color="green",shape="box"];8342[label="vuz31600",fontsize=16,color="green",shape="box"];8343[label="Succ vuz31700",fontsize=16,color="green",shape="box"];8344[label="primQuotInt (primMinusNat (Succ vuz4650) (Succ vuz4640)) (reduce2D (primMinusNat vuz467 vuz466) (Pos vuz3190 * Neg (Succ vuz31700)))",fontsize=16,color="black",shape="box"];8344 -> 8430[label="",style="solid", color="black", weight=3];
67.83/34.96	8345[label="primQuotInt (primMinusNat (Succ vuz4650) Zero) (reduce2D (primMinusNat vuz467 vuz466) (Pos vuz3190 * Neg (Succ vuz31700)))",fontsize=16,color="black",shape="box"];8345 -> 8431[label="",style="solid", color="black", weight=3];
67.83/34.96	8346[label="primQuotInt (primMinusNat Zero (Succ vuz4640)) (reduce2D (primMinusNat vuz467 vuz466) (Pos vuz3190 * Neg (Succ vuz31700)))",fontsize=16,color="black",shape="box"];8346 -> 8432[label="",style="solid", color="black", weight=3];
67.83/34.96	8347[label="primQuotInt (primMinusNat Zero Zero) (reduce2D (primMinusNat vuz467 vuz466) (Pos vuz3190 * Neg (Succ vuz31700)))",fontsize=16,color="black",shape="box"];8347 -> 8433[label="",style="solid", color="black", weight=3];
67.83/34.96	8348[label="primQuotInt (Neg (Succ vuz4700)) (reduce2D (Neg (Succ vuz4700)) (Pos vuz3190 * Neg Zero))",fontsize=16,color="black",shape="box"];8348 -> 8434[label="",style="solid", color="black", weight=3];
67.83/34.96	8349[label="primQuotInt (Pos Zero) (reduce2D (Pos Zero) (Pos vuz3190 * Neg Zero))",fontsize=16,color="black",shape="box"];8349 -> 8435[label="",style="solid", color="black", weight=3];
67.83/34.96	9996[label="Pos vuz361",fontsize=16,color="green",shape="box"];8354[label="primQuotInt (Pos vuz360) (gcd2 False (Pos vuz361) (Neg vuz3190 * Neg vuz3170))",fontsize=16,color="black",shape="box"];8354 -> 8436[label="",style="solid", color="black", weight=3];
67.83/34.96	8355[label="primQuotInt (Pos vuz360) (gcd2 True (Pos vuz361) (Neg vuz3190 * Neg vuz3170))",fontsize=16,color="black",shape="box"];8355 -> 8437[label="",style="solid", color="black", weight=3];
67.83/34.96	8356 -> 8438[label="",style="dashed", color="red", weight=0];
67.83/34.96	8356[label="primQuotInt (Pos vuz366) (gcd2 (primEqInt (primPlusInt (Pos vuz369) (Pos (primMulNat vuz3180 vuz3190))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz368) (Pos (primMulNat vuz3180 vuz3190))) (Pos vuz367))",fontsize=16,color="magenta"];8356 -> 8439[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8356 -> 8440[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8357 -> 8447[label="",style="dashed", color="red", weight=0];
67.83/34.96	8357[label="primQuotInt (Pos vuz366) (gcd2 (primEqInt (primPlusInt (Pos vuz369) (Neg (primMulNat vuz3180 vuz3190))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz368) (Neg (primMulNat vuz3180 vuz3190))) (Pos vuz367))",fontsize=16,color="magenta"];8357 -> 8448[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8357 -> 8449[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8358 -> 8456[label="",style="dashed", color="red", weight=0];
67.83/34.96	8358[label="primQuotInt (Pos vuz370) (gcd2 (primEqInt (primPlusInt (Neg vuz373) (Pos (primMulNat vuz3180 vuz3190))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz372) (Pos (primMulNat vuz3180 vuz3190))) (Pos vuz371))",fontsize=16,color="magenta"];8358 -> 8457[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8358 -> 8458[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8359 -> 8465[label="",style="dashed", color="red", weight=0];
67.83/34.96	8359[label="primQuotInt (Pos vuz370) (gcd2 (primEqInt (primPlusInt (Neg vuz373) (Neg (primMulNat vuz3180 vuz3190))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz372) (Neg (primMulNat vuz3180 vuz3190))) (Pos vuz371))",fontsize=16,color="magenta"];8359 -> 8466[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8359 -> 8467[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8360 -> 8474[label="",style="dashed", color="red", weight=0];
67.83/34.96	8360[label="primQuotInt (Neg vuz374) (gcd2 (primEqInt (primPlusInt (Neg vuz377) (Pos (primMulNat vuz3180 vuz3190))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz376) (Pos (primMulNat vuz3180 vuz3190))) (Neg vuz375))",fontsize=16,color="magenta"];8360 -> 8475[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8360 -> 8476[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8361 -> 8483[label="",style="dashed", color="red", weight=0];
67.83/34.96	8361[label="primQuotInt (Neg vuz374) (gcd2 (primEqInt (primPlusInt (Neg vuz377) (Neg (primMulNat vuz3180 vuz3190))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz376) (Neg (primMulNat vuz3180 vuz3190))) (Neg vuz375))",fontsize=16,color="magenta"];8361 -> 8484[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8361 -> 8485[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8362 -> 8492[label="",style="dashed", color="red", weight=0];
67.83/34.96	8362[label="primQuotInt (Neg vuz378) (gcd2 (primEqInt (primPlusInt (Pos vuz381) (Pos (primMulNat vuz3180 vuz3190))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz380) (Pos (primMulNat vuz3180 vuz3190))) (Neg vuz379))",fontsize=16,color="magenta"];8362 -> 8493[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8362 -> 8494[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8363 -> 8501[label="",style="dashed", color="red", weight=0];
67.83/34.96	8363[label="primQuotInt (Neg vuz378) (gcd2 (primEqInt (primPlusInt (Pos vuz381) (Neg (primMulNat vuz3180 vuz3190))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz380) (Neg (primMulNat vuz3180 vuz3190))) (Neg vuz379))",fontsize=16,color="magenta"];8363 -> 8502[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8363 -> 8503[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8364 -> 8501[label="",style="dashed", color="red", weight=0];
67.83/34.96	8364[label="primQuotInt (Neg vuz382) (gcd2 (primEqInt (primPlusInt (Pos vuz385) (Neg (primMulNat vuz3180 vuz3190))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz384) (Neg (primMulNat vuz3180 vuz3190))) (Neg vuz383))",fontsize=16,color="magenta"];8364 -> 8504[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8364 -> 8505[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8364 -> 8506[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8364 -> 8507[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8364 -> 8508[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8364 -> 8509[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8365 -> 8492[label="",style="dashed", color="red", weight=0];
67.83/34.96	8365[label="primQuotInt (Neg vuz382) (gcd2 (primEqInt (primPlusInt (Pos vuz385) (Pos (primMulNat vuz3180 vuz3190))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz384) (Pos (primMulNat vuz3180 vuz3190))) (Neg vuz383))",fontsize=16,color="magenta"];8365 -> 8495[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8365 -> 8496[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8365 -> 8497[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8365 -> 8498[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8365 -> 8499[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8365 -> 8500[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8366 -> 8483[label="",style="dashed", color="red", weight=0];
67.83/34.96	8366[label="primQuotInt (Neg vuz386) (gcd2 (primEqInt (primPlusInt (Neg vuz389) (Neg (primMulNat vuz3180 vuz3190))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz388) (Neg (primMulNat vuz3180 vuz3190))) (Neg vuz387))",fontsize=16,color="magenta"];8366 -> 8486[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8366 -> 8487[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8366 -> 8488[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8366 -> 8489[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8366 -> 8490[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8366 -> 8491[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8367 -> 8474[label="",style="dashed", color="red", weight=0];
67.83/34.96	8367[label="primQuotInt (Neg vuz386) (gcd2 (primEqInt (primPlusInt (Neg vuz389) (Pos (primMulNat vuz3180 vuz3190))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz388) (Pos (primMulNat vuz3180 vuz3190))) (Neg vuz387))",fontsize=16,color="magenta"];8367 -> 8477[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8367 -> 8478[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8367 -> 8479[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8367 -> 8480[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8367 -> 8481[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8367 -> 8482[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8368 -> 8465[label="",style="dashed", color="red", weight=0];
67.83/34.96	8368[label="primQuotInt (Pos vuz390) (gcd2 (primEqInt (primPlusInt (Neg vuz393) (Neg (primMulNat vuz3180 vuz3190))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz392) (Neg (primMulNat vuz3180 vuz3190))) (Pos vuz391))",fontsize=16,color="magenta"];8368 -> 8468[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8368 -> 8469[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8368 -> 8470[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8368 -> 8471[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8368 -> 8472[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8368 -> 8473[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8369 -> 8456[label="",style="dashed", color="red", weight=0];
67.83/34.96	8369[label="primQuotInt (Pos vuz390) (gcd2 (primEqInt (primPlusInt (Neg vuz393) (Pos (primMulNat vuz3180 vuz3190))) (fromInt (Pos Zero))) (primPlusInt (Neg vuz392) (Pos (primMulNat vuz3180 vuz3190))) (Pos vuz391))",fontsize=16,color="magenta"];8369 -> 8459[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8369 -> 8460[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8369 -> 8461[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8369 -> 8462[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8369 -> 8463[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8369 -> 8464[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8370 -> 8447[label="",style="dashed", color="red", weight=0];
67.83/34.96	8370[label="primQuotInt (Pos vuz394) (gcd2 (primEqInt (primPlusInt (Pos vuz397) (Neg (primMulNat vuz3180 vuz3190))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz396) (Neg (primMulNat vuz3180 vuz3190))) (Pos vuz395))",fontsize=16,color="magenta"];8370 -> 8450[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8370 -> 8451[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8370 -> 8452[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8370 -> 8453[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8370 -> 8454[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8370 -> 8455[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8371 -> 8438[label="",style="dashed", color="red", weight=0];
67.83/34.96	8371[label="primQuotInt (Pos vuz394) (gcd2 (primEqInt (primPlusInt (Pos vuz397) (Pos (primMulNat vuz3180 vuz3190))) (fromInt (Pos Zero))) (primPlusInt (Pos vuz396) (Pos (primMulNat vuz3180 vuz3190))) (Pos vuz395))",fontsize=16,color="magenta"];8371 -> 8441[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8371 -> 8442[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8371 -> 8443[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8371 -> 8444[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8371 -> 8445[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8371 -> 8446[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8373[label="primQuotInt (Pos vuz398) (gcd0 (Pos vuz399) (Pos vuz3190 * Pos vuz3170))",fontsize=16,color="black",shape="triangle"];8373 -> 8510[label="",style="solid", color="black", weight=3];
67.83/34.96	8374 -> 8511[label="",style="dashed", color="red", weight=0];
67.83/34.96	8374[label="primQuotInt (Pos vuz398) (gcd1 (Pos vuz3190 * Pos vuz3170 == fromInt (Pos Zero)) (Pos vuz399) (Pos vuz3190 * Pos vuz3170))",fontsize=16,color="magenta"];8374 -> 8512[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8375 -> 7677[label="",style="dashed", color="red", weight=0];
67.83/34.96	8375[label="primQuotInt (primMinusNat vuz4010 vuz4000) (reduce2D (primMinusNat vuz4010 vuz4000) (Neg vuz3190 * Pos (Succ vuz31700)))",fontsize=16,color="magenta"];8375 -> 8513[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8375 -> 8514[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8375 -> 8515[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8375 -> 8516[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8376[label="primQuotInt (Pos (Succ vuz4010)) (reduce2D (Pos (Succ vuz4010)) (Neg vuz3190 * Pos (Succ vuz31700)))",fontsize=16,color="black",shape="box"];8376 -> 8517[label="",style="solid", color="black", weight=3];
67.83/34.96	8377[label="primQuotInt (Neg (Succ vuz4000)) (reduce2D (Neg (Succ vuz4000)) (Neg vuz3190 * Pos (Succ vuz31700)))",fontsize=16,color="black",shape="box"];8377 -> 8518[label="",style="solid", color="black", weight=3];
67.83/34.96	8378[label="primQuotInt (Pos Zero) (reduce2D (Pos Zero) (Neg vuz3190 * Pos (Succ vuz31700)))",fontsize=16,color="black",shape="box"];8378 -> 8519[label="",style="solid", color="black", weight=3];
67.83/34.96	8379[label="primQuotInt (Neg (Succ vuz4060)) (gcd (Neg (Succ vuz4060)) (Neg vuz3190 * Pos Zero))",fontsize=16,color="black",shape="box"];8379 -> 8520[label="",style="solid", color="black", weight=3];
67.83/34.96	8380[label="primQuotInt (Pos Zero) (gcd (Pos Zero) (Neg vuz3190 * Pos Zero))",fontsize=16,color="black",shape="box"];8380 -> 8521[label="",style="solid", color="black", weight=3];
67.83/34.96	8381 -> 7691[label="",style="dashed", color="red", weight=0];
67.83/34.96	8381[label="primQuotInt (primMinusNat vuz4090 vuz4080) (reduce2D (primMinusNat vuz4090 vuz4080) (Pos vuz3190 * Pos (Succ vuz31700)))",fontsize=16,color="magenta"];8381 -> 8522[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8381 -> 8523[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8381 -> 8524[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8381 -> 8525[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8382[label="primQuotInt (Pos (Succ vuz4090)) (reduce2D (Pos (Succ vuz4090)) (Pos vuz3190 * Pos (Succ vuz31700)))",fontsize=16,color="black",shape="box"];8382 -> 8526[label="",style="solid", color="black", weight=3];
67.83/34.96	8383[label="primQuotInt (Neg (Succ vuz4080)) (reduce2D (Neg (Succ vuz4080)) (Pos vuz3190 * Pos (Succ vuz31700)))",fontsize=16,color="black",shape="box"];8383 -> 8527[label="",style="solid", color="black", weight=3];
67.83/34.96	8384[label="primQuotInt (Pos Zero) (reduce2D (Pos Zero) (Pos vuz3190 * Pos (Succ vuz31700)))",fontsize=16,color="black",shape="box"];8384 -> 8528[label="",style="solid", color="black", weight=3];
67.83/34.96	8385[label="primQuotInt (Neg (Succ vuz4140)) (gcd (Neg (Succ vuz4140)) (Pos vuz3190 * Pos Zero))",fontsize=16,color="black",shape="box"];8385 -> 8529[label="",style="solid", color="black", weight=3];
67.83/34.96	8386[label="primQuotInt (Pos Zero) (gcd (Pos Zero) (Pos vuz3190 * Pos Zero))",fontsize=16,color="black",shape="box"];8386 -> 8530[label="",style="solid", color="black", weight=3];
67.83/34.96	8387[label="primQuotInt (Pos vuz416) (gcd0 (Pos vuz417) (Neg vuz3190 * Pos vuz3170))",fontsize=16,color="black",shape="triangle"];8387 -> 8531[label="",style="solid", color="black", weight=3];
67.83/34.96	8388 -> 8532[label="",style="dashed", color="red", weight=0];
67.83/34.96	8388[label="primQuotInt (Pos vuz416) (gcd1 (Neg vuz3190 * Pos vuz3170 == fromInt (Pos Zero)) (Pos vuz417) (Neg vuz3190 * Pos vuz3170))",fontsize=16,color="magenta"];8388 -> 8533[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8389 -> 7723[label="",style="dashed", color="red", weight=0];
67.83/34.96	8389[label="primQuotInt (primMinusNat vuz4190 vuz4180) (reduce2D (primMinusNat vuz4190 vuz4180) (Pos (Succ vuz31900) * Neg vuz3170))",fontsize=16,color="magenta"];8389 -> 8534[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8389 -> 8535[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8389 -> 8536[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8389 -> 8537[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8390[label="primQuotInt (Pos (Succ vuz4190)) (reduce2D (Pos (Succ vuz4190)) (Pos (Succ vuz31900) * Neg vuz3170))",fontsize=16,color="black",shape="box"];8390 -> 8538[label="",style="solid", color="black", weight=3];
67.83/34.96	8391[label="primQuotInt (Neg (Succ vuz4180)) (reduce2D (Neg (Succ vuz4180)) (Pos (Succ vuz31900) * Neg vuz3170))",fontsize=16,color="black",shape="box"];8391 -> 8539[label="",style="solid", color="black", weight=3];
67.83/34.96	8392[label="primQuotInt (Pos Zero) (reduce2D (Pos Zero) (Pos (Succ vuz31900) * Neg vuz3170))",fontsize=16,color="black",shape="box"];8392 -> 8540[label="",style="solid", color="black", weight=3];
67.83/34.96	8393[label="primQuotInt (Neg (Succ vuz4240)) (gcd (Neg (Succ vuz4240)) (Pos Zero * Neg vuz3170))",fontsize=16,color="black",shape="box"];8393 -> 8541[label="",style="solid", color="black", weight=3];
67.83/34.96	8394[label="primQuotInt (Pos Zero) (gcd (Pos Zero) (Pos Zero * Neg vuz3170))",fontsize=16,color="black",shape="box"];8394 -> 8542[label="",style="solid", color="black", weight=3];
67.83/34.96	8396[label="primQuotInt (Neg vuz426) (gcd0 (Neg vuz427) (Neg vuz3190 * Neg vuz3170))",fontsize=16,color="black",shape="triangle"];8396 -> 8543[label="",style="solid", color="black", weight=3];
67.83/34.96	8397 -> 8544[label="",style="dashed", color="red", weight=0];
67.83/34.96	8397[label="primQuotInt (Neg vuz426) (gcd1 (Neg vuz3190 * Neg vuz3170 == fromInt (Pos Zero)) (Neg vuz427) (Neg vuz3190 * Neg vuz3170))",fontsize=16,color="magenta"];8397 -> 8545[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8398[label="primQuotInt (Neg vuz428) (gcd0 (Neg vuz429) (Pos vuz3190 * Neg vuz3170))",fontsize=16,color="black",shape="triangle"];8398 -> 8546[label="",style="solid", color="black", weight=3];
67.83/34.96	8399 -> 8547[label="",style="dashed", color="red", weight=0];
67.83/34.96	8399[label="primQuotInt (Neg vuz428) (gcd1 (Pos vuz3190 * Neg vuz3170 == fromInt (Pos Zero)) (Neg vuz429) (Pos vuz3190 * Neg vuz3170))",fontsize=16,color="magenta"];8399 -> 8548[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8400 -> 7773[label="",style="dashed", color="red", weight=0];
67.83/34.96	8400[label="primQuotInt (primMinusNat vuz4310 vuz4300) (reduce2D (primMinusNat vuz4310 vuz4300) (Neg (Succ vuz31900) * Neg vuz3170))",fontsize=16,color="magenta"];8400 -> 8549[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8400 -> 8550[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8400 -> 8551[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8400 -> 8552[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8401[label="primQuotInt (Pos (Succ vuz4310)) (reduce2D (Pos (Succ vuz4310)) (Neg (Succ vuz31900) * Neg vuz3170))",fontsize=16,color="black",shape="box"];8401 -> 8553[label="",style="solid", color="black", weight=3];
67.83/34.96	8402[label="primQuotInt (Neg (Succ vuz4300)) (reduce2D (Neg (Succ vuz4300)) (Neg (Succ vuz31900) * Neg vuz3170))",fontsize=16,color="black",shape="box"];8402 -> 8554[label="",style="solid", color="black", weight=3];
67.83/34.96	8403[label="primQuotInt (Pos Zero) (reduce2D (Pos Zero) (Neg (Succ vuz31900) * Neg vuz3170))",fontsize=16,color="black",shape="box"];8403 -> 8555[label="",style="solid", color="black", weight=3];
67.83/34.96	8404[label="primQuotInt (Neg (Succ vuz4360)) (gcd (Neg (Succ vuz4360)) (Neg Zero * Neg vuz3170))",fontsize=16,color="black",shape="box"];8404 -> 8556[label="",style="solid", color="black", weight=3];
67.83/34.96	8405[label="primQuotInt (Pos Zero) (gcd (Pos Zero) (Neg Zero * Neg vuz3170))",fontsize=16,color="black",shape="box"];8405 -> 8557[label="",style="solid", color="black", weight=3];
67.83/34.96	8406 -> 7787[label="",style="dashed", color="red", weight=0];
67.83/34.96	8406[label="primQuotInt (primMinusNat vuz4390 vuz4380) (reduce2D (primMinusNat vuz4390 vuz4380) (Pos (Succ vuz31900) * Pos vuz3170))",fontsize=16,color="magenta"];8406 -> 8558[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8406 -> 8559[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8406 -> 8560[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8406 -> 8561[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8407[label="primQuotInt (Pos (Succ vuz4390)) (reduce2D (Pos (Succ vuz4390)) (Pos (Succ vuz31900) * Pos vuz3170))",fontsize=16,color="black",shape="box"];8407 -> 8562[label="",style="solid", color="black", weight=3];
67.83/34.96	8408[label="primQuotInt (Neg (Succ vuz4380)) (reduce2D (Neg (Succ vuz4380)) (Pos (Succ vuz31900) * Pos vuz3170))",fontsize=16,color="black",shape="box"];8408 -> 8563[label="",style="solid", color="black", weight=3];
67.83/34.96	8409[label="primQuotInt (Pos Zero) (reduce2D (Pos Zero) (Pos (Succ vuz31900) * Pos vuz3170))",fontsize=16,color="black",shape="box"];8409 -> 8564[label="",style="solid", color="black", weight=3];
67.83/34.96	8410[label="primQuotInt (Neg (Succ vuz4440)) (gcd (Neg (Succ vuz4440)) (Pos Zero * Pos vuz3170))",fontsize=16,color="black",shape="box"];8410 -> 8565[label="",style="solid", color="black", weight=3];
67.83/34.96	8411[label="primQuotInt (Pos Zero) (gcd (Pos Zero) (Pos Zero * Pos vuz3170))",fontsize=16,color="black",shape="box"];8411 -> 8566[label="",style="solid", color="black", weight=3];
67.83/34.96	8412[label="primQuotInt (Neg vuz446) (gcd0 (Neg vuz447) (Neg vuz3190 * Pos vuz3170))",fontsize=16,color="black",shape="triangle"];8412 -> 8567[label="",style="solid", color="black", weight=3];
67.83/34.96	8413 -> 8568[label="",style="dashed", color="red", weight=0];
67.83/34.96	8413[label="primQuotInt (Neg vuz446) (gcd1 (Neg vuz3190 * Pos vuz3170 == fromInt (Pos Zero)) (Neg vuz447) (Neg vuz3190 * Pos vuz3170))",fontsize=16,color="magenta"];8413 -> 8569[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8414[label="primQuotInt (Neg vuz348) (gcd0 (Neg vuz349) (Pos vuz3190 * Pos vuz3170))",fontsize=16,color="black",shape="triangle"];8414 -> 8570[label="",style="solid", color="black", weight=3];
67.83/34.96	8415 -> 8571[label="",style="dashed", color="red", weight=0];
67.83/34.96	8415[label="primQuotInt (Neg vuz348) (gcd1 (Pos vuz3190 * Pos vuz3170 == fromInt (Pos Zero)) (Neg vuz349) (Pos vuz3190 * Pos vuz3170))",fontsize=16,color="magenta"];8415 -> 8572[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8416 -> 7824[label="",style="dashed", color="red", weight=0];
67.83/34.96	8416[label="primQuotInt (primMinusNat vuz4490 vuz4480) (reduce2D (primMinusNat vuz4490 vuz4480) (Neg (Succ vuz31900) * Pos vuz3170))",fontsize=16,color="magenta"];8416 -> 8573[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8416 -> 8574[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8416 -> 8575[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8416 -> 8576[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8417[label="primQuotInt (Pos (Succ vuz4490)) (reduce2D (Pos (Succ vuz4490)) (Neg (Succ vuz31900) * Pos vuz3170))",fontsize=16,color="black",shape="box"];8417 -> 8577[label="",style="solid", color="black", weight=3];
67.83/34.96	8418[label="primQuotInt (Neg (Succ vuz4480)) (reduce2D (Neg (Succ vuz4480)) (Neg (Succ vuz31900) * Pos vuz3170))",fontsize=16,color="black",shape="box"];8418 -> 8578[label="",style="solid", color="black", weight=3];
67.83/34.96	8419[label="primQuotInt (Pos Zero) (reduce2D (Pos Zero) (Neg (Succ vuz31900) * Pos vuz3170))",fontsize=16,color="black",shape="box"];8419 -> 8579[label="",style="solid", color="black", weight=3];
67.83/34.96	8420[label="primQuotInt (Neg (Succ vuz4540)) (gcd (Neg (Succ vuz4540)) (Neg Zero * Pos vuz3170))",fontsize=16,color="black",shape="box"];8420 -> 8580[label="",style="solid", color="black", weight=3];
67.83/34.96	8421[label="primQuotInt (Pos Zero) (gcd (Pos Zero) (Neg Zero * Pos vuz3170))",fontsize=16,color="black",shape="box"];8421 -> 8581[label="",style="solid", color="black", weight=3];
67.83/34.96	8422[label="primQuotInt (Pos vuz354) (gcd0 (Pos vuz355) (Pos vuz3190 * Neg vuz3170))",fontsize=16,color="black",shape="triangle"];8422 -> 8582[label="",style="solid", color="black", weight=3];
67.83/34.96	8423 -> 8583[label="",style="dashed", color="red", weight=0];
67.83/34.96	8423[label="primQuotInt (Pos vuz354) (gcd1 (Pos vuz3190 * Neg vuz3170 == fromInt (Pos Zero)) (Pos vuz355) (Pos vuz3190 * Neg vuz3170))",fontsize=16,color="magenta"];8423 -> 8584[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8424 -> 7843[label="",style="dashed", color="red", weight=0];
67.83/34.96	8424[label="primQuotInt (primMinusNat vuz4570 vuz4560) (reduce2D (primMinusNat vuz4570 vuz4560) (Neg vuz3190 * Neg (Succ vuz31700)))",fontsize=16,color="magenta"];8424 -> 8585[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8424 -> 8586[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8424 -> 8587[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8424 -> 8588[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8425[label="primQuotInt (Pos (Succ vuz4570)) (reduce2D (Pos (Succ vuz4570)) (Neg vuz3190 * Neg (Succ vuz31700)))",fontsize=16,color="black",shape="box"];8425 -> 8589[label="",style="solid", color="black", weight=3];
67.83/34.96	8426[label="primQuotInt (Neg (Succ vuz4560)) (reduce2D (Neg (Succ vuz4560)) (Neg vuz3190 * Neg (Succ vuz31700)))",fontsize=16,color="black",shape="box"];8426 -> 8590[label="",style="solid", color="black", weight=3];
67.83/34.96	8427[label="primQuotInt (Pos Zero) (reduce2D (Pos Zero) (Neg vuz3190 * Neg (Succ vuz31700)))",fontsize=16,color="black",shape="box"];8427 -> 8591[label="",style="solid", color="black", weight=3];
67.83/34.96	8428[label="primQuotInt (Neg (Succ vuz4620)) (gcd (Neg (Succ vuz4620)) (Neg vuz3190 * Neg Zero))",fontsize=16,color="black",shape="box"];8428 -> 8592[label="",style="solid", color="black", weight=3];
67.83/34.96	8429[label="primQuotInt (Pos Zero) (gcd (Pos Zero) (Neg vuz3190 * Neg Zero))",fontsize=16,color="black",shape="box"];8429 -> 8593[label="",style="solid", color="black", weight=3];
67.83/34.96	8430 -> 7857[label="",style="dashed", color="red", weight=0];
67.83/34.96	8430[label="primQuotInt (primMinusNat vuz4650 vuz4640) (reduce2D (primMinusNat vuz4650 vuz4640) (Pos vuz3190 * Neg (Succ vuz31700)))",fontsize=16,color="magenta"];8430 -> 8594[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8430 -> 8595[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8430 -> 8596[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8430 -> 8597[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8431[label="primQuotInt (Pos (Succ vuz4650)) (reduce2D (Pos (Succ vuz4650)) (Pos vuz3190 * Neg (Succ vuz31700)))",fontsize=16,color="black",shape="box"];8431 -> 8598[label="",style="solid", color="black", weight=3];
67.83/34.96	8432[label="primQuotInt (Neg (Succ vuz4640)) (reduce2D (Neg (Succ vuz4640)) (Pos vuz3190 * Neg (Succ vuz31700)))",fontsize=16,color="black",shape="box"];8432 -> 8599[label="",style="solid", color="black", weight=3];
67.83/34.96	8433[label="primQuotInt (Pos Zero) (reduce2D (Pos Zero) (Pos vuz3190 * Neg (Succ vuz31700)))",fontsize=16,color="black",shape="box"];8433 -> 8600[label="",style="solid", color="black", weight=3];
67.83/34.96	8434[label="primQuotInt (Neg (Succ vuz4700)) (gcd (Neg (Succ vuz4700)) (Pos vuz3190 * Neg Zero))",fontsize=16,color="black",shape="box"];8434 -> 8601[label="",style="solid", color="black", weight=3];
67.83/34.96	8435[label="primQuotInt (Pos Zero) (gcd (Pos Zero) (Pos vuz3190 * Neg Zero))",fontsize=16,color="black",shape="box"];8435 -> 8602[label="",style="solid", color="black", weight=3];
67.83/34.96	8436[label="primQuotInt (Pos vuz360) (gcd0 (Pos vuz361) (Neg vuz3190 * Neg vuz3170))",fontsize=16,color="black",shape="triangle"];8436 -> 8603[label="",style="solid", color="black", weight=3];
67.83/34.96	8437 -> 8604[label="",style="dashed", color="red", weight=0];
67.83/34.96	8437[label="primQuotInt (Pos vuz360) (gcd1 (Neg vuz3190 * Neg vuz3170 == fromInt (Pos Zero)) (Pos vuz361) (Neg vuz3190 * Neg vuz3170))",fontsize=16,color="magenta"];8437 -> 8605[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8439 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.96	8439[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];8439 -> 8606[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8439 -> 8607[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8440 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.96	8440[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];8440 -> 8608[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8440 -> 8609[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8438[label="primQuotInt (Pos vuz366) (gcd2 (primEqInt (primPlusInt (Pos vuz369) (Pos vuz481)) (fromInt (Pos Zero))) (primPlusInt (Pos vuz368) (Pos vuz480)) (Pos vuz367))",fontsize=16,color="black",shape="triangle"];8438 -> 8610[label="",style="solid", color="black", weight=3];
67.83/34.96	8448 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.96	8448[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];8448 -> 8611[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8448 -> 8612[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8449 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.96	8449[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];8449 -> 8613[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8449 -> 8614[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8447[label="primQuotInt (Pos vuz366) (gcd2 (primEqInt (primPlusInt (Pos vuz369) (Neg vuz483)) (fromInt (Pos Zero))) (primPlusInt (Pos vuz368) (Neg vuz482)) (Pos vuz367))",fontsize=16,color="black",shape="triangle"];8447 -> 8615[label="",style="solid", color="black", weight=3];
67.83/34.96	8457 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.96	8457[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];8457 -> 8616[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8457 -> 8617[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8458 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.96	8458[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];8458 -> 8618[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8458 -> 8619[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8456[label="primQuotInt (Pos vuz370) (gcd2 (primEqInt (primPlusInt (Neg vuz373) (Pos vuz485)) (fromInt (Pos Zero))) (primPlusInt (Neg vuz372) (Pos vuz484)) (Pos vuz371))",fontsize=16,color="black",shape="triangle"];8456 -> 8620[label="",style="solid", color="black", weight=3];
67.83/34.96	8466 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.96	8466[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];8466 -> 8621[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8466 -> 8622[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8467 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.96	8467[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];8467 -> 8623[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8467 -> 8624[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8465[label="primQuotInt (Pos vuz370) (gcd2 (primEqInt (primPlusInt (Neg vuz373) (Neg vuz487)) (fromInt (Pos Zero))) (primPlusInt (Neg vuz372) (Neg vuz486)) (Pos vuz371))",fontsize=16,color="black",shape="triangle"];8465 -> 8625[label="",style="solid", color="black", weight=3];
67.83/34.96	8475 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.96	8475[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];8475 -> 8626[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8475 -> 8627[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8476 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.96	8476[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];8476 -> 8628[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8476 -> 8629[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8474[label="primQuotInt (Neg vuz374) (gcd2 (primEqInt (primPlusInt (Neg vuz377) (Pos vuz489)) (fromInt (Pos Zero))) (primPlusInt (Neg vuz376) (Pos vuz488)) (Neg vuz375))",fontsize=16,color="black",shape="triangle"];8474 -> 8630[label="",style="solid", color="black", weight=3];
67.83/34.96	8484 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.96	8484[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];8484 -> 8631[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8484 -> 8632[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8485 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.96	8485[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];8485 -> 8633[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8485 -> 8634[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8483[label="primQuotInt (Neg vuz374) (gcd2 (primEqInt (primPlusInt (Neg vuz377) (Neg vuz491)) (fromInt (Pos Zero))) (primPlusInt (Neg vuz376) (Neg vuz490)) (Neg vuz375))",fontsize=16,color="black",shape="triangle"];8483 -> 8635[label="",style="solid", color="black", weight=3];
67.83/34.96	8493 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.96	8493[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];8493 -> 8636[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8493 -> 8637[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8494 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.96	8494[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];8494 -> 8638[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8494 -> 8639[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8492[label="primQuotInt (Neg vuz378) (gcd2 (primEqInt (primPlusInt (Pos vuz381) (Pos vuz493)) (fromInt (Pos Zero))) (primPlusInt (Pos vuz380) (Pos vuz492)) (Neg vuz379))",fontsize=16,color="black",shape="triangle"];8492 -> 8640[label="",style="solid", color="black", weight=3];
67.83/34.96	8502 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.96	8502[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];8502 -> 8641[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8502 -> 8642[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8503 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.96	8503[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];8503 -> 8643[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8503 -> 8644[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8501[label="primQuotInt (Neg vuz378) (gcd2 (primEqInt (primPlusInt (Pos vuz381) (Neg vuz495)) (fromInt (Pos Zero))) (primPlusInt (Pos vuz380) (Neg vuz494)) (Neg vuz379))",fontsize=16,color="black",shape="triangle"];8501 -> 8645[label="",style="solid", color="black", weight=3];
67.83/34.96	8504[label="vuz383",fontsize=16,color="green",shape="box"];8505[label="vuz384",fontsize=16,color="green",shape="box"];8506 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.96	8506[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];8506 -> 8646[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8506 -> 8647[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8507[label="vuz385",fontsize=16,color="green",shape="box"];8508 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.96	8508[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];8508 -> 8648[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8508 -> 8649[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8509[label="vuz382",fontsize=16,color="green",shape="box"];8495[label="vuz383",fontsize=16,color="green",shape="box"];8496[label="vuz384",fontsize=16,color="green",shape="box"];8497[label="vuz385",fontsize=16,color="green",shape="box"];8498 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.96	8498[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];8498 -> 8650[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8498 -> 8651[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8499[label="vuz382",fontsize=16,color="green",shape="box"];8500 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.96	8500[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];8500 -> 8652[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8500 -> 8653[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8486 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.96	8486[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];8486 -> 8654[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8486 -> 8655[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8487[label="vuz387",fontsize=16,color="green",shape="box"];8488[label="vuz388",fontsize=16,color="green",shape="box"];8489[label="vuz386",fontsize=16,color="green",shape="box"];8490[label="vuz389",fontsize=16,color="green",shape="box"];8491 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.96	8491[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];8491 -> 8656[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8491 -> 8657[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8477 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.96	8477[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];8477 -> 8658[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8477 -> 8659[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8478[label="vuz387",fontsize=16,color="green",shape="box"];8479[label="vuz388",fontsize=16,color="green",shape="box"];8480 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.96	8480[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];8480 -> 8660[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8480 -> 8661[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8481[label="vuz386",fontsize=16,color="green",shape="box"];8482[label="vuz389",fontsize=16,color="green",shape="box"];8468[label="vuz392",fontsize=16,color="green",shape="box"];8469 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.96	8469[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];8469 -> 8662[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8469 -> 8663[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8470[label="vuz393",fontsize=16,color="green",shape="box"];8471[label="vuz390",fontsize=16,color="green",shape="box"];8472[label="vuz391",fontsize=16,color="green",shape="box"];8473 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.96	8473[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];8473 -> 8664[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8473 -> 8665[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8459[label="vuz392",fontsize=16,color="green",shape="box"];8460 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.96	8460[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];8460 -> 8666[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8460 -> 8667[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8461[label="vuz393",fontsize=16,color="green",shape="box"];8462[label="vuz390",fontsize=16,color="green",shape="box"];8463[label="vuz391",fontsize=16,color="green",shape="box"];8464 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.96	8464[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];8464 -> 8668[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8464 -> 8669[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8450[label="vuz395",fontsize=16,color="green",shape="box"];8451[label="vuz397",fontsize=16,color="green",shape="box"];8452[label="vuz396",fontsize=16,color="green",shape="box"];8453 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.96	8453[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];8453 -> 8670[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8453 -> 8671[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8454 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.96	8454[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];8454 -> 8672[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8454 -> 8673[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8455[label="vuz394",fontsize=16,color="green",shape="box"];8441 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.96	8441[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];8441 -> 8674[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8441 -> 8675[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8442[label="vuz395",fontsize=16,color="green",shape="box"];8443[label="vuz397",fontsize=16,color="green",shape="box"];8444 -> 7480[label="",style="dashed", color="red", weight=0];
67.83/34.96	8444[label="primMulNat vuz3180 vuz3190",fontsize=16,color="magenta"];8444 -> 8676[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8444 -> 8677[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8445[label="vuz396",fontsize=16,color="green",shape="box"];8446[label="vuz394",fontsize=16,color="green",shape="box"];8510[label="primQuotInt (Pos vuz398) (gcd0Gcd' (abs (Pos vuz399)) (abs (Pos vuz3190 * Pos vuz3170)))",fontsize=16,color="black",shape="box"];8510 -> 8678[label="",style="solid", color="black", weight=3];
67.83/34.96	8512 -> 9987[label="",style="dashed", color="red", weight=0];
67.83/34.96	8512[label="Pos vuz3190 * Pos vuz3170 == fromInt (Pos Zero)",fontsize=16,color="magenta"];8512 -> 9997[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8511[label="primQuotInt (Pos vuz398) (gcd1 vuz496 (Pos vuz399) (Pos vuz3190 * Pos vuz3170))",fontsize=16,color="burlywood",shape="triangle"];11047[label="vuz496/False",fontsize=10,color="white",style="solid",shape="box"];8511 -> 11047[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	11047 -> 8681[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	11048[label="vuz496/True",fontsize=10,color="white",style="solid",shape="box"];8511 -> 11048[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	11048 -> 8682[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	8513[label="vuz4000",fontsize=16,color="green",shape="box"];8514[label="vuz4010",fontsize=16,color="green",shape="box"];8515[label="vuz4010",fontsize=16,color="green",shape="box"];8516[label="vuz4000",fontsize=16,color="green",shape="box"];8517[label="primQuotInt (Pos (Succ vuz4010)) (gcd (Pos (Succ vuz4010)) (Neg vuz3190 * Pos (Succ vuz31700)))",fontsize=16,color="black",shape="box"];8517 -> 8683[label="",style="solid", color="black", weight=3];
67.83/34.96	8518[label="primQuotInt (Neg (Succ vuz4000)) (gcd (Neg (Succ vuz4000)) (Neg vuz3190 * Pos (Succ vuz31700)))",fontsize=16,color="black",shape="box"];8518 -> 8684[label="",style="solid", color="black", weight=3];
67.83/34.96	8519[label="primQuotInt (Pos Zero) (gcd (Pos Zero) (Neg vuz3190 * Pos (Succ vuz31700)))",fontsize=16,color="black",shape="box"];8519 -> 8685[label="",style="solid", color="black", weight=3];
67.83/34.96	8520 -> 7809[label="",style="dashed", color="red", weight=0];
67.83/34.96	8520[label="primQuotInt (Neg (Succ vuz4060)) (gcd3 (Neg (Succ vuz4060)) (Neg vuz3190 * Pos Zero))",fontsize=16,color="magenta"];8520 -> 8686[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8520 -> 8687[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8520 -> 8688[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8521 -> 7713[label="",style="dashed", color="red", weight=0];
67.83/34.96	8521[label="primQuotInt (Pos Zero) (gcd3 (Pos Zero) (Neg vuz3190 * Pos Zero))",fontsize=16,color="magenta"];8521 -> 8689[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8521 -> 8690[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8521 -> 8691[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8522[label="vuz4090",fontsize=16,color="green",shape="box"];8523[label="vuz4080",fontsize=16,color="green",shape="box"];8524[label="vuz4090",fontsize=16,color="green",shape="box"];8525[label="vuz4080",fontsize=16,color="green",shape="box"];8526[label="primQuotInt (Pos (Succ vuz4090)) (gcd (Pos (Succ vuz4090)) (Pos vuz3190 * Pos (Succ vuz31700)))",fontsize=16,color="black",shape="box"];8526 -> 8692[label="",style="solid", color="black", weight=3];
67.83/34.96	8527[label="primQuotInt (Neg (Succ vuz4080)) (gcd (Neg (Succ vuz4080)) (Pos vuz3190 * Pos (Succ vuz31700)))",fontsize=16,color="black",shape="box"];8527 -> 8693[label="",style="solid", color="black", weight=3];
67.83/34.96	8528[label="primQuotInt (Pos Zero) (gcd (Pos Zero) (Pos vuz3190 * Pos (Succ vuz31700)))",fontsize=16,color="black",shape="box"];8528 -> 8694[label="",style="solid", color="black", weight=3];
67.83/34.96	8529 -> 7587[label="",style="dashed", color="red", weight=0];
67.83/34.96	8529[label="primQuotInt (Neg (Succ vuz4140)) (gcd3 (Neg (Succ vuz4140)) (Pos vuz3190 * Pos Zero))",fontsize=16,color="magenta"];8529 -> 8695[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8529 -> 8696[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8529 -> 8697[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8530 -> 7667[label="",style="dashed", color="red", weight=0];
67.83/34.96	8530[label="primQuotInt (Pos Zero) (gcd3 (Pos Zero) (Pos vuz3190 * Pos Zero))",fontsize=16,color="magenta"];8530 -> 8698[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8530 -> 8699[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8530 -> 8700[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8531[label="primQuotInt (Pos vuz416) (gcd0Gcd' (abs (Pos vuz417)) (abs (Neg vuz3190 * Pos vuz3170)))",fontsize=16,color="black",shape="box"];8531 -> 8701[label="",style="solid", color="black", weight=3];
67.83/34.96	8533 -> 9987[label="",style="dashed", color="red", weight=0];
67.83/34.96	8533[label="Neg vuz3190 * Pos vuz3170 == fromInt (Pos Zero)",fontsize=16,color="magenta"];8533 -> 9998[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8532[label="primQuotInt (Pos vuz416) (gcd1 vuz497 (Pos vuz417) (Neg vuz3190 * Pos vuz3170))",fontsize=16,color="burlywood",shape="triangle"];11049[label="vuz497/False",fontsize=10,color="white",style="solid",shape="box"];8532 -> 11049[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	11049 -> 8704[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	11050[label="vuz497/True",fontsize=10,color="white",style="solid",shape="box"];8532 -> 11050[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	11050 -> 8705[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	8534[label="vuz4180",fontsize=16,color="green",shape="box"];8535[label="vuz4190",fontsize=16,color="green",shape="box"];8536[label="vuz4180",fontsize=16,color="green",shape="box"];8537[label="vuz4190",fontsize=16,color="green",shape="box"];8538[label="primQuotInt (Pos (Succ vuz4190)) (gcd (Pos (Succ vuz4190)) (Pos (Succ vuz31900) * Neg vuz3170))",fontsize=16,color="black",shape="box"];8538 -> 8706[label="",style="solid", color="black", weight=3];
67.83/34.96	8539[label="primQuotInt (Neg (Succ vuz4180)) (gcd (Neg (Succ vuz4180)) (Pos (Succ vuz31900) * Neg vuz3170))",fontsize=16,color="black",shape="box"];8539 -> 8707[label="",style="solid", color="black", weight=3];
67.83/34.96	8540[label="primQuotInt (Pos Zero) (gcd (Pos Zero) (Pos (Succ vuz31900) * Neg vuz3170))",fontsize=16,color="black",shape="box"];8540 -> 8708[label="",style="solid", color="black", weight=3];
67.83/34.96	8541 -> 7763[label="",style="dashed", color="red", weight=0];
67.83/34.96	8541[label="primQuotInt (Neg (Succ vuz4240)) (gcd3 (Neg (Succ vuz4240)) (Pos Zero * Neg vuz3170))",fontsize=16,color="magenta"];8541 -> 8709[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8541 -> 8710[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8541 -> 8711[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8542 -> 7598[label="",style="dashed", color="red", weight=0];
67.83/34.96	8542[label="primQuotInt (Pos Zero) (gcd3 (Pos Zero) (Pos Zero * Neg vuz3170))",fontsize=16,color="magenta"];8542 -> 8712[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8542 -> 8713[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8542 -> 8714[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8543[label="primQuotInt (Neg vuz426) (gcd0Gcd' (abs (Neg vuz427)) (abs (Neg vuz3190 * Neg vuz3170)))",fontsize=16,color="black",shape="box"];8543 -> 8715[label="",style="solid", color="black", weight=3];
67.83/34.96	8545 -> 9987[label="",style="dashed", color="red", weight=0];
67.83/34.96	8545[label="Neg vuz3190 * Neg vuz3170 == fromInt (Pos Zero)",fontsize=16,color="magenta"];8545 -> 9999[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8544[label="primQuotInt (Neg vuz426) (gcd1 vuz498 (Neg vuz427) (Neg vuz3190 * Neg vuz3170))",fontsize=16,color="burlywood",shape="triangle"];11051[label="vuz498/False",fontsize=10,color="white",style="solid",shape="box"];8544 -> 11051[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	11051 -> 8718[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	11052[label="vuz498/True",fontsize=10,color="white",style="solid",shape="box"];8544 -> 11052[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	11052 -> 8719[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	8546[label="primQuotInt (Neg vuz428) (gcd0Gcd' (abs (Neg vuz429)) (abs (Pos vuz3190 * Neg vuz3170)))",fontsize=16,color="black",shape="box"];8546 -> 8720[label="",style="solid", color="black", weight=3];
67.83/34.96	8548 -> 9987[label="",style="dashed", color="red", weight=0];
67.83/34.96	8548[label="Pos vuz3190 * Neg vuz3170 == fromInt (Pos Zero)",fontsize=16,color="magenta"];8548 -> 10000[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8547[label="primQuotInt (Neg vuz428) (gcd1 vuz499 (Neg vuz429) (Pos vuz3190 * Neg vuz3170))",fontsize=16,color="burlywood",shape="triangle"];11053[label="vuz499/False",fontsize=10,color="white",style="solid",shape="box"];8547 -> 11053[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	11053 -> 8723[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	11054[label="vuz499/True",fontsize=10,color="white",style="solid",shape="box"];8547 -> 11054[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	11054 -> 8724[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	8549[label="vuz4310",fontsize=16,color="green",shape="box"];8550[label="vuz4300",fontsize=16,color="green",shape="box"];8551[label="vuz4300",fontsize=16,color="green",shape="box"];8552[label="vuz4310",fontsize=16,color="green",shape="box"];8553[label="primQuotInt (Pos (Succ vuz4310)) (gcd (Pos (Succ vuz4310)) (Neg (Succ vuz31900) * Neg vuz3170))",fontsize=16,color="black",shape="box"];8553 -> 8725[label="",style="solid", color="black", weight=3];
67.83/34.96	8554[label="primQuotInt (Neg (Succ vuz4300)) (gcd (Neg (Succ vuz4300)) (Neg (Succ vuz31900) * Neg vuz3170))",fontsize=16,color="black",shape="box"];8554 -> 8726[label="",style="solid", color="black", weight=3];
67.83/34.96	8555[label="primQuotInt (Pos Zero) (gcd (Pos Zero) (Neg (Succ vuz31900) * Neg vuz3170))",fontsize=16,color="black",shape="box"];8555 -> 8727[label="",style="solid", color="black", weight=3];
67.83/34.96	8556 -> 7745[label="",style="dashed", color="red", weight=0];
67.83/34.96	8556[label="primQuotInt (Neg (Succ vuz4360)) (gcd3 (Neg (Succ vuz4360)) (Neg Zero * Neg vuz3170))",fontsize=16,color="magenta"];8556 -> 8728[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8556 -> 8729[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8556 -> 8730[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8557 -> 7613[label="",style="dashed", color="red", weight=0];
67.83/34.96	8557[label="primQuotInt (Pos Zero) (gcd3 (Pos Zero) (Neg Zero * Neg vuz3170))",fontsize=16,color="magenta"];8557 -> 8731[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8557 -> 8732[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8557 -> 8733[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8558[label="vuz4390",fontsize=16,color="green",shape="box"];8559[label="vuz4380",fontsize=16,color="green",shape="box"];8560[label="vuz4380",fontsize=16,color="green",shape="box"];8561[label="vuz4390",fontsize=16,color="green",shape="box"];8562[label="primQuotInt (Pos (Succ vuz4390)) (gcd (Pos (Succ vuz4390)) (Pos (Succ vuz31900) * Pos vuz3170))",fontsize=16,color="black",shape="box"];8562 -> 8734[label="",style="solid", color="black", weight=3];
67.83/34.96	8563[label="primQuotInt (Neg (Succ vuz4380)) (gcd (Neg (Succ vuz4380)) (Pos (Succ vuz31900) * Pos vuz3170))",fontsize=16,color="black",shape="box"];8563 -> 8735[label="",style="solid", color="black", weight=3];
67.83/34.96	8564[label="primQuotInt (Pos Zero) (gcd (Pos Zero) (Pos (Succ vuz31900) * Pos vuz3170))",fontsize=16,color="black",shape="box"];8564 -> 8736[label="",style="solid", color="black", weight=3];
67.83/34.96	8565 -> 7587[label="",style="dashed", color="red", weight=0];
67.83/34.96	8565[label="primQuotInt (Neg (Succ vuz4440)) (gcd3 (Neg (Succ vuz4440)) (Pos Zero * Pos vuz3170))",fontsize=16,color="magenta"];8565 -> 8737[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8565 -> 8738[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8565 -> 8739[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8566 -> 7667[label="",style="dashed", color="red", weight=0];
67.83/34.96	8566[label="primQuotInt (Pos Zero) (gcd3 (Pos Zero) (Pos Zero * Pos vuz3170))",fontsize=16,color="magenta"];8566 -> 8740[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8566 -> 8741[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8566 -> 8742[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8567[label="primQuotInt (Neg vuz446) (gcd0Gcd' (abs (Neg vuz447)) (abs (Neg vuz3190 * Pos vuz3170)))",fontsize=16,color="black",shape="box"];8567 -> 8743[label="",style="solid", color="black", weight=3];
67.83/34.96	8569 -> 9987[label="",style="dashed", color="red", weight=0];
67.83/34.96	8569[label="Neg vuz3190 * Pos vuz3170 == fromInt (Pos Zero)",fontsize=16,color="magenta"];8569 -> 10001[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8568[label="primQuotInt (Neg vuz446) (gcd1 vuz500 (Neg vuz447) (Neg vuz3190 * Pos vuz3170))",fontsize=16,color="burlywood",shape="triangle"];11055[label="vuz500/False",fontsize=10,color="white",style="solid",shape="box"];8568 -> 11055[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	11055 -> 8746[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	11056[label="vuz500/True",fontsize=10,color="white",style="solid",shape="box"];8568 -> 11056[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	11056 -> 8747[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	8570[label="primQuotInt (Neg vuz348) (gcd0Gcd' (abs (Neg vuz349)) (abs (Pos vuz3190 * Pos vuz3170)))",fontsize=16,color="black",shape="box"];8570 -> 8748[label="",style="solid", color="black", weight=3];
67.83/34.96	8572 -> 9987[label="",style="dashed", color="red", weight=0];
67.83/34.96	8572[label="Pos vuz3190 * Pos vuz3170 == fromInt (Pos Zero)",fontsize=16,color="magenta"];8572 -> 10002[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8571[label="primQuotInt (Neg vuz348) (gcd1 vuz501 (Neg vuz349) (Pos vuz3190 * Pos vuz3170))",fontsize=16,color="burlywood",shape="triangle"];11057[label="vuz501/False",fontsize=10,color="white",style="solid",shape="box"];8571 -> 11057[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	11057 -> 8751[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	11058[label="vuz501/True",fontsize=10,color="white",style="solid",shape="box"];8571 -> 11058[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	11058 -> 8752[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	8573[label="vuz4490",fontsize=16,color="green",shape="box"];8574[label="vuz4490",fontsize=16,color="green",shape="box"];8575[label="vuz4480",fontsize=16,color="green",shape="box"];8576[label="vuz4480",fontsize=16,color="green",shape="box"];8577[label="primQuotInt (Pos (Succ vuz4490)) (gcd (Pos (Succ vuz4490)) (Neg (Succ vuz31900) * Pos vuz3170))",fontsize=16,color="black",shape="box"];8577 -> 8753[label="",style="solid", color="black", weight=3];
67.83/34.96	8578[label="primQuotInt (Neg (Succ vuz4480)) (gcd (Neg (Succ vuz4480)) (Neg (Succ vuz31900) * Pos vuz3170))",fontsize=16,color="black",shape="box"];8578 -> 8754[label="",style="solid", color="black", weight=3];
67.83/34.96	8579[label="primQuotInt (Pos Zero) (gcd (Pos Zero) (Neg (Succ vuz31900) * Pos vuz3170))",fontsize=16,color="black",shape="box"];8579 -> 8755[label="",style="solid", color="black", weight=3];
67.83/34.96	8580 -> 7809[label="",style="dashed", color="red", weight=0];
67.83/34.96	8580[label="primQuotInt (Neg (Succ vuz4540)) (gcd3 (Neg (Succ vuz4540)) (Neg Zero * Pos vuz3170))",fontsize=16,color="magenta"];8580 -> 8756[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8580 -> 8757[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8580 -> 8758[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8581 -> 7713[label="",style="dashed", color="red", weight=0];
67.83/34.96	8581[label="primQuotInt (Pos Zero) (gcd3 (Pos Zero) (Neg Zero * Pos vuz3170))",fontsize=16,color="magenta"];8581 -> 8759[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8581 -> 8760[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8581 -> 8761[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8582[label="primQuotInt (Pos vuz354) (gcd0Gcd' (abs (Pos vuz355)) (abs (Pos vuz3190 * Neg vuz3170)))",fontsize=16,color="black",shape="box"];8582 -> 8762[label="",style="solid", color="black", weight=3];
67.83/34.96	8584 -> 9987[label="",style="dashed", color="red", weight=0];
67.83/34.96	8584[label="Pos vuz3190 * Neg vuz3170 == fromInt (Pos Zero)",fontsize=16,color="magenta"];8584 -> 10003[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8583[label="primQuotInt (Pos vuz354) (gcd1 vuz502 (Pos vuz355) (Pos vuz3190 * Neg vuz3170))",fontsize=16,color="burlywood",shape="triangle"];11059[label="vuz502/False",fontsize=10,color="white",style="solid",shape="box"];8583 -> 11059[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	11059 -> 8765[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	11060[label="vuz502/True",fontsize=10,color="white",style="solid",shape="box"];8583 -> 11060[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	11060 -> 8766[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	8585[label="vuz4570",fontsize=16,color="green",shape="box"];8586[label="vuz4560",fontsize=16,color="green",shape="box"];8587[label="vuz4560",fontsize=16,color="green",shape="box"];8588[label="vuz4570",fontsize=16,color="green",shape="box"];8589[label="primQuotInt (Pos (Succ vuz4570)) (gcd (Pos (Succ vuz4570)) (Neg vuz3190 * Neg (Succ vuz31700)))",fontsize=16,color="black",shape="box"];8589 -> 8767[label="",style="solid", color="black", weight=3];
67.83/34.96	8590[label="primQuotInt (Neg (Succ vuz4560)) (gcd (Neg (Succ vuz4560)) (Neg vuz3190 * Neg (Succ vuz31700)))",fontsize=16,color="black",shape="box"];8590 -> 8768[label="",style="solid", color="black", weight=3];
67.83/34.96	8591[label="primQuotInt (Pos Zero) (gcd (Pos Zero) (Neg vuz3190 * Neg (Succ vuz31700)))",fontsize=16,color="black",shape="box"];8591 -> 8769[label="",style="solid", color="black", weight=3];
67.83/34.96	8592 -> 7745[label="",style="dashed", color="red", weight=0];
67.83/34.96	8592[label="primQuotInt (Neg (Succ vuz4620)) (gcd3 (Neg (Succ vuz4620)) (Neg vuz3190 * Neg Zero))",fontsize=16,color="magenta"];8592 -> 8770[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8592 -> 8771[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8592 -> 8772[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8593 -> 7613[label="",style="dashed", color="red", weight=0];
67.83/34.96	8593[label="primQuotInt (Pos Zero) (gcd3 (Pos Zero) (Neg vuz3190 * Neg Zero))",fontsize=16,color="magenta"];8593 -> 8773[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8593 -> 8774[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8593 -> 8775[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8594[label="vuz4650",fontsize=16,color="green",shape="box"];8595[label="vuz4640",fontsize=16,color="green",shape="box"];8596[label="vuz4640",fontsize=16,color="green",shape="box"];8597[label="vuz4650",fontsize=16,color="green",shape="box"];8598[label="primQuotInt (Pos (Succ vuz4650)) (gcd (Pos (Succ vuz4650)) (Pos vuz3190 * Neg (Succ vuz31700)))",fontsize=16,color="black",shape="box"];8598 -> 8776[label="",style="solid", color="black", weight=3];
67.83/34.96	8599[label="primQuotInt (Neg (Succ vuz4640)) (gcd (Neg (Succ vuz4640)) (Pos vuz3190 * Neg (Succ vuz31700)))",fontsize=16,color="black",shape="box"];8599 -> 8777[label="",style="solid", color="black", weight=3];
67.83/34.96	8600[label="primQuotInt (Pos Zero) (gcd (Pos Zero) (Pos vuz3190 * Neg (Succ vuz31700)))",fontsize=16,color="black",shape="box"];8600 -> 8778[label="",style="solid", color="black", weight=3];
67.83/34.96	8601 -> 7763[label="",style="dashed", color="red", weight=0];
67.83/34.96	8601[label="primQuotInt (Neg (Succ vuz4700)) (gcd3 (Neg (Succ vuz4700)) (Pos vuz3190 * Neg Zero))",fontsize=16,color="magenta"];8601 -> 8779[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8601 -> 8780[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8601 -> 8781[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8602 -> 7598[label="",style="dashed", color="red", weight=0];
67.83/34.96	8602[label="primQuotInt (Pos Zero) (gcd3 (Pos Zero) (Pos vuz3190 * Neg Zero))",fontsize=16,color="magenta"];8602 -> 8782[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8602 -> 8783[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8602 -> 8784[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8603[label="primQuotInt (Pos vuz360) (gcd0Gcd' (abs (Pos vuz361)) (abs (Neg vuz3190 * Neg vuz3170)))",fontsize=16,color="black",shape="box"];8603 -> 8785[label="",style="solid", color="black", weight=3];
67.83/34.96	8605 -> 9987[label="",style="dashed", color="red", weight=0];
67.83/34.96	8605[label="Neg vuz3190 * Neg vuz3170 == fromInt (Pos Zero)",fontsize=16,color="magenta"];8605 -> 10004[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8604[label="primQuotInt (Pos vuz360) (gcd1 vuz503 (Pos vuz361) (Neg vuz3190 * Neg vuz3170))",fontsize=16,color="burlywood",shape="triangle"];11061[label="vuz503/False",fontsize=10,color="white",style="solid",shape="box"];8604 -> 11061[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	11061 -> 8788[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	11062[label="vuz503/True",fontsize=10,color="white",style="solid",shape="box"];8604 -> 11062[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	11062 -> 8789[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	8606[label="vuz3180",fontsize=16,color="green",shape="box"];8607[label="vuz3190",fontsize=16,color="green",shape="box"];8608[label="vuz3180",fontsize=16,color="green",shape="box"];8609[label="vuz3190",fontsize=16,color="green",shape="box"];8610 -> 8790[label="",style="dashed", color="red", weight=0];
67.83/34.96	8610[label="primQuotInt (Pos vuz366) (gcd2 (primEqInt (Pos (primPlusNat vuz369 vuz481)) (fromInt (Pos Zero))) (Pos (primPlusNat vuz369 vuz481)) (Pos vuz367))",fontsize=16,color="magenta"];8610 -> 8791[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8610 -> 8792[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8611[label="vuz3180",fontsize=16,color="green",shape="box"];8612[label="vuz3190",fontsize=16,color="green",shape="box"];8613[label="vuz3180",fontsize=16,color="green",shape="box"];8614[label="vuz3190",fontsize=16,color="green",shape="box"];8615[label="primQuotInt (Pos vuz366) (gcd2 (primEqInt (primMinusNat vuz369 vuz483) (fromInt (Pos Zero))) (primMinusNat vuz369 vuz483) (Pos vuz367))",fontsize=16,color="burlywood",shape="triangle"];11063[label="vuz369/Succ vuz3690",fontsize=10,color="white",style="solid",shape="box"];8615 -> 11063[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	11063 -> 8793[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	11064[label="vuz369/Zero",fontsize=10,color="white",style="solid",shape="box"];8615 -> 11064[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	11064 -> 8794[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	8616[label="vuz3180",fontsize=16,color="green",shape="box"];8617[label="vuz3190",fontsize=16,color="green",shape="box"];8618[label="vuz3180",fontsize=16,color="green",shape="box"];8619[label="vuz3190",fontsize=16,color="green",shape="box"];8620 -> 8615[label="",style="dashed", color="red", weight=0];
67.83/34.96	8620[label="primQuotInt (Pos vuz370) (gcd2 (primEqInt (primMinusNat vuz485 vuz373) (fromInt (Pos Zero))) (primMinusNat vuz485 vuz373) (Pos vuz371))",fontsize=16,color="magenta"];8620 -> 8795[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8620 -> 8796[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8620 -> 8797[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8620 -> 8798[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8621[label="vuz3180",fontsize=16,color="green",shape="box"];8622[label="vuz3190",fontsize=16,color="green",shape="box"];8623[label="vuz3180",fontsize=16,color="green",shape="box"];8624[label="vuz3190",fontsize=16,color="green",shape="box"];8625 -> 8799[label="",style="dashed", color="red", weight=0];
67.83/34.96	8625[label="primQuotInt (Pos vuz370) (gcd2 (primEqInt (Neg (primPlusNat vuz373 vuz487)) (fromInt (Pos Zero))) (Neg (primPlusNat vuz373 vuz487)) (Pos vuz371))",fontsize=16,color="magenta"];8625 -> 8800[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8625 -> 8801[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8626[label="vuz3180",fontsize=16,color="green",shape="box"];8627[label="vuz3190",fontsize=16,color="green",shape="box"];8628[label="vuz3180",fontsize=16,color="green",shape="box"];8629[label="vuz3190",fontsize=16,color="green",shape="box"];8630[label="primQuotInt (Neg vuz374) (gcd2 (primEqInt (primMinusNat vuz489 vuz377) (fromInt (Pos Zero))) (primMinusNat vuz489 vuz377) (Neg vuz375))",fontsize=16,color="burlywood",shape="triangle"];11065[label="vuz489/Succ vuz4890",fontsize=10,color="white",style="solid",shape="box"];8630 -> 11065[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	11065 -> 8802[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	11066[label="vuz489/Zero",fontsize=10,color="white",style="solid",shape="box"];8630 -> 11066[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	11066 -> 8803[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	8631[label="vuz3180",fontsize=16,color="green",shape="box"];8632[label="vuz3190",fontsize=16,color="green",shape="box"];8633[label="vuz3180",fontsize=16,color="green",shape="box"];8634[label="vuz3190",fontsize=16,color="green",shape="box"];8635 -> 8804[label="",style="dashed", color="red", weight=0];
67.83/34.96	8635[label="primQuotInt (Neg vuz374) (gcd2 (primEqInt (Neg (primPlusNat vuz377 vuz491)) (fromInt (Pos Zero))) (Neg (primPlusNat vuz377 vuz491)) (Neg vuz375))",fontsize=16,color="magenta"];8635 -> 8805[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8635 -> 8806[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8636[label="vuz3180",fontsize=16,color="green",shape="box"];8637[label="vuz3190",fontsize=16,color="green",shape="box"];8638[label="vuz3180",fontsize=16,color="green",shape="box"];8639[label="vuz3190",fontsize=16,color="green",shape="box"];8640 -> 8807[label="",style="dashed", color="red", weight=0];
67.83/34.96	8640[label="primQuotInt (Neg vuz378) (gcd2 (primEqInt (Pos (primPlusNat vuz381 vuz493)) (fromInt (Pos Zero))) (Pos (primPlusNat vuz381 vuz493)) (Neg vuz379))",fontsize=16,color="magenta"];8640 -> 8808[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8640 -> 8809[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8641[label="vuz3180",fontsize=16,color="green",shape="box"];8642[label="vuz3190",fontsize=16,color="green",shape="box"];8643[label="vuz3180",fontsize=16,color="green",shape="box"];8644[label="vuz3190",fontsize=16,color="green",shape="box"];8645 -> 8630[label="",style="dashed", color="red", weight=0];
67.83/34.96	8645[label="primQuotInt (Neg vuz378) (gcd2 (primEqInt (primMinusNat vuz381 vuz495) (fromInt (Pos Zero))) (primMinusNat vuz381 vuz495) (Neg vuz379))",fontsize=16,color="magenta"];8645 -> 8810[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8645 -> 8811[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8645 -> 8812[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8645 -> 8813[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8646[label="vuz3180",fontsize=16,color="green",shape="box"];8647[label="vuz3190",fontsize=16,color="green",shape="box"];8648[label="vuz3180",fontsize=16,color="green",shape="box"];8649[label="vuz3190",fontsize=16,color="green",shape="box"];8650[label="vuz3180",fontsize=16,color="green",shape="box"];8651[label="vuz3190",fontsize=16,color="green",shape="box"];8652[label="vuz3180",fontsize=16,color="green",shape="box"];8653[label="vuz3190",fontsize=16,color="green",shape="box"];8654[label="vuz3180",fontsize=16,color="green",shape="box"];8655[label="vuz3190",fontsize=16,color="green",shape="box"];8656[label="vuz3180",fontsize=16,color="green",shape="box"];8657[label="vuz3190",fontsize=16,color="green",shape="box"];8658[label="vuz3180",fontsize=16,color="green",shape="box"];8659[label="vuz3190",fontsize=16,color="green",shape="box"];8660[label="vuz3180",fontsize=16,color="green",shape="box"];8661[label="vuz3190",fontsize=16,color="green",shape="box"];8662[label="vuz3180",fontsize=16,color="green",shape="box"];8663[label="vuz3190",fontsize=16,color="green",shape="box"];8664[label="vuz3180",fontsize=16,color="green",shape="box"];8665[label="vuz3190",fontsize=16,color="green",shape="box"];8666[label="vuz3180",fontsize=16,color="green",shape="box"];8667[label="vuz3190",fontsize=16,color="green",shape="box"];8668[label="vuz3180",fontsize=16,color="green",shape="box"];8669[label="vuz3190",fontsize=16,color="green",shape="box"];8670[label="vuz3180",fontsize=16,color="green",shape="box"];8671[label="vuz3190",fontsize=16,color="green",shape="box"];8672[label="vuz3180",fontsize=16,color="green",shape="box"];8673[label="vuz3190",fontsize=16,color="green",shape="box"];8674[label="vuz3180",fontsize=16,color="green",shape="box"];8675[label="vuz3190",fontsize=16,color="green",shape="box"];8676[label="vuz3180",fontsize=16,color="green",shape="box"];8677[label="vuz3190",fontsize=16,color="green",shape="box"];8678[label="primQuotInt (Pos vuz398) (gcd0Gcd'2 (abs (Pos vuz399)) (abs (Pos vuz3190 * Pos vuz3170)))",fontsize=16,color="black",shape="box"];8678 -> 8814[label="",style="solid", color="black", weight=3];
67.83/34.96	9997 -> 9988[label="",style="dashed", color="red", weight=0];
67.83/34.96	9997[label="Pos vuz3190 * Pos vuz3170",fontsize=16,color="magenta"];9997 -> 10017[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	9997 -> 10018[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8681[label="primQuotInt (Pos vuz398) (gcd1 False (Pos vuz399) (Pos vuz3190 * Pos vuz3170))",fontsize=16,color="black",shape="box"];8681 -> 8815[label="",style="solid", color="black", weight=3];
67.83/34.96	8682[label="primQuotInt (Pos vuz398) (gcd1 True (Pos vuz399) (Pos vuz3190 * Pos vuz3170))",fontsize=16,color="black",shape="box"];8682 -> 8816[label="",style="solid", color="black", weight=3];
67.83/34.96	8683 -> 7713[label="",style="dashed", color="red", weight=0];
67.83/34.96	8683[label="primQuotInt (Pos (Succ vuz4010)) (gcd3 (Pos (Succ vuz4010)) (Neg vuz3190 * Pos (Succ vuz31700)))",fontsize=16,color="magenta"];8683 -> 8817[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8683 -> 8818[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8683 -> 8819[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8684 -> 7809[label="",style="dashed", color="red", weight=0];
67.83/34.96	8684[label="primQuotInt (Neg (Succ vuz4000)) (gcd3 (Neg (Succ vuz4000)) (Neg vuz3190 * Pos (Succ vuz31700)))",fontsize=16,color="magenta"];8684 -> 8820[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8684 -> 8821[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8684 -> 8822[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8685 -> 7713[label="",style="dashed", color="red", weight=0];
67.83/34.96	8685[label="primQuotInt (Pos Zero) (gcd3 (Pos Zero) (Neg vuz3190 * Pos (Succ vuz31700)))",fontsize=16,color="magenta"];8685 -> 8823[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8685 -> 8824[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8685 -> 8825[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8686[label="Succ vuz4060",fontsize=16,color="green",shape="box"];8687[label="Zero",fontsize=16,color="green",shape="box"];8688[label="Succ vuz4060",fontsize=16,color="green",shape="box"];8689[label="Zero",fontsize=16,color="green",shape="box"];8690[label="Zero",fontsize=16,color="green",shape="box"];8691[label="Zero",fontsize=16,color="green",shape="box"];8692 -> 7667[label="",style="dashed", color="red", weight=0];
67.83/34.96	8692[label="primQuotInt (Pos (Succ vuz4090)) (gcd3 (Pos (Succ vuz4090)) (Pos vuz3190 * Pos (Succ vuz31700)))",fontsize=16,color="magenta"];8692 -> 8826[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8692 -> 8827[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8692 -> 8828[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8693 -> 7587[label="",style="dashed", color="red", weight=0];
67.83/34.96	8693[label="primQuotInt (Neg (Succ vuz4080)) (gcd3 (Neg (Succ vuz4080)) (Pos vuz3190 * Pos (Succ vuz31700)))",fontsize=16,color="magenta"];8693 -> 8829[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8693 -> 8830[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8693 -> 8831[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8694 -> 7667[label="",style="dashed", color="red", weight=0];
67.83/34.96	8694[label="primQuotInt (Pos Zero) (gcd3 (Pos Zero) (Pos vuz3190 * Pos (Succ vuz31700)))",fontsize=16,color="magenta"];8694 -> 8832[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8694 -> 8833[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8694 -> 8834[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8695[label="Succ vuz4140",fontsize=16,color="green",shape="box"];8696[label="Zero",fontsize=16,color="green",shape="box"];8697[label="Succ vuz4140",fontsize=16,color="green",shape="box"];8698[label="Zero",fontsize=16,color="green",shape="box"];8699[label="Zero",fontsize=16,color="green",shape="box"];8700[label="Zero",fontsize=16,color="green",shape="box"];8701[label="primQuotInt (Pos vuz416) (gcd0Gcd'2 (abs (Pos vuz417)) (abs (Neg vuz3190 * Pos vuz3170)))",fontsize=16,color="black",shape="box"];8701 -> 8835[label="",style="solid", color="black", weight=3];
67.83/34.96	9998 -> 9988[label="",style="dashed", color="red", weight=0];
67.83/34.96	9998[label="Neg vuz3190 * Pos vuz3170",fontsize=16,color="magenta"];9998 -> 10019[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	9998 -> 10020[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8704[label="primQuotInt (Pos vuz416) (gcd1 False (Pos vuz417) (Neg vuz3190 * Pos vuz3170))",fontsize=16,color="black",shape="box"];8704 -> 8836[label="",style="solid", color="black", weight=3];
67.83/34.96	8705[label="primQuotInt (Pos vuz416) (gcd1 True (Pos vuz417) (Neg vuz3190 * Pos vuz3170))",fontsize=16,color="black",shape="box"];8705 -> 8837[label="",style="solid", color="black", weight=3];
67.83/34.96	8706 -> 7598[label="",style="dashed", color="red", weight=0];
67.83/34.96	8706[label="primQuotInt (Pos (Succ vuz4190)) (gcd3 (Pos (Succ vuz4190)) (Pos (Succ vuz31900) * Neg vuz3170))",fontsize=16,color="magenta"];8706 -> 8838[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8706 -> 8839[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8706 -> 8840[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8707 -> 7763[label="",style="dashed", color="red", weight=0];
67.83/34.96	8707[label="primQuotInt (Neg (Succ vuz4180)) (gcd3 (Neg (Succ vuz4180)) (Pos (Succ vuz31900) * Neg vuz3170))",fontsize=16,color="magenta"];8707 -> 8841[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8707 -> 8842[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8707 -> 8843[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8708 -> 7598[label="",style="dashed", color="red", weight=0];
67.83/34.96	8708[label="primQuotInt (Pos Zero) (gcd3 (Pos Zero) (Pos (Succ vuz31900) * Neg vuz3170))",fontsize=16,color="magenta"];8708 -> 8844[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8708 -> 8845[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8708 -> 8846[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8709[label="Succ vuz4240",fontsize=16,color="green",shape="box"];8710[label="Succ vuz4240",fontsize=16,color="green",shape="box"];8711[label="Zero",fontsize=16,color="green",shape="box"];8712[label="Zero",fontsize=16,color="green",shape="box"];8713[label="Zero",fontsize=16,color="green",shape="box"];8714[label="Zero",fontsize=16,color="green",shape="box"];8715[label="primQuotInt (Neg vuz426) (gcd0Gcd'2 (abs (Neg vuz427)) (abs (Neg vuz3190 * Neg vuz3170)))",fontsize=16,color="black",shape="box"];8715 -> 8847[label="",style="solid", color="black", weight=3];
67.83/34.96	9999 -> 9988[label="",style="dashed", color="red", weight=0];
67.83/34.96	9999[label="Neg vuz3190 * Neg vuz3170",fontsize=16,color="magenta"];9999 -> 10021[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	9999 -> 10022[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8718[label="primQuotInt (Neg vuz426) (gcd1 False (Neg vuz427) (Neg vuz3190 * Neg vuz3170))",fontsize=16,color="black",shape="box"];8718 -> 8848[label="",style="solid", color="black", weight=3];
67.83/34.96	8719[label="primQuotInt (Neg vuz426) (gcd1 True (Neg vuz427) (Neg vuz3190 * Neg vuz3170))",fontsize=16,color="black",shape="box"];8719 -> 8849[label="",style="solid", color="black", weight=3];
67.83/34.96	8720[label="primQuotInt (Neg vuz428) (gcd0Gcd'2 (abs (Neg vuz429)) (abs (Pos vuz3190 * Neg vuz3170)))",fontsize=16,color="black",shape="box"];8720 -> 8850[label="",style="solid", color="black", weight=3];
67.83/34.96	10000 -> 9988[label="",style="dashed", color="red", weight=0];
67.83/34.96	10000[label="Pos vuz3190 * Neg vuz3170",fontsize=16,color="magenta"];10000 -> 10023[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	10000 -> 10024[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8723[label="primQuotInt (Neg vuz428) (gcd1 False (Neg vuz429) (Pos vuz3190 * Neg vuz3170))",fontsize=16,color="black",shape="box"];8723 -> 8851[label="",style="solid", color="black", weight=3];
67.83/34.96	8724[label="primQuotInt (Neg vuz428) (gcd1 True (Neg vuz429) (Pos vuz3190 * Neg vuz3170))",fontsize=16,color="black",shape="box"];8724 -> 8852[label="",style="solid", color="black", weight=3];
67.83/34.96	8725 -> 7613[label="",style="dashed", color="red", weight=0];
67.83/34.96	8725[label="primQuotInt (Pos (Succ vuz4310)) (gcd3 (Pos (Succ vuz4310)) (Neg (Succ vuz31900) * Neg vuz3170))",fontsize=16,color="magenta"];8725 -> 8853[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8725 -> 8854[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8725 -> 8855[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8726 -> 7745[label="",style="dashed", color="red", weight=0];
67.83/34.96	8726[label="primQuotInt (Neg (Succ vuz4300)) (gcd3 (Neg (Succ vuz4300)) (Neg (Succ vuz31900) * Neg vuz3170))",fontsize=16,color="magenta"];8726 -> 8856[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8726 -> 8857[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8726 -> 8858[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8727 -> 7613[label="",style="dashed", color="red", weight=0];
67.83/34.96	8727[label="primQuotInt (Pos Zero) (gcd3 (Pos Zero) (Neg (Succ vuz31900) * Neg vuz3170))",fontsize=16,color="magenta"];8727 -> 8859[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8727 -> 8860[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8727 -> 8861[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8728[label="Succ vuz4360",fontsize=16,color="green",shape="box"];8729[label="Zero",fontsize=16,color="green",shape="box"];8730[label="Succ vuz4360",fontsize=16,color="green",shape="box"];8731[label="Zero",fontsize=16,color="green",shape="box"];8732[label="Zero",fontsize=16,color="green",shape="box"];8733[label="Zero",fontsize=16,color="green",shape="box"];8734 -> 7667[label="",style="dashed", color="red", weight=0];
67.83/34.96	8734[label="primQuotInt (Pos (Succ vuz4390)) (gcd3 (Pos (Succ vuz4390)) (Pos (Succ vuz31900) * Pos vuz3170))",fontsize=16,color="magenta"];8734 -> 8862[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8734 -> 8863[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8734 -> 8864[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8735 -> 7587[label="",style="dashed", color="red", weight=0];
67.83/34.96	8735[label="primQuotInt (Neg (Succ vuz4380)) (gcd3 (Neg (Succ vuz4380)) (Pos (Succ vuz31900) * Pos vuz3170))",fontsize=16,color="magenta"];8735 -> 8865[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8735 -> 8866[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8735 -> 8867[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8736 -> 7667[label="",style="dashed", color="red", weight=0];
67.83/34.96	8736[label="primQuotInt (Pos Zero) (gcd3 (Pos Zero) (Pos (Succ vuz31900) * Pos vuz3170))",fontsize=16,color="magenta"];8736 -> 8868[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8736 -> 8869[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8736 -> 8870[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8737[label="Succ vuz4440",fontsize=16,color="green",shape="box"];8738[label="Zero",fontsize=16,color="green",shape="box"];8739[label="Succ vuz4440",fontsize=16,color="green",shape="box"];8740[label="Zero",fontsize=16,color="green",shape="box"];8741[label="Zero",fontsize=16,color="green",shape="box"];8742[label="Zero",fontsize=16,color="green",shape="box"];8743[label="primQuotInt (Neg vuz446) (gcd0Gcd'2 (abs (Neg vuz447)) (abs (Neg vuz3190 * Pos vuz3170)))",fontsize=16,color="black",shape="box"];8743 -> 8871[label="",style="solid", color="black", weight=3];
67.83/34.96	10001 -> 9988[label="",style="dashed", color="red", weight=0];
67.83/34.96	10001[label="Neg vuz3190 * Pos vuz3170",fontsize=16,color="magenta"];10001 -> 10025[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	10001 -> 10026[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8746[label="primQuotInt (Neg vuz446) (gcd1 False (Neg vuz447) (Neg vuz3190 * Pos vuz3170))",fontsize=16,color="black",shape="box"];8746 -> 8872[label="",style="solid", color="black", weight=3];
67.83/34.96	8747[label="primQuotInt (Neg vuz446) (gcd1 True (Neg vuz447) (Neg vuz3190 * Pos vuz3170))",fontsize=16,color="black",shape="box"];8747 -> 8873[label="",style="solid", color="black", weight=3];
67.83/34.96	8748[label="primQuotInt (Neg vuz348) (gcd0Gcd'2 (abs (Neg vuz349)) (abs (Pos vuz3190 * Pos vuz3170)))",fontsize=16,color="black",shape="box"];8748 -> 8874[label="",style="solid", color="black", weight=3];
67.83/34.96	10002 -> 9988[label="",style="dashed", color="red", weight=0];
67.83/34.96	10002[label="Pos vuz3190 * Pos vuz3170",fontsize=16,color="magenta"];10002 -> 10027[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	10002 -> 10028[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8751[label="primQuotInt (Neg vuz348) (gcd1 False (Neg vuz349) (Pos vuz3190 * Pos vuz3170))",fontsize=16,color="black",shape="box"];8751 -> 8875[label="",style="solid", color="black", weight=3];
67.83/34.96	8752[label="primQuotInt (Neg vuz348) (gcd1 True (Neg vuz349) (Pos vuz3190 * Pos vuz3170))",fontsize=16,color="black",shape="box"];8752 -> 8876[label="",style="solid", color="black", weight=3];
67.83/34.96	8753 -> 7713[label="",style="dashed", color="red", weight=0];
67.83/34.96	8753[label="primQuotInt (Pos (Succ vuz4490)) (gcd3 (Pos (Succ vuz4490)) (Neg (Succ vuz31900) * Pos vuz3170))",fontsize=16,color="magenta"];8753 -> 8877[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8753 -> 8878[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8753 -> 8879[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8754 -> 7809[label="",style="dashed", color="red", weight=0];
67.83/34.96	8754[label="primQuotInt (Neg (Succ vuz4480)) (gcd3 (Neg (Succ vuz4480)) (Neg (Succ vuz31900) * Pos vuz3170))",fontsize=16,color="magenta"];8754 -> 8880[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8754 -> 8881[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8754 -> 8882[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8755 -> 7713[label="",style="dashed", color="red", weight=0];
67.83/34.96	8755[label="primQuotInt (Pos Zero) (gcd3 (Pos Zero) (Neg (Succ vuz31900) * Pos vuz3170))",fontsize=16,color="magenta"];8755 -> 8883[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8755 -> 8884[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8755 -> 8885[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8756[label="Succ vuz4540",fontsize=16,color="green",shape="box"];8757[label="Zero",fontsize=16,color="green",shape="box"];8758[label="Succ vuz4540",fontsize=16,color="green",shape="box"];8759[label="Zero",fontsize=16,color="green",shape="box"];8760[label="Zero",fontsize=16,color="green",shape="box"];8761[label="Zero",fontsize=16,color="green",shape="box"];8762[label="primQuotInt (Pos vuz354) (gcd0Gcd'2 (abs (Pos vuz355)) (abs (Pos vuz3190 * Neg vuz3170)))",fontsize=16,color="black",shape="box"];8762 -> 8886[label="",style="solid", color="black", weight=3];
67.83/34.96	10003 -> 9988[label="",style="dashed", color="red", weight=0];
67.83/34.96	10003[label="Pos vuz3190 * Neg vuz3170",fontsize=16,color="magenta"];10003 -> 10029[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	10003 -> 10030[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8765[label="primQuotInt (Pos vuz354) (gcd1 False (Pos vuz355) (Pos vuz3190 * Neg vuz3170))",fontsize=16,color="black",shape="box"];8765 -> 8887[label="",style="solid", color="black", weight=3];
67.83/34.96	8766[label="primQuotInt (Pos vuz354) (gcd1 True (Pos vuz355) (Pos vuz3190 * Neg vuz3170))",fontsize=16,color="black",shape="box"];8766 -> 8888[label="",style="solid", color="black", weight=3];
67.83/34.96	8767 -> 7613[label="",style="dashed", color="red", weight=0];
67.83/34.96	8767[label="primQuotInt (Pos (Succ vuz4570)) (gcd3 (Pos (Succ vuz4570)) (Neg vuz3190 * Neg (Succ vuz31700)))",fontsize=16,color="magenta"];8767 -> 8889[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8767 -> 8890[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8767 -> 8891[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8768 -> 7745[label="",style="dashed", color="red", weight=0];
67.83/34.96	8768[label="primQuotInt (Neg (Succ vuz4560)) (gcd3 (Neg (Succ vuz4560)) (Neg vuz3190 * Neg (Succ vuz31700)))",fontsize=16,color="magenta"];8768 -> 8892[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8768 -> 8893[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8768 -> 8894[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8769 -> 7613[label="",style="dashed", color="red", weight=0];
67.83/34.96	8769[label="primQuotInt (Pos Zero) (gcd3 (Pos Zero) (Neg vuz3190 * Neg (Succ vuz31700)))",fontsize=16,color="magenta"];8769 -> 8895[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8769 -> 8896[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8769 -> 8897[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8770[label="Succ vuz4620",fontsize=16,color="green",shape="box"];8771[label="Zero",fontsize=16,color="green",shape="box"];8772[label="Succ vuz4620",fontsize=16,color="green",shape="box"];8773[label="Zero",fontsize=16,color="green",shape="box"];8774[label="Zero",fontsize=16,color="green",shape="box"];8775[label="Zero",fontsize=16,color="green",shape="box"];8776 -> 7598[label="",style="dashed", color="red", weight=0];
67.83/34.96	8776[label="primQuotInt (Pos (Succ vuz4650)) (gcd3 (Pos (Succ vuz4650)) (Pos vuz3190 * Neg (Succ vuz31700)))",fontsize=16,color="magenta"];8776 -> 8898[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8776 -> 8899[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8776 -> 8900[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8777 -> 7763[label="",style="dashed", color="red", weight=0];
67.83/34.96	8777[label="primQuotInt (Neg (Succ vuz4640)) (gcd3 (Neg (Succ vuz4640)) (Pos vuz3190 * Neg (Succ vuz31700)))",fontsize=16,color="magenta"];8777 -> 8901[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8777 -> 8902[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8777 -> 8903[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8778 -> 7598[label="",style="dashed", color="red", weight=0];
67.83/34.96	8778[label="primQuotInt (Pos Zero) (gcd3 (Pos Zero) (Pos vuz3190 * Neg (Succ vuz31700)))",fontsize=16,color="magenta"];8778 -> 8904[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8778 -> 8905[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8778 -> 8906[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8779[label="Succ vuz4700",fontsize=16,color="green",shape="box"];8780[label="Succ vuz4700",fontsize=16,color="green",shape="box"];8781[label="Zero",fontsize=16,color="green",shape="box"];8782[label="Zero",fontsize=16,color="green",shape="box"];8783[label="Zero",fontsize=16,color="green",shape="box"];8784[label="Zero",fontsize=16,color="green",shape="box"];8785[label="primQuotInt (Pos vuz360) (gcd0Gcd'2 (abs (Pos vuz361)) (abs (Neg vuz3190 * Neg vuz3170)))",fontsize=16,color="black",shape="box"];8785 -> 8907[label="",style="solid", color="black", weight=3];
67.83/34.96	10004 -> 9988[label="",style="dashed", color="red", weight=0];
67.83/34.96	10004[label="Neg vuz3190 * Neg vuz3170",fontsize=16,color="magenta"];10004 -> 10031[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	10004 -> 10032[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8788[label="primQuotInt (Pos vuz360) (gcd1 False (Pos vuz361) (Neg vuz3190 * Neg vuz3170))",fontsize=16,color="black",shape="box"];8788 -> 8908[label="",style="solid", color="black", weight=3];
67.83/34.96	8789[label="primQuotInt (Pos vuz360) (gcd1 True (Pos vuz361) (Neg vuz3190 * Neg vuz3170))",fontsize=16,color="black",shape="box"];8789 -> 8909[label="",style="solid", color="black", weight=3];
67.83/34.96	8791 -> 7571[label="",style="dashed", color="red", weight=0];
67.83/34.96	8791[label="primPlusNat vuz369 vuz481",fontsize=16,color="magenta"];8791 -> 8910[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8791 -> 8911[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8792 -> 7479[label="",style="dashed", color="red", weight=0];
67.83/34.96	8792[label="primEqInt (Pos (primPlusNat vuz369 vuz481)) (fromInt (Pos Zero))",fontsize=16,color="magenta"];8792 -> 8912[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8790[label="primQuotInt (Pos vuz366) (gcd2 vuz504 (Pos vuz505) (Pos vuz367))",fontsize=16,color="burlywood",shape="triangle"];11067[label="vuz504/False",fontsize=10,color="white",style="solid",shape="box"];8790 -> 11067[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	11067 -> 8913[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	11068[label="vuz504/True",fontsize=10,color="white",style="solid",shape="box"];8790 -> 11068[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	11068 -> 8914[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	8793[label="primQuotInt (Pos vuz366) (gcd2 (primEqInt (primMinusNat (Succ vuz3690) vuz483) (fromInt (Pos Zero))) (primMinusNat (Succ vuz3690) vuz483) (Pos vuz367))",fontsize=16,color="burlywood",shape="box"];11069[label="vuz483/Succ vuz4830",fontsize=10,color="white",style="solid",shape="box"];8793 -> 11069[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	11069 -> 8915[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	11070[label="vuz483/Zero",fontsize=10,color="white",style="solid",shape="box"];8793 -> 11070[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	11070 -> 8916[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	8794[label="primQuotInt (Pos vuz366) (gcd2 (primEqInt (primMinusNat Zero vuz483) (fromInt (Pos Zero))) (primMinusNat Zero vuz483) (Pos vuz367))",fontsize=16,color="burlywood",shape="box"];11071[label="vuz483/Succ vuz4830",fontsize=10,color="white",style="solid",shape="box"];8794 -> 11071[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	11071 -> 8917[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	11072[label="vuz483/Zero",fontsize=10,color="white",style="solid",shape="box"];8794 -> 11072[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	11072 -> 8918[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	8795[label="vuz371",fontsize=16,color="green",shape="box"];8796[label="vuz485",fontsize=16,color="green",shape="box"];8797[label="vuz373",fontsize=16,color="green",shape="box"];8798[label="vuz370",fontsize=16,color="green",shape="box"];8800 -> 7498[label="",style="dashed", color="red", weight=0];
67.83/34.96	8800[label="primEqInt (Neg (primPlusNat vuz373 vuz487)) (fromInt (Pos Zero))",fontsize=16,color="magenta"];8800 -> 8919[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8801 -> 7571[label="",style="dashed", color="red", weight=0];
67.83/34.96	8801[label="primPlusNat vuz373 vuz487",fontsize=16,color="magenta"];8801 -> 8920[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8801 -> 8921[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8799[label="primQuotInt (Pos vuz370) (gcd2 vuz507 (Neg vuz508) (Pos vuz371))",fontsize=16,color="burlywood",shape="triangle"];11073[label="vuz507/False",fontsize=10,color="white",style="solid",shape="box"];8799 -> 11073[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	11073 -> 8922[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	11074[label="vuz507/True",fontsize=10,color="white",style="solid",shape="box"];8799 -> 11074[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	11074 -> 8923[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	8802[label="primQuotInt (Neg vuz374) (gcd2 (primEqInt (primMinusNat (Succ vuz4890) vuz377) (fromInt (Pos Zero))) (primMinusNat (Succ vuz4890) vuz377) (Neg vuz375))",fontsize=16,color="burlywood",shape="box"];11075[label="vuz377/Succ vuz3770",fontsize=10,color="white",style="solid",shape="box"];8802 -> 11075[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	11075 -> 8924[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	11076[label="vuz377/Zero",fontsize=10,color="white",style="solid",shape="box"];8802 -> 11076[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	11076 -> 8925[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	8803[label="primQuotInt (Neg vuz374) (gcd2 (primEqInt (primMinusNat Zero vuz377) (fromInt (Pos Zero))) (primMinusNat Zero vuz377) (Neg vuz375))",fontsize=16,color="burlywood",shape="box"];11077[label="vuz377/Succ vuz3770",fontsize=10,color="white",style="solid",shape="box"];8803 -> 11077[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	11077 -> 8926[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	11078[label="vuz377/Zero",fontsize=10,color="white",style="solid",shape="box"];8803 -> 11078[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	11078 -> 8927[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	8805 -> 7498[label="",style="dashed", color="red", weight=0];
67.83/34.96	8805[label="primEqInt (Neg (primPlusNat vuz377 vuz491)) (fromInt (Pos Zero))",fontsize=16,color="magenta"];8805 -> 8928[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8806 -> 7571[label="",style="dashed", color="red", weight=0];
67.83/34.96	8806[label="primPlusNat vuz377 vuz491",fontsize=16,color="magenta"];8806 -> 8929[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8806 -> 8930[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8804[label="primQuotInt (Neg vuz374) (gcd2 vuz510 (Neg vuz511) (Neg vuz375))",fontsize=16,color="burlywood",shape="triangle"];11079[label="vuz510/False",fontsize=10,color="white",style="solid",shape="box"];8804 -> 11079[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	11079 -> 8931[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	11080[label="vuz510/True",fontsize=10,color="white",style="solid",shape="box"];8804 -> 11080[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	11080 -> 8932[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	8808 -> 7479[label="",style="dashed", color="red", weight=0];
67.83/34.96	8808[label="primEqInt (Pos (primPlusNat vuz381 vuz493)) (fromInt (Pos Zero))",fontsize=16,color="magenta"];8808 -> 8933[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8809 -> 7571[label="",style="dashed", color="red", weight=0];
67.83/34.96	8809[label="primPlusNat vuz381 vuz493",fontsize=16,color="magenta"];8809 -> 8934[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8809 -> 8935[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8807[label="primQuotInt (Neg vuz378) (gcd2 vuz513 (Pos vuz514) (Neg vuz379))",fontsize=16,color="burlywood",shape="triangle"];11081[label="vuz513/False",fontsize=10,color="white",style="solid",shape="box"];8807 -> 11081[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	11081 -> 8936[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	11082[label="vuz513/True",fontsize=10,color="white",style="solid",shape="box"];8807 -> 11082[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	11082 -> 8937[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	8810[label="vuz379",fontsize=16,color="green",shape="box"];8811[label="vuz381",fontsize=16,color="green",shape="box"];8812[label="vuz378",fontsize=16,color="green",shape="box"];8813[label="vuz495",fontsize=16,color="green",shape="box"];8814 -> 9854[label="",style="dashed", color="red", weight=0];
67.83/34.96	8814[label="primQuotInt (Pos vuz398) (gcd0Gcd'1 (abs (Pos vuz3190 * Pos vuz3170) == fromInt (Pos Zero)) (abs (Pos vuz399)) (abs (Pos vuz3190 * Pos vuz3170)))",fontsize=16,color="magenta"];8814 -> 9855[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8814 -> 9856[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8814 -> 9857[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8814 -> 9858[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	10017[label="Pos vuz3170",fontsize=16,color="green",shape="box"];10018[label="Pos vuz3190",fontsize=16,color="green",shape="box"];8815 -> 8373[label="",style="dashed", color="red", weight=0];
67.83/34.96	8815[label="primQuotInt (Pos vuz398) (gcd0 (Pos vuz399) (Pos vuz3190 * Pos vuz3170))",fontsize=16,color="magenta"];8816[label="primQuotInt (Pos vuz398) (error [])",fontsize=16,color="black",shape="triangle"];8816 -> 8939[label="",style="solid", color="black", weight=3];
67.83/34.96	8817[label="Succ vuz4010",fontsize=16,color="green",shape="box"];8818[label="Succ vuz31700",fontsize=16,color="green",shape="box"];8819[label="Succ vuz4010",fontsize=16,color="green",shape="box"];8820[label="Succ vuz4000",fontsize=16,color="green",shape="box"];8821[label="Succ vuz31700",fontsize=16,color="green",shape="box"];8822[label="Succ vuz4000",fontsize=16,color="green",shape="box"];8823[label="Zero",fontsize=16,color="green",shape="box"];8824[label="Succ vuz31700",fontsize=16,color="green",shape="box"];8825[label="Zero",fontsize=16,color="green",shape="box"];8826[label="Succ vuz4090",fontsize=16,color="green",shape="box"];8827[label="Succ vuz4090",fontsize=16,color="green",shape="box"];8828[label="Succ vuz31700",fontsize=16,color="green",shape="box"];8829[label="Succ vuz4080",fontsize=16,color="green",shape="box"];8830[label="Succ vuz31700",fontsize=16,color="green",shape="box"];8831[label="Succ vuz4080",fontsize=16,color="green",shape="box"];8832[label="Zero",fontsize=16,color="green",shape="box"];8833[label="Zero",fontsize=16,color="green",shape="box"];8834[label="Succ vuz31700",fontsize=16,color="green",shape="box"];8835 -> 9854[label="",style="dashed", color="red", weight=0];
67.83/34.96	8835[label="primQuotInt (Pos vuz416) (gcd0Gcd'1 (abs (Neg vuz3190 * Pos vuz3170) == fromInt (Pos Zero)) (abs (Pos vuz417)) (abs (Neg vuz3190 * Pos vuz3170)))",fontsize=16,color="magenta"];8835 -> 9859[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8835 -> 9860[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8835 -> 9861[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	10019[label="Pos vuz3170",fontsize=16,color="green",shape="box"];10020[label="Neg vuz3190",fontsize=16,color="green",shape="box"];8836 -> 8387[label="",style="dashed", color="red", weight=0];
67.83/34.96	8836[label="primQuotInt (Pos vuz416) (gcd0 (Pos vuz417) (Neg vuz3190 * Pos vuz3170))",fontsize=16,color="magenta"];8837 -> 8816[label="",style="dashed", color="red", weight=0];
67.83/34.96	8837[label="primQuotInt (Pos vuz416) (error [])",fontsize=16,color="magenta"];8837 -> 8941[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8838[label="Succ vuz4190",fontsize=16,color="green",shape="box"];8839[label="Succ vuz4190",fontsize=16,color="green",shape="box"];8840[label="Succ vuz31900",fontsize=16,color="green",shape="box"];8841[label="Succ vuz4180",fontsize=16,color="green",shape="box"];8842[label="Succ vuz4180",fontsize=16,color="green",shape="box"];8843[label="Succ vuz31900",fontsize=16,color="green",shape="box"];8844[label="Zero",fontsize=16,color="green",shape="box"];8845[label="Zero",fontsize=16,color="green",shape="box"];8846[label="Succ vuz31900",fontsize=16,color="green",shape="box"];8847 -> 10039[label="",style="dashed", color="red", weight=0];
67.83/34.96	8847[label="primQuotInt (Neg vuz426) (gcd0Gcd'1 (abs (Neg vuz3190 * Neg vuz3170) == fromInt (Pos Zero)) (abs (Neg vuz427)) (abs (Neg vuz3190 * Neg vuz3170)))",fontsize=16,color="magenta"];8847 -> 10040[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8847 -> 10041[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8847 -> 10042[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8847 -> 10043[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	10021[label="Neg vuz3170",fontsize=16,color="green",shape="box"];10022[label="Neg vuz3190",fontsize=16,color="green",shape="box"];8848 -> 8396[label="",style="dashed", color="red", weight=0];
67.83/34.96	8848[label="primQuotInt (Neg vuz426) (gcd0 (Neg vuz427) (Neg vuz3190 * Neg vuz3170))",fontsize=16,color="magenta"];8849[label="primQuotInt (Neg vuz426) (error [])",fontsize=16,color="black",shape="triangle"];8849 -> 8943[label="",style="solid", color="black", weight=3];
67.83/34.96	8850 -> 10039[label="",style="dashed", color="red", weight=0];
67.83/34.96	8850[label="primQuotInt (Neg vuz428) (gcd0Gcd'1 (abs (Pos vuz3190 * Neg vuz3170) == fromInt (Pos Zero)) (abs (Neg vuz429)) (abs (Pos vuz3190 * Neg vuz3170)))",fontsize=16,color="magenta"];8850 -> 10044[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8850 -> 10045[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8850 -> 10046[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	10023[label="Neg vuz3170",fontsize=16,color="green",shape="box"];10024[label="Pos vuz3190",fontsize=16,color="green",shape="box"];8851 -> 8398[label="",style="dashed", color="red", weight=0];
67.83/34.96	8851[label="primQuotInt (Neg vuz428) (gcd0 (Neg vuz429) (Pos vuz3190 * Neg vuz3170))",fontsize=16,color="magenta"];8852 -> 8849[label="",style="dashed", color="red", weight=0];
67.83/34.96	8852[label="primQuotInt (Neg vuz428) (error [])",fontsize=16,color="magenta"];8852 -> 8945[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8853[label="Succ vuz4310",fontsize=16,color="green",shape="box"];8854[label="Succ vuz31900",fontsize=16,color="green",shape="box"];8855[label="Succ vuz4310",fontsize=16,color="green",shape="box"];8856[label="Succ vuz4300",fontsize=16,color="green",shape="box"];8857[label="Succ vuz31900",fontsize=16,color="green",shape="box"];8858[label="Succ vuz4300",fontsize=16,color="green",shape="box"];8859[label="Zero",fontsize=16,color="green",shape="box"];8860[label="Succ vuz31900",fontsize=16,color="green",shape="box"];8861[label="Zero",fontsize=16,color="green",shape="box"];8862[label="Succ vuz4390",fontsize=16,color="green",shape="box"];8863[label="Succ vuz4390",fontsize=16,color="green",shape="box"];8864[label="Succ vuz31900",fontsize=16,color="green",shape="box"];8865[label="Succ vuz4380",fontsize=16,color="green",shape="box"];8866[label="Succ vuz31900",fontsize=16,color="green",shape="box"];8867[label="Succ vuz4380",fontsize=16,color="green",shape="box"];8868[label="Zero",fontsize=16,color="green",shape="box"];8869[label="Zero",fontsize=16,color="green",shape="box"];8870[label="Succ vuz31900",fontsize=16,color="green",shape="box"];8871 -> 10039[label="",style="dashed", color="red", weight=0];
67.83/34.96	8871[label="primQuotInt (Neg vuz446) (gcd0Gcd'1 (abs (Neg vuz3190 * Pos vuz3170) == fromInt (Pos Zero)) (abs (Neg vuz447)) (abs (Neg vuz3190 * Pos vuz3170)))",fontsize=16,color="magenta"];8871 -> 10047[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8871 -> 10048[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8871 -> 10049[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8871 -> 10050[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	10025[label="Pos vuz3170",fontsize=16,color="green",shape="box"];10026[label="Neg vuz3190",fontsize=16,color="green",shape="box"];8872 -> 8412[label="",style="dashed", color="red", weight=0];
67.83/34.96	8872[label="primQuotInt (Neg vuz446) (gcd0 (Neg vuz447) (Neg vuz3190 * Pos vuz3170))",fontsize=16,color="magenta"];8873 -> 8849[label="",style="dashed", color="red", weight=0];
67.83/34.96	8873[label="primQuotInt (Neg vuz446) (error [])",fontsize=16,color="magenta"];8873 -> 8947[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8874 -> 10039[label="",style="dashed", color="red", weight=0];
67.83/34.96	8874[label="primQuotInt (Neg vuz348) (gcd0Gcd'1 (abs (Pos vuz3190 * Pos vuz3170) == fromInt (Pos Zero)) (abs (Neg vuz349)) (abs (Pos vuz3190 * Pos vuz3170)))",fontsize=16,color="magenta"];8874 -> 10051[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8874 -> 10052[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8874 -> 10053[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8874 -> 10054[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	10027[label="Pos vuz3170",fontsize=16,color="green",shape="box"];10028[label="Pos vuz3190",fontsize=16,color="green",shape="box"];8875 -> 8414[label="",style="dashed", color="red", weight=0];
67.83/34.96	8875[label="primQuotInt (Neg vuz348) (gcd0 (Neg vuz349) (Pos vuz3190 * Pos vuz3170))",fontsize=16,color="magenta"];8876 -> 8849[label="",style="dashed", color="red", weight=0];
67.83/34.96	8876[label="primQuotInt (Neg vuz348) (error [])",fontsize=16,color="magenta"];8876 -> 8949[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8877[label="Succ vuz31900",fontsize=16,color="green",shape="box"];8878[label="Succ vuz4490",fontsize=16,color="green",shape="box"];8879[label="Succ vuz4490",fontsize=16,color="green",shape="box"];8880[label="Succ vuz4480",fontsize=16,color="green",shape="box"];8881[label="Succ vuz31900",fontsize=16,color="green",shape="box"];8882[label="Succ vuz4480",fontsize=16,color="green",shape="box"];8883[label="Succ vuz31900",fontsize=16,color="green",shape="box"];8884[label="Zero",fontsize=16,color="green",shape="box"];8885[label="Zero",fontsize=16,color="green",shape="box"];8886 -> 9854[label="",style="dashed", color="red", weight=0];
67.83/34.96	8886[label="primQuotInt (Pos vuz354) (gcd0Gcd'1 (abs (Pos vuz3190 * Neg vuz3170) == fromInt (Pos Zero)) (abs (Pos vuz355)) (abs (Pos vuz3190 * Neg vuz3170)))",fontsize=16,color="magenta"];8886 -> 9862[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8886 -> 9863[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8886 -> 9864[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8886 -> 9865[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	10029[label="Neg vuz3170",fontsize=16,color="green",shape="box"];10030[label="Pos vuz3190",fontsize=16,color="green",shape="box"];8887 -> 8422[label="",style="dashed", color="red", weight=0];
67.83/34.96	8887[label="primQuotInt (Pos vuz354) (gcd0 (Pos vuz355) (Pos vuz3190 * Neg vuz3170))",fontsize=16,color="magenta"];8888 -> 8816[label="",style="dashed", color="red", weight=0];
67.83/34.96	8888[label="primQuotInt (Pos vuz354) (error [])",fontsize=16,color="magenta"];8888 -> 8951[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8889[label="Succ vuz4570",fontsize=16,color="green",shape="box"];8890[label="Succ vuz4570",fontsize=16,color="green",shape="box"];8891[label="Succ vuz31700",fontsize=16,color="green",shape="box"];8892[label="Succ vuz4560",fontsize=16,color="green",shape="box"];8893[label="Succ vuz31700",fontsize=16,color="green",shape="box"];8894[label="Succ vuz4560",fontsize=16,color="green",shape="box"];8895[label="Zero",fontsize=16,color="green",shape="box"];8896[label="Zero",fontsize=16,color="green",shape="box"];8897[label="Succ vuz31700",fontsize=16,color="green",shape="box"];8898[label="Succ vuz4650",fontsize=16,color="green",shape="box"];8899[label="Succ vuz4650",fontsize=16,color="green",shape="box"];8900[label="Succ vuz31700",fontsize=16,color="green",shape="box"];8901[label="Succ vuz4640",fontsize=16,color="green",shape="box"];8902[label="Succ vuz4640",fontsize=16,color="green",shape="box"];8903[label="Succ vuz31700",fontsize=16,color="green",shape="box"];8904[label="Zero",fontsize=16,color="green",shape="box"];8905[label="Zero",fontsize=16,color="green",shape="box"];8906[label="Succ vuz31700",fontsize=16,color="green",shape="box"];8907 -> 9854[label="",style="dashed", color="red", weight=0];
67.83/34.96	8907[label="primQuotInt (Pos vuz360) (gcd0Gcd'1 (abs (Neg vuz3190 * Neg vuz3170) == fromInt (Pos Zero)) (abs (Pos vuz361)) (abs (Neg vuz3190 * Neg vuz3170)))",fontsize=16,color="magenta"];8907 -> 9866[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8907 -> 9867[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8907 -> 9868[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8907 -> 9869[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	10031[label="Neg vuz3170",fontsize=16,color="green",shape="box"];10032[label="Neg vuz3190",fontsize=16,color="green",shape="box"];8908 -> 8436[label="",style="dashed", color="red", weight=0];
67.83/34.96	8908[label="primQuotInt (Pos vuz360) (gcd0 (Pos vuz361) (Neg vuz3190 * Neg vuz3170))",fontsize=16,color="magenta"];8909 -> 8816[label="",style="dashed", color="red", weight=0];
67.83/34.96	8909[label="primQuotInt (Pos vuz360) (error [])",fontsize=16,color="magenta"];8909 -> 8953[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8910[label="vuz369",fontsize=16,color="green",shape="box"];8911[label="vuz481",fontsize=16,color="green",shape="box"];8912 -> 7571[label="",style="dashed", color="red", weight=0];
67.83/34.96	8912[label="primPlusNat vuz369 vuz481",fontsize=16,color="magenta"];8912 -> 8954[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8912 -> 8955[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7479[label="primEqInt (Pos vuz325) (fromInt (Pos Zero))",fontsize=16,color="burlywood",shape="triangle"];11083[label="vuz325/Succ vuz3250",fontsize=10,color="white",style="solid",shape="box"];7479 -> 11083[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	11083 -> 7494[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	11084[label="vuz325/Zero",fontsize=10,color="white",style="solid",shape="box"];7479 -> 11084[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	11084 -> 7495[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	8913[label="primQuotInt (Pos vuz366) (gcd2 False (Pos vuz505) (Pos vuz367))",fontsize=16,color="black",shape="box"];8913 -> 8956[label="",style="solid", color="black", weight=3];
67.83/34.96	8914[label="primQuotInt (Pos vuz366) (gcd2 True (Pos vuz505) (Pos vuz367))",fontsize=16,color="black",shape="box"];8914 -> 8957[label="",style="solid", color="black", weight=3];
67.83/34.96	8915[label="primQuotInt (Pos vuz366) (gcd2 (primEqInt (primMinusNat (Succ vuz3690) (Succ vuz4830)) (fromInt (Pos Zero))) (primMinusNat (Succ vuz3690) (Succ vuz4830)) (Pos vuz367))",fontsize=16,color="black",shape="box"];8915 -> 8958[label="",style="solid", color="black", weight=3];
67.83/34.96	8916[label="primQuotInt (Pos vuz366) (gcd2 (primEqInt (primMinusNat (Succ vuz3690) Zero) (fromInt (Pos Zero))) (primMinusNat (Succ vuz3690) Zero) (Pos vuz367))",fontsize=16,color="black",shape="box"];8916 -> 8959[label="",style="solid", color="black", weight=3];
67.83/34.96	8917[label="primQuotInt (Pos vuz366) (gcd2 (primEqInt (primMinusNat Zero (Succ vuz4830)) (fromInt (Pos Zero))) (primMinusNat Zero (Succ vuz4830)) (Pos vuz367))",fontsize=16,color="black",shape="box"];8917 -> 8960[label="",style="solid", color="black", weight=3];
67.83/34.96	8918[label="primQuotInt (Pos vuz366) (gcd2 (primEqInt (primMinusNat Zero Zero) (fromInt (Pos Zero))) (primMinusNat Zero Zero) (Pos vuz367))",fontsize=16,color="black",shape="box"];8918 -> 8961[label="",style="solid", color="black", weight=3];
67.83/34.96	8919 -> 7571[label="",style="dashed", color="red", weight=0];
67.83/34.96	8919[label="primPlusNat vuz373 vuz487",fontsize=16,color="magenta"];8919 -> 8962[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8919 -> 8963[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	7498[label="primEqInt (Neg vuz326) (fromInt (Pos Zero))",fontsize=16,color="burlywood",shape="triangle"];11085[label="vuz326/Succ vuz3260",fontsize=10,color="white",style="solid",shape="box"];7498 -> 11085[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	11085 -> 7512[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	11086[label="vuz326/Zero",fontsize=10,color="white",style="solid",shape="box"];7498 -> 11086[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	11086 -> 7513[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	8920[label="vuz373",fontsize=16,color="green",shape="box"];8921[label="vuz487",fontsize=16,color="green",shape="box"];8922[label="primQuotInt (Pos vuz370) (gcd2 False (Neg vuz508) (Pos vuz371))",fontsize=16,color="black",shape="box"];8922 -> 8964[label="",style="solid", color="black", weight=3];
67.83/34.96	8923[label="primQuotInt (Pos vuz370) (gcd2 True (Neg vuz508) (Pos vuz371))",fontsize=16,color="black",shape="box"];8923 -> 8965[label="",style="solid", color="black", weight=3];
67.83/34.96	8924[label="primQuotInt (Neg vuz374) (gcd2 (primEqInt (primMinusNat (Succ vuz4890) (Succ vuz3770)) (fromInt (Pos Zero))) (primMinusNat (Succ vuz4890) (Succ vuz3770)) (Neg vuz375))",fontsize=16,color="black",shape="box"];8924 -> 8966[label="",style="solid", color="black", weight=3];
67.83/34.96	8925[label="primQuotInt (Neg vuz374) (gcd2 (primEqInt (primMinusNat (Succ vuz4890) Zero) (fromInt (Pos Zero))) (primMinusNat (Succ vuz4890) Zero) (Neg vuz375))",fontsize=16,color="black",shape="box"];8925 -> 8967[label="",style="solid", color="black", weight=3];
67.83/34.96	8926[label="primQuotInt (Neg vuz374) (gcd2 (primEqInt (primMinusNat Zero (Succ vuz3770)) (fromInt (Pos Zero))) (primMinusNat Zero (Succ vuz3770)) (Neg vuz375))",fontsize=16,color="black",shape="box"];8926 -> 8968[label="",style="solid", color="black", weight=3];
67.83/34.96	8927[label="primQuotInt (Neg vuz374) (gcd2 (primEqInt (primMinusNat Zero Zero) (fromInt (Pos Zero))) (primMinusNat Zero Zero) (Neg vuz375))",fontsize=16,color="black",shape="box"];8927 -> 8969[label="",style="solid", color="black", weight=3];
67.83/34.96	8928 -> 7571[label="",style="dashed", color="red", weight=0];
67.83/34.96	8928[label="primPlusNat vuz377 vuz491",fontsize=16,color="magenta"];8928 -> 8970[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8928 -> 8971[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8929[label="vuz377",fontsize=16,color="green",shape="box"];8930[label="vuz491",fontsize=16,color="green",shape="box"];8931[label="primQuotInt (Neg vuz374) (gcd2 False (Neg vuz511) (Neg vuz375))",fontsize=16,color="black",shape="box"];8931 -> 8972[label="",style="solid", color="black", weight=3];
67.83/34.96	8932[label="primQuotInt (Neg vuz374) (gcd2 True (Neg vuz511) (Neg vuz375))",fontsize=16,color="black",shape="box"];8932 -> 8973[label="",style="solid", color="black", weight=3];
67.83/34.96	8933 -> 7571[label="",style="dashed", color="red", weight=0];
67.83/34.96	8933[label="primPlusNat vuz381 vuz493",fontsize=16,color="magenta"];8933 -> 8974[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8933 -> 8975[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	8934[label="vuz381",fontsize=16,color="green",shape="box"];8935[label="vuz493",fontsize=16,color="green",shape="box"];8936[label="primQuotInt (Neg vuz378) (gcd2 False (Pos vuz514) (Neg vuz379))",fontsize=16,color="black",shape="box"];8936 -> 8976[label="",style="solid", color="black", weight=3];
67.83/34.96	8937[label="primQuotInt (Neg vuz378) (gcd2 True (Pos vuz514) (Neg vuz379))",fontsize=16,color="black",shape="box"];8937 -> 8977[label="",style="solid", color="black", weight=3];
67.83/34.96	9855 -> 9987[label="",style="dashed", color="red", weight=0];
67.83/34.96	9855[label="abs (Pos vuz3190 * Pos vuz3170) == fromInt (Pos Zero)",fontsize=16,color="magenta"];9855 -> 10005[label="",style="dashed", color="magenta", weight=3];
67.83/34.96	9856[label="vuz398",fontsize=16,color="green",shape="box"];9857[label="abs (Pos vuz399)",fontsize=16,color="black",shape="triangle"];9857 -> 10033[label="",style="solid", color="black", weight=3];
67.83/34.96	9858 -> 9366[label="",style="dashed", color="red", weight=0];
67.83/34.96	9858[label="abs (Pos vuz3190 * Pos vuz3170)",fontsize=16,color="magenta"];9854[label="primQuotInt (Pos vuz416) (gcd0Gcd'1 vuz550 vuz549 vuz542)",fontsize=16,color="burlywood",shape="triangle"];11087[label="vuz550/False",fontsize=10,color="white",style="solid",shape="box"];9854 -> 11087[label="",style="solid", color="burlywood", weight=9];
67.83/34.96	11087 -> 10034[label="",style="solid", color="burlywood", weight=3];
67.83/34.96	11088[label="vuz550/True",fontsize=10,color="white",style="solid",shape="box"];9854 -> 11088[label="",style="solid", color="burlywood", weight=9];
67.83/34.97	11088 -> 10035[label="",style="solid", color="burlywood", weight=3];
67.83/34.97	8939[label="error []",fontsize=16,color="red",shape="box"];9859 -> 9987[label="",style="dashed", color="red", weight=0];
67.83/34.97	9859[label="abs (Neg vuz3190 * Pos vuz3170) == fromInt (Pos Zero)",fontsize=16,color="magenta"];9859 -> 10006[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	9860 -> 9857[label="",style="dashed", color="red", weight=0];
67.83/34.97	9860[label="abs (Pos vuz417)",fontsize=16,color="magenta"];9860 -> 10036[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	9861 -> 9369[label="",style="dashed", color="red", weight=0];
67.83/34.97	9861[label="abs (Neg vuz3190 * Pos vuz3170)",fontsize=16,color="magenta"];8941[label="vuz416",fontsize=16,color="green",shape="box"];10040[label="vuz426",fontsize=16,color="green",shape="box"];10041 -> 9376[label="",style="dashed", color="red", weight=0];
67.83/34.97	10041[label="abs (Neg vuz3190 * Neg vuz3170)",fontsize=16,color="magenta"];10042[label="abs (Neg vuz427)",fontsize=16,color="black",shape="triangle"];10042 -> 10172[label="",style="solid", color="black", weight=3];
67.83/34.97	10043 -> 9987[label="",style="dashed", color="red", weight=0];
67.83/34.97	10043[label="abs (Neg vuz3190 * Neg vuz3170) == fromInt (Pos Zero)",fontsize=16,color="magenta"];10043 -> 10173[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	10039[label="primQuotInt (Neg vuz428) (gcd0Gcd'1 vuz553 vuz552 vuz544)",fontsize=16,color="burlywood",shape="triangle"];11089[label="vuz553/False",fontsize=10,color="white",style="solid",shape="box"];10039 -> 11089[label="",style="solid", color="burlywood", weight=9];
67.83/34.97	11089 -> 10174[label="",style="solid", color="burlywood", weight=3];
67.83/34.97	11090[label="vuz553/True",fontsize=10,color="white",style="solid",shape="box"];10039 -> 11090[label="",style="solid", color="burlywood", weight=9];
67.83/34.97	11090 -> 10175[label="",style="solid", color="burlywood", weight=3];
67.83/34.97	8943[label="error []",fontsize=16,color="red",shape="box"];10044 -> 9372[label="",style="dashed", color="red", weight=0];
67.83/34.97	10044[label="abs (Pos vuz3190 * Neg vuz3170)",fontsize=16,color="magenta"];10045 -> 10042[label="",style="dashed", color="red", weight=0];
67.83/34.97	10045[label="abs (Neg vuz429)",fontsize=16,color="magenta"];10045 -> 10176[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	10046 -> 9987[label="",style="dashed", color="red", weight=0];
67.83/34.97	10046[label="abs (Pos vuz3190 * Neg vuz3170) == fromInt (Pos Zero)",fontsize=16,color="magenta"];10046 -> 10177[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	8945[label="vuz428",fontsize=16,color="green",shape="box"];10047[label="vuz446",fontsize=16,color="green",shape="box"];10048 -> 9369[label="",style="dashed", color="red", weight=0];
67.83/34.97	10048[label="abs (Neg vuz3190 * Pos vuz3170)",fontsize=16,color="magenta"];10049 -> 10042[label="",style="dashed", color="red", weight=0];
67.83/34.97	10049[label="abs (Neg vuz447)",fontsize=16,color="magenta"];10049 -> 10178[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	10050 -> 9987[label="",style="dashed", color="red", weight=0];
67.83/34.97	10050[label="abs (Neg vuz3190 * Pos vuz3170) == fromInt (Pos Zero)",fontsize=16,color="magenta"];10050 -> 10179[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	8947[label="vuz446",fontsize=16,color="green",shape="box"];10051[label="vuz348",fontsize=16,color="green",shape="box"];10052 -> 9366[label="",style="dashed", color="red", weight=0];
67.83/34.97	10052[label="abs (Pos vuz3190 * Pos vuz3170)",fontsize=16,color="magenta"];10053 -> 10042[label="",style="dashed", color="red", weight=0];
67.83/34.97	10053[label="abs (Neg vuz349)",fontsize=16,color="magenta"];10053 -> 10180[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	10054 -> 9987[label="",style="dashed", color="red", weight=0];
67.83/34.97	10054[label="abs (Pos vuz3190 * Pos vuz3170) == fromInt (Pos Zero)",fontsize=16,color="magenta"];10054 -> 10181[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	8949[label="vuz348",fontsize=16,color="green",shape="box"];9862 -> 9987[label="",style="dashed", color="red", weight=0];
67.83/34.97	9862[label="abs (Pos vuz3190 * Neg vuz3170) == fromInt (Pos Zero)",fontsize=16,color="magenta"];9862 -> 10007[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	9863[label="vuz354",fontsize=16,color="green",shape="box"];9864 -> 9857[label="",style="dashed", color="red", weight=0];
67.83/34.97	9864[label="abs (Pos vuz355)",fontsize=16,color="magenta"];9864 -> 10037[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	9865 -> 9372[label="",style="dashed", color="red", weight=0];
67.83/34.97	9865[label="abs (Pos vuz3190 * Neg vuz3170)",fontsize=16,color="magenta"];8951[label="vuz354",fontsize=16,color="green",shape="box"];9866 -> 9987[label="",style="dashed", color="red", weight=0];
67.83/34.97	9866[label="abs (Neg vuz3190 * Neg vuz3170) == fromInt (Pos Zero)",fontsize=16,color="magenta"];9866 -> 10008[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	9867[label="vuz360",fontsize=16,color="green",shape="box"];9868 -> 9857[label="",style="dashed", color="red", weight=0];
67.83/34.97	9868[label="abs (Pos vuz361)",fontsize=16,color="magenta"];9868 -> 10038[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	9869 -> 9376[label="",style="dashed", color="red", weight=0];
67.83/34.97	9869[label="abs (Neg vuz3190 * Neg vuz3170)",fontsize=16,color="magenta"];8953[label="vuz360",fontsize=16,color="green",shape="box"];8954[label="vuz369",fontsize=16,color="green",shape="box"];8955[label="vuz481",fontsize=16,color="green",shape="box"];7494[label="primEqInt (Pos (Succ vuz3250)) (fromInt (Pos Zero))",fontsize=16,color="black",shape="box"];7494 -> 7519[label="",style="solid", color="black", weight=3];
67.83/34.97	7495[label="primEqInt (Pos Zero) (fromInt (Pos Zero))",fontsize=16,color="black",shape="box"];7495 -> 7520[label="",style="solid", color="black", weight=3];
67.83/34.97	8956[label="primQuotInt (Pos vuz366) (gcd0 (Pos vuz505) (Pos vuz367))",fontsize=16,color="black",shape="triangle"];8956 -> 8986[label="",style="solid", color="black", weight=3];
67.83/34.97	8957 -> 8987[label="",style="dashed", color="red", weight=0];
67.83/34.97	8957[label="primQuotInt (Pos vuz366) (gcd1 (Pos vuz367 == fromInt (Pos Zero)) (Pos vuz505) (Pos vuz367))",fontsize=16,color="magenta"];8957 -> 8988[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	8958 -> 8615[label="",style="dashed", color="red", weight=0];
67.83/34.97	8958[label="primQuotInt (Pos vuz366) (gcd2 (primEqInt (primMinusNat vuz3690 vuz4830) (fromInt (Pos Zero))) (primMinusNat vuz3690 vuz4830) (Pos vuz367))",fontsize=16,color="magenta"];8958 -> 8989[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	8958 -> 8990[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	8959 -> 8790[label="",style="dashed", color="red", weight=0];
67.83/34.97	8959[label="primQuotInt (Pos vuz366) (gcd2 (primEqInt (Pos (Succ vuz3690)) (fromInt (Pos Zero))) (Pos (Succ vuz3690)) (Pos vuz367))",fontsize=16,color="magenta"];8959 -> 8991[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	8959 -> 8992[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	8960 -> 8799[label="",style="dashed", color="red", weight=0];
67.83/34.97	8960[label="primQuotInt (Pos vuz366) (gcd2 (primEqInt (Neg (Succ vuz4830)) (fromInt (Pos Zero))) (Neg (Succ vuz4830)) (Pos vuz367))",fontsize=16,color="magenta"];8960 -> 8993[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	8960 -> 8994[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	8960 -> 8995[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	8960 -> 8996[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	8961 -> 8790[label="",style="dashed", color="red", weight=0];
67.83/34.97	8961[label="primQuotInt (Pos vuz366) (gcd2 (primEqInt (Pos Zero) (fromInt (Pos Zero))) (Pos Zero) (Pos vuz367))",fontsize=16,color="magenta"];8961 -> 8997[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	8961 -> 8998[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	8962[label="vuz373",fontsize=16,color="green",shape="box"];8963[label="vuz487",fontsize=16,color="green",shape="box"];7512[label="primEqInt (Neg (Succ vuz3260)) (fromInt (Pos Zero))",fontsize=16,color="black",shape="box"];7512 -> 7526[label="",style="solid", color="black", weight=3];
67.83/34.97	7513[label="primEqInt (Neg Zero) (fromInt (Pos Zero))",fontsize=16,color="black",shape="box"];7513 -> 7527[label="",style="solid", color="black", weight=3];
67.83/34.97	8964[label="primQuotInt (Pos vuz370) (gcd0 (Neg vuz508) (Pos vuz371))",fontsize=16,color="black",shape="triangle"];8964 -> 8999[label="",style="solid", color="black", weight=3];
67.83/34.97	8965 -> 9000[label="",style="dashed", color="red", weight=0];
67.83/34.97	8965[label="primQuotInt (Pos vuz370) (gcd1 (Pos vuz371 == fromInt (Pos Zero)) (Neg vuz508) (Pos vuz371))",fontsize=16,color="magenta"];8965 -> 9001[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	8966 -> 8630[label="",style="dashed", color="red", weight=0];
67.83/34.97	8966[label="primQuotInt (Neg vuz374) (gcd2 (primEqInt (primMinusNat vuz4890 vuz3770) (fromInt (Pos Zero))) (primMinusNat vuz4890 vuz3770) (Neg vuz375))",fontsize=16,color="magenta"];8966 -> 9002[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	8966 -> 9003[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	8967 -> 8807[label="",style="dashed", color="red", weight=0];
67.83/34.97	8967[label="primQuotInt (Neg vuz374) (gcd2 (primEqInt (Pos (Succ vuz4890)) (fromInt (Pos Zero))) (Pos (Succ vuz4890)) (Neg vuz375))",fontsize=16,color="magenta"];8967 -> 9004[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	8967 -> 9005[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	8967 -> 9006[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	8967 -> 9007[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	8968 -> 8804[label="",style="dashed", color="red", weight=0];
67.83/34.97	8968[label="primQuotInt (Neg vuz374) (gcd2 (primEqInt (Neg (Succ vuz3770)) (fromInt (Pos Zero))) (Neg (Succ vuz3770)) (Neg vuz375))",fontsize=16,color="magenta"];8968 -> 9008[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	8968 -> 9009[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	8969 -> 8807[label="",style="dashed", color="red", weight=0];
67.83/34.97	8969[label="primQuotInt (Neg vuz374) (gcd2 (primEqInt (Pos Zero) (fromInt (Pos Zero))) (Pos Zero) (Neg vuz375))",fontsize=16,color="magenta"];8969 -> 9010[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	8969 -> 9011[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	8969 -> 9012[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	8969 -> 9013[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	8970[label="vuz377",fontsize=16,color="green",shape="box"];8971[label="vuz491",fontsize=16,color="green",shape="box"];8972[label="primQuotInt (Neg vuz374) (gcd0 (Neg vuz511) (Neg vuz375))",fontsize=16,color="black",shape="triangle"];8972 -> 9014[label="",style="solid", color="black", weight=3];
67.83/34.97	8973 -> 9015[label="",style="dashed", color="red", weight=0];
67.83/34.97	8973[label="primQuotInt (Neg vuz374) (gcd1 (Neg vuz375 == fromInt (Pos Zero)) (Neg vuz511) (Neg vuz375))",fontsize=16,color="magenta"];8973 -> 9016[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	8974[label="vuz381",fontsize=16,color="green",shape="box"];8975[label="vuz493",fontsize=16,color="green",shape="box"];8976[label="primQuotInt (Neg vuz378) (gcd0 (Pos vuz514) (Neg vuz379))",fontsize=16,color="black",shape="triangle"];8976 -> 9017[label="",style="solid", color="black", weight=3];
67.83/34.97	8977 -> 9018[label="",style="dashed", color="red", weight=0];
67.83/34.97	8977[label="primQuotInt (Neg vuz378) (gcd1 (Neg vuz379 == fromInt (Pos Zero)) (Pos vuz514) (Neg vuz379))",fontsize=16,color="magenta"];8977 -> 9019[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	10005 -> 9366[label="",style="dashed", color="red", weight=0];
67.83/34.97	10005[label="abs (Pos vuz3190 * Pos vuz3170)",fontsize=16,color="magenta"];10033[label="absReal (Pos vuz399)",fontsize=16,color="black",shape="box"];10033 -> 10182[label="",style="solid", color="black", weight=3];
67.83/34.97	9366[label="abs (Pos vuz3190 * Pos vuz3170)",fontsize=16,color="black",shape="triangle"];9366 -> 9585[label="",style="solid", color="black", weight=3];
67.83/34.97	10034[label="primQuotInt (Pos vuz416) (gcd0Gcd'1 False vuz549 vuz542)",fontsize=16,color="black",shape="box"];10034 -> 10183[label="",style="solid", color="black", weight=3];
67.83/34.97	10035[label="primQuotInt (Pos vuz416) (gcd0Gcd'1 True vuz549 vuz542)",fontsize=16,color="black",shape="box"];10035 -> 10184[label="",style="solid", color="black", weight=3];
67.83/34.97	10006 -> 9369[label="",style="dashed", color="red", weight=0];
67.83/34.97	10006[label="abs (Neg vuz3190 * Pos vuz3170)",fontsize=16,color="magenta"];10036[label="vuz417",fontsize=16,color="green",shape="box"];9369[label="abs (Neg vuz3190 * Pos vuz3170)",fontsize=16,color="black",shape="triangle"];9369 -> 9588[label="",style="solid", color="black", weight=3];
67.83/34.97	9376[label="abs (Neg vuz3190 * Neg vuz3170)",fontsize=16,color="black",shape="triangle"];9376 -> 9590[label="",style="solid", color="black", weight=3];
67.83/34.97	10172[label="absReal (Neg vuz427)",fontsize=16,color="black",shape="box"];10172 -> 10202[label="",style="solid", color="black", weight=3];
67.83/34.97	10173 -> 9376[label="",style="dashed", color="red", weight=0];
67.83/34.97	10173[label="abs (Neg vuz3190 * Neg vuz3170)",fontsize=16,color="magenta"];10174[label="primQuotInt (Neg vuz428) (gcd0Gcd'1 False vuz552 vuz544)",fontsize=16,color="black",shape="box"];10174 -> 10203[label="",style="solid", color="black", weight=3];
67.83/34.97	10175[label="primQuotInt (Neg vuz428) (gcd0Gcd'1 True vuz552 vuz544)",fontsize=16,color="black",shape="box"];10175 -> 10204[label="",style="solid", color="black", weight=3];
67.83/34.97	9372[label="abs (Pos vuz3190 * Neg vuz3170)",fontsize=16,color="black",shape="triangle"];9372 -> 9589[label="",style="solid", color="black", weight=3];
67.83/34.97	10176[label="vuz429",fontsize=16,color="green",shape="box"];10177 -> 9372[label="",style="dashed", color="red", weight=0];
67.83/34.97	10177[label="abs (Pos vuz3190 * Neg vuz3170)",fontsize=16,color="magenta"];10178[label="vuz447",fontsize=16,color="green",shape="box"];10179 -> 9369[label="",style="dashed", color="red", weight=0];
67.83/34.97	10179[label="abs (Neg vuz3190 * Pos vuz3170)",fontsize=16,color="magenta"];10180[label="vuz349",fontsize=16,color="green",shape="box"];10181 -> 9366[label="",style="dashed", color="red", weight=0];
67.83/34.97	10181[label="abs (Pos vuz3190 * Pos vuz3170)",fontsize=16,color="magenta"];10007 -> 9372[label="",style="dashed", color="red", weight=0];
67.83/34.97	10007[label="abs (Pos vuz3190 * Neg vuz3170)",fontsize=16,color="magenta"];10037[label="vuz355",fontsize=16,color="green",shape="box"];10008 -> 9376[label="",style="dashed", color="red", weight=0];
67.83/34.97	10008[label="abs (Neg vuz3190 * Neg vuz3170)",fontsize=16,color="magenta"];10038[label="vuz361",fontsize=16,color="green",shape="box"];8986[label="primQuotInt (Pos vuz366) (gcd0Gcd' (abs (Pos vuz505)) (abs (Pos vuz367)))",fontsize=16,color="black",shape="box"];8986 -> 9028[label="",style="solid", color="black", weight=3];
67.83/34.97	8988 -> 9987[label="",style="dashed", color="red", weight=0];
67.83/34.97	8988[label="Pos vuz367 == fromInt (Pos Zero)",fontsize=16,color="magenta"];8988 -> 10009[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	8987[label="primQuotInt (Pos vuz366) (gcd1 vuz516 (Pos vuz505) (Pos vuz367))",fontsize=16,color="burlywood",shape="triangle"];11091[label="vuz516/False",fontsize=10,color="white",style="solid",shape="box"];8987 -> 11091[label="",style="solid", color="burlywood", weight=9];
67.83/34.97	11091 -> 9030[label="",style="solid", color="burlywood", weight=3];
67.83/34.97	11092[label="vuz516/True",fontsize=10,color="white",style="solid",shape="box"];8987 -> 11092[label="",style="solid", color="burlywood", weight=9];
67.83/34.97	11092 -> 9031[label="",style="solid", color="burlywood", weight=3];
67.83/34.97	8989[label="vuz3690",fontsize=16,color="green",shape="box"];8990[label="vuz4830",fontsize=16,color="green",shape="box"];8991[label="Succ vuz3690",fontsize=16,color="green",shape="box"];8992 -> 7479[label="",style="dashed", color="red", weight=0];
67.83/34.97	8992[label="primEqInt (Pos (Succ vuz3690)) (fromInt (Pos Zero))",fontsize=16,color="magenta"];8992 -> 9032[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	8993 -> 7498[label="",style="dashed", color="red", weight=0];
67.83/34.97	8993[label="primEqInt (Neg (Succ vuz4830)) (fromInt (Pos Zero))",fontsize=16,color="magenta"];8993 -> 9033[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	8994[label="Succ vuz4830",fontsize=16,color="green",shape="box"];8995[label="vuz366",fontsize=16,color="green",shape="box"];8996[label="vuz367",fontsize=16,color="green",shape="box"];8997[label="Zero",fontsize=16,color="green",shape="box"];8998 -> 7479[label="",style="dashed", color="red", weight=0];
67.83/34.97	8998[label="primEqInt (Pos Zero) (fromInt (Pos Zero))",fontsize=16,color="magenta"];8998 -> 9034[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	8999[label="primQuotInt (Pos vuz370) (gcd0Gcd' (abs (Neg vuz508)) (abs (Pos vuz371)))",fontsize=16,color="black",shape="box"];8999 -> 9035[label="",style="solid", color="black", weight=3];
67.83/34.97	9001 -> 9987[label="",style="dashed", color="red", weight=0];
67.83/34.97	9001[label="Pos vuz371 == fromInt (Pos Zero)",fontsize=16,color="magenta"];9001 -> 10010[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	9000[label="primQuotInt (Pos vuz370) (gcd1 vuz517 (Neg vuz508) (Pos vuz371))",fontsize=16,color="burlywood",shape="triangle"];11093[label="vuz517/False",fontsize=10,color="white",style="solid",shape="box"];9000 -> 11093[label="",style="solid", color="burlywood", weight=9];
67.83/34.97	11093 -> 9037[label="",style="solid", color="burlywood", weight=3];
67.83/34.97	11094[label="vuz517/True",fontsize=10,color="white",style="solid",shape="box"];9000 -> 11094[label="",style="solid", color="burlywood", weight=9];
67.83/34.97	11094 -> 9038[label="",style="solid", color="burlywood", weight=3];
67.83/34.97	9002[label="vuz4890",fontsize=16,color="green",shape="box"];9003[label="vuz3770",fontsize=16,color="green",shape="box"];9004[label="vuz375",fontsize=16,color="green",shape="box"];9005 -> 7479[label="",style="dashed", color="red", weight=0];
67.83/34.97	9005[label="primEqInt (Pos (Succ vuz4890)) (fromInt (Pos Zero))",fontsize=16,color="magenta"];9005 -> 9039[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	9006[label="Succ vuz4890",fontsize=16,color="green",shape="box"];9007[label="vuz374",fontsize=16,color="green",shape="box"];9008 -> 7498[label="",style="dashed", color="red", weight=0];
67.83/34.97	9008[label="primEqInt (Neg (Succ vuz3770)) (fromInt (Pos Zero))",fontsize=16,color="magenta"];9008 -> 9040[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	9009[label="Succ vuz3770",fontsize=16,color="green",shape="box"];9010[label="vuz375",fontsize=16,color="green",shape="box"];9011 -> 7479[label="",style="dashed", color="red", weight=0];
67.83/34.97	9011[label="primEqInt (Pos Zero) (fromInt (Pos Zero))",fontsize=16,color="magenta"];9011 -> 9041[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	9012[label="Zero",fontsize=16,color="green",shape="box"];9013[label="vuz374",fontsize=16,color="green",shape="box"];9014[label="primQuotInt (Neg vuz374) (gcd0Gcd' (abs (Neg vuz511)) (abs (Neg vuz375)))",fontsize=16,color="black",shape="box"];9014 -> 9042[label="",style="solid", color="black", weight=3];
67.83/34.97	9016 -> 9987[label="",style="dashed", color="red", weight=0];
67.83/34.97	9016[label="Neg vuz375 == fromInt (Pos Zero)",fontsize=16,color="magenta"];9016 -> 10011[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	9015[label="primQuotInt (Neg vuz374) (gcd1 vuz518 (Neg vuz511) (Neg vuz375))",fontsize=16,color="burlywood",shape="triangle"];11095[label="vuz518/False",fontsize=10,color="white",style="solid",shape="box"];9015 -> 11095[label="",style="solid", color="burlywood", weight=9];
67.83/34.97	11095 -> 9044[label="",style="solid", color="burlywood", weight=3];
67.83/34.97	11096[label="vuz518/True",fontsize=10,color="white",style="solid",shape="box"];9015 -> 11096[label="",style="solid", color="burlywood", weight=9];
67.83/34.97	11096 -> 9045[label="",style="solid", color="burlywood", weight=3];
67.83/34.97	9017[label="primQuotInt (Neg vuz378) (gcd0Gcd' (abs (Pos vuz514)) (abs (Neg vuz379)))",fontsize=16,color="black",shape="box"];9017 -> 9046[label="",style="solid", color="black", weight=3];
67.83/34.97	9019 -> 9987[label="",style="dashed", color="red", weight=0];
67.83/34.97	9019[label="Neg vuz379 == fromInt (Pos Zero)",fontsize=16,color="magenta"];9019 -> 10012[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	9018[label="primQuotInt (Neg vuz378) (gcd1 vuz519 (Pos vuz514) (Neg vuz379))",fontsize=16,color="burlywood",shape="triangle"];11097[label="vuz519/False",fontsize=10,color="white",style="solid",shape="box"];9018 -> 11097[label="",style="solid", color="burlywood", weight=9];
67.83/34.97	11097 -> 9048[label="",style="solid", color="burlywood", weight=3];
67.83/34.97	11098[label="vuz519/True",fontsize=10,color="white",style="solid",shape="box"];9018 -> 11098[label="",style="solid", color="burlywood", weight=9];
67.83/34.97	11098 -> 9049[label="",style="solid", color="burlywood", weight=3];
67.83/34.97	10182[label="absReal2 (Pos vuz399)",fontsize=16,color="black",shape="box"];10182 -> 10205[label="",style="solid", color="black", weight=3];
67.83/34.97	9585[label="absReal (Pos vuz3190 * Pos vuz3170)",fontsize=16,color="black",shape="box"];9585 -> 9817[label="",style="solid", color="black", weight=3];
67.83/34.97	10183[label="primQuotInt (Pos vuz416) (gcd0Gcd'0 vuz549 vuz542)",fontsize=16,color="black",shape="box"];10183 -> 10206[label="",style="solid", color="black", weight=3];
67.83/34.97	10184[label="primQuotInt (Pos vuz416) vuz549",fontsize=16,color="burlywood",shape="triangle"];11099[label="vuz549/Pos vuz5490",fontsize=10,color="white",style="solid",shape="box"];10184 -> 11099[label="",style="solid", color="burlywood", weight=9];
67.83/34.97	11099 -> 10207[label="",style="solid", color="burlywood", weight=3];
67.83/34.97	11100[label="vuz549/Neg vuz5490",fontsize=10,color="white",style="solid",shape="box"];10184 -> 11100[label="",style="solid", color="burlywood", weight=9];
67.83/34.97	11100 -> 10208[label="",style="solid", color="burlywood", weight=3];
67.83/34.97	9588[label="absReal (Neg vuz3190 * Pos vuz3170)",fontsize=16,color="black",shape="box"];9588 -> 9822[label="",style="solid", color="black", weight=3];
67.83/34.97	9590[label="absReal (Neg vuz3190 * Neg vuz3170)",fontsize=16,color="black",shape="box"];9590 -> 9824[label="",style="solid", color="black", weight=3];
67.83/34.97	10202[label="absReal2 (Neg vuz427)",fontsize=16,color="black",shape="box"];10202 -> 10246[label="",style="solid", color="black", weight=3];
67.83/34.97	10203[label="primQuotInt (Neg vuz428) (gcd0Gcd'0 vuz552 vuz544)",fontsize=16,color="black",shape="box"];10203 -> 10247[label="",style="solid", color="black", weight=3];
67.83/34.97	10204[label="primQuotInt (Neg vuz428) vuz552",fontsize=16,color="burlywood",shape="triangle"];11101[label="vuz552/Pos vuz5520",fontsize=10,color="white",style="solid",shape="box"];10204 -> 11101[label="",style="solid", color="burlywood", weight=9];
67.83/34.97	11101 -> 10248[label="",style="solid", color="burlywood", weight=3];
67.83/34.97	11102[label="vuz552/Neg vuz5520",fontsize=10,color="white",style="solid",shape="box"];10204 -> 11102[label="",style="solid", color="burlywood", weight=9];
67.83/34.97	11102 -> 10249[label="",style="solid", color="burlywood", weight=3];
67.83/34.97	9589[label="absReal (Pos vuz3190 * Neg vuz3170)",fontsize=16,color="black",shape="box"];9589 -> 9823[label="",style="solid", color="black", weight=3];
67.83/34.97	9028[label="primQuotInt (Pos vuz366) (gcd0Gcd'2 (abs (Pos vuz505)) (abs (Pos vuz367)))",fontsize=16,color="black",shape="box"];9028 -> 9058[label="",style="solid", color="black", weight=3];
67.83/34.97	10009[label="Pos vuz367",fontsize=16,color="green",shape="box"];9030[label="primQuotInt (Pos vuz366) (gcd1 False (Pos vuz505) (Pos vuz367))",fontsize=16,color="black",shape="box"];9030 -> 9059[label="",style="solid", color="black", weight=3];
67.83/34.97	9031[label="primQuotInt (Pos vuz366) (gcd1 True (Pos vuz505) (Pos vuz367))",fontsize=16,color="black",shape="box"];9031 -> 9060[label="",style="solid", color="black", weight=3];
67.83/34.97	9032[label="Succ vuz3690",fontsize=16,color="green",shape="box"];9033[label="Succ vuz4830",fontsize=16,color="green",shape="box"];9034[label="Zero",fontsize=16,color="green",shape="box"];9035[label="primQuotInt (Pos vuz370) (gcd0Gcd'2 (abs (Neg vuz508)) (abs (Pos vuz371)))",fontsize=16,color="black",shape="box"];9035 -> 9061[label="",style="solid", color="black", weight=3];
67.83/34.97	10010[label="Pos vuz371",fontsize=16,color="green",shape="box"];9037[label="primQuotInt (Pos vuz370) (gcd1 False (Neg vuz508) (Pos vuz371))",fontsize=16,color="black",shape="box"];9037 -> 9062[label="",style="solid", color="black", weight=3];
67.83/34.97	9038[label="primQuotInt (Pos vuz370) (gcd1 True (Neg vuz508) (Pos vuz371))",fontsize=16,color="black",shape="box"];9038 -> 9063[label="",style="solid", color="black", weight=3];
67.83/34.97	9039[label="Succ vuz4890",fontsize=16,color="green",shape="box"];9040[label="Succ vuz3770",fontsize=16,color="green",shape="box"];9041[label="Zero",fontsize=16,color="green",shape="box"];9042[label="primQuotInt (Neg vuz374) (gcd0Gcd'2 (abs (Neg vuz511)) (abs (Neg vuz375)))",fontsize=16,color="black",shape="box"];9042 -> 9064[label="",style="solid", color="black", weight=3];
67.83/34.97	10011[label="Neg vuz375",fontsize=16,color="green",shape="box"];9044[label="primQuotInt (Neg vuz374) (gcd1 False (Neg vuz511) (Neg vuz375))",fontsize=16,color="black",shape="box"];9044 -> 9065[label="",style="solid", color="black", weight=3];
67.83/34.97	9045[label="primQuotInt (Neg vuz374) (gcd1 True (Neg vuz511) (Neg vuz375))",fontsize=16,color="black",shape="box"];9045 -> 9066[label="",style="solid", color="black", weight=3];
67.83/34.97	9046[label="primQuotInt (Neg vuz378) (gcd0Gcd'2 (abs (Pos vuz514)) (abs (Neg vuz379)))",fontsize=16,color="black",shape="box"];9046 -> 9067[label="",style="solid", color="black", weight=3];
67.83/34.97	10012[label="Neg vuz379",fontsize=16,color="green",shape="box"];9048[label="primQuotInt (Neg vuz378) (gcd1 False (Pos vuz514) (Neg vuz379))",fontsize=16,color="black",shape="box"];9048 -> 9068[label="",style="solid", color="black", weight=3];
67.83/34.97	9049[label="primQuotInt (Neg vuz378) (gcd1 True (Pos vuz514) (Neg vuz379))",fontsize=16,color="black",shape="box"];9049 -> 9069[label="",style="solid", color="black", weight=3];
67.83/34.97	10205 -> 10185[label="",style="dashed", color="red", weight=0];
67.83/34.97	10205[label="absReal1 (Pos vuz399) (Pos vuz399 >= fromInt (Pos Zero))",fontsize=16,color="magenta"];10205 -> 10250[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	10205 -> 10251[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	9817[label="absReal2 (Pos vuz3190 * Pos vuz3170)",fontsize=16,color="black",shape="box"];9817 -> 9834[label="",style="solid", color="black", weight=3];
67.83/34.97	10206 -> 10184[label="",style="dashed", color="red", weight=0];
67.83/34.97	10206[label="primQuotInt (Pos vuz416) (gcd0Gcd' vuz542 (vuz549 `rem` vuz542))",fontsize=16,color="magenta"];10206 -> 10252[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	10207[label="primQuotInt (Pos vuz416) (Pos vuz5490)",fontsize=16,color="burlywood",shape="box"];11103[label="vuz5490/Succ vuz54900",fontsize=10,color="white",style="solid",shape="box"];10207 -> 11103[label="",style="solid", color="burlywood", weight=9];
67.83/34.97	11103 -> 10253[label="",style="solid", color="burlywood", weight=3];
67.83/34.97	11104[label="vuz5490/Zero",fontsize=10,color="white",style="solid",shape="box"];10207 -> 11104[label="",style="solid", color="burlywood", weight=9];
67.83/34.97	11104 -> 10254[label="",style="solid", color="burlywood", weight=3];
67.83/34.97	10208[label="primQuotInt (Pos vuz416) (Neg vuz5490)",fontsize=16,color="burlywood",shape="box"];11105[label="vuz5490/Succ vuz54900",fontsize=10,color="white",style="solid",shape="box"];10208 -> 11105[label="",style="solid", color="burlywood", weight=9];
67.83/34.97	11105 -> 10255[label="",style="solid", color="burlywood", weight=3];
67.83/34.97	11106[label="vuz5490/Zero",fontsize=10,color="white",style="solid",shape="box"];10208 -> 11106[label="",style="solid", color="burlywood", weight=9];
67.83/34.97	11106 -> 10256[label="",style="solid", color="burlywood", weight=3];
67.83/34.97	9822[label="absReal2 (Neg vuz3190 * Pos vuz3170)",fontsize=16,color="black",shape="box"];9822 -> 9839[label="",style="solid", color="black", weight=3];
67.83/34.97	9824[label="absReal2 (Neg vuz3190 * Neg vuz3170)",fontsize=16,color="black",shape="box"];9824 -> 9841[label="",style="solid", color="black", weight=3];
67.83/34.97	10246 -> 10185[label="",style="dashed", color="red", weight=0];
67.83/34.97	10246[label="absReal1 (Neg vuz427) (Neg vuz427 >= fromInt (Pos Zero))",fontsize=16,color="magenta"];10246 -> 10266[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	10246 -> 10267[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	10247 -> 10204[label="",style="dashed", color="red", weight=0];
67.83/34.97	10247[label="primQuotInt (Neg vuz428) (gcd0Gcd' vuz544 (vuz552 `rem` vuz544))",fontsize=16,color="magenta"];10247 -> 10268[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	10248[label="primQuotInt (Neg vuz428) (Pos vuz5520)",fontsize=16,color="burlywood",shape="box"];11107[label="vuz5520/Succ vuz55200",fontsize=10,color="white",style="solid",shape="box"];10248 -> 11107[label="",style="solid", color="burlywood", weight=9];
67.83/34.97	11107 -> 10269[label="",style="solid", color="burlywood", weight=3];
67.83/34.97	11108[label="vuz5520/Zero",fontsize=10,color="white",style="solid",shape="box"];10248 -> 11108[label="",style="solid", color="burlywood", weight=9];
67.83/34.97	11108 -> 10270[label="",style="solid", color="burlywood", weight=3];
67.83/34.97	10249[label="primQuotInt (Neg vuz428) (Neg vuz5520)",fontsize=16,color="burlywood",shape="box"];11109[label="vuz5520/Succ vuz55200",fontsize=10,color="white",style="solid",shape="box"];10249 -> 11109[label="",style="solid", color="burlywood", weight=9];
67.83/34.97	11109 -> 10271[label="",style="solid", color="burlywood", weight=3];
67.83/34.97	11110[label="vuz5520/Zero",fontsize=10,color="white",style="solid",shape="box"];10249 -> 11110[label="",style="solid", color="burlywood", weight=9];
67.83/34.97	11110 -> 10272[label="",style="solid", color="burlywood", weight=3];
67.83/34.97	9823[label="absReal2 (Pos vuz3190 * Neg vuz3170)",fontsize=16,color="black",shape="box"];9823 -> 9840[label="",style="solid", color="black", weight=3];
67.83/34.97	9058 -> 9854[label="",style="dashed", color="red", weight=0];
67.83/34.97	9058[label="primQuotInt (Pos vuz366) (gcd0Gcd'1 (abs (Pos vuz367) == fromInt (Pos Zero)) (abs (Pos vuz505)) (abs (Pos vuz367)))",fontsize=16,color="magenta"];9058 -> 9887[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	9058 -> 9888[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	9058 -> 9889[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	9058 -> 9890[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	9059 -> 8956[label="",style="dashed", color="red", weight=0];
67.83/34.97	9059[label="primQuotInt (Pos vuz366) (gcd0 (Pos vuz505) (Pos vuz367))",fontsize=16,color="magenta"];9060 -> 8816[label="",style="dashed", color="red", weight=0];
67.83/34.97	9060[label="primQuotInt (Pos vuz366) (error [])",fontsize=16,color="magenta"];9060 -> 9079[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	9061 -> 9854[label="",style="dashed", color="red", weight=0];
67.83/34.97	9061[label="primQuotInt (Pos vuz370) (gcd0Gcd'1 (abs (Pos vuz371) == fromInt (Pos Zero)) (abs (Neg vuz508)) (abs (Pos vuz371)))",fontsize=16,color="magenta"];9061 -> 9891[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	9061 -> 9892[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	9061 -> 9893[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	9061 -> 9894[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	9062 -> 8964[label="",style="dashed", color="red", weight=0];
67.83/34.97	9062[label="primQuotInt (Pos vuz370) (gcd0 (Neg vuz508) (Pos vuz371))",fontsize=16,color="magenta"];9063 -> 8816[label="",style="dashed", color="red", weight=0];
67.83/34.97	9063[label="primQuotInt (Pos vuz370) (error [])",fontsize=16,color="magenta"];9063 -> 9081[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	9064 -> 10039[label="",style="dashed", color="red", weight=0];
67.83/34.97	9064[label="primQuotInt (Neg vuz374) (gcd0Gcd'1 (abs (Neg vuz375) == fromInt (Pos Zero)) (abs (Neg vuz511)) (abs (Neg vuz375)))",fontsize=16,color="magenta"];9064 -> 10072[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	9064 -> 10073[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	9064 -> 10074[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	9064 -> 10075[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	9065 -> 8972[label="",style="dashed", color="red", weight=0];
67.83/34.97	9065[label="primQuotInt (Neg vuz374) (gcd0 (Neg vuz511) (Neg vuz375))",fontsize=16,color="magenta"];9066 -> 8849[label="",style="dashed", color="red", weight=0];
67.83/34.97	9066[label="primQuotInt (Neg vuz374) (error [])",fontsize=16,color="magenta"];9066 -> 9083[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	9067 -> 10039[label="",style="dashed", color="red", weight=0];
67.83/34.97	9067[label="primQuotInt (Neg vuz378) (gcd0Gcd'1 (abs (Neg vuz379) == fromInt (Pos Zero)) (abs (Pos vuz514)) (abs (Neg vuz379)))",fontsize=16,color="magenta"];9067 -> 10076[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	9067 -> 10077[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	9067 -> 10078[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	9067 -> 10079[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	9068 -> 8976[label="",style="dashed", color="red", weight=0];
67.83/34.97	9068[label="primQuotInt (Neg vuz378) (gcd0 (Pos vuz514) (Neg vuz379))",fontsize=16,color="magenta"];9069 -> 8849[label="",style="dashed", color="red", weight=0];
67.83/34.97	9069[label="primQuotInt (Neg vuz378) (error [])",fontsize=16,color="magenta"];9069 -> 9085[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	10250[label="Pos vuz399",fontsize=16,color="green",shape="box"];10251[label="Pos vuz399",fontsize=16,color="green",shape="box"];10185[label="absReal1 vuz554 (vuz555 >= fromInt (Pos Zero))",fontsize=16,color="black",shape="triangle"];10185 -> 10223[label="",style="solid", color="black", weight=3];
67.83/34.97	9834 -> 10185[label="",style="dashed", color="red", weight=0];
67.83/34.97	9834[label="absReal1 (Pos vuz3190 * Pos vuz3170) (Pos vuz3190 * Pos vuz3170 >= fromInt (Pos Zero))",fontsize=16,color="magenta"];9834 -> 10186[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	9834 -> 10187[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	10252[label="gcd0Gcd' vuz542 (vuz549 `rem` vuz542)",fontsize=16,color="black",shape="triangle"];10252 -> 10273[label="",style="solid", color="black", weight=3];
67.83/34.97	10253[label="primQuotInt (Pos vuz416) (Pos (Succ vuz54900))",fontsize=16,color="black",shape="box"];10253 -> 10274[label="",style="solid", color="black", weight=3];
67.83/34.97	10254[label="primQuotInt (Pos vuz416) (Pos Zero)",fontsize=16,color="black",shape="box"];10254 -> 10275[label="",style="solid", color="black", weight=3];
67.83/34.97	10255[label="primQuotInt (Pos vuz416) (Neg (Succ vuz54900))",fontsize=16,color="black",shape="box"];10255 -> 10276[label="",style="solid", color="black", weight=3];
67.83/34.97	10256[label="primQuotInt (Pos vuz416) (Neg Zero)",fontsize=16,color="black",shape="box"];10256 -> 10277[label="",style="solid", color="black", weight=3];
67.83/34.97	9839 -> 10185[label="",style="dashed", color="red", weight=0];
67.83/34.97	9839[label="absReal1 (Neg vuz3190 * Pos vuz3170) (Neg vuz3190 * Pos vuz3170 >= fromInt (Pos Zero))",fontsize=16,color="magenta"];9839 -> 10188[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	9839 -> 10189[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	9841 -> 10185[label="",style="dashed", color="red", weight=0];
67.83/34.97	9841[label="absReal1 (Neg vuz3190 * Neg vuz3170) (Neg vuz3190 * Neg vuz3170 >= fromInt (Pos Zero))",fontsize=16,color="magenta"];9841 -> 10190[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	9841 -> 10191[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	10266[label="Neg vuz427",fontsize=16,color="green",shape="box"];10267[label="Neg vuz427",fontsize=16,color="green",shape="box"];10268 -> 10252[label="",style="dashed", color="red", weight=0];
67.83/34.97	10268[label="gcd0Gcd' vuz544 (vuz552 `rem` vuz544)",fontsize=16,color="magenta"];10268 -> 10283[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	10268 -> 10284[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	10269[label="primQuotInt (Neg vuz428) (Pos (Succ vuz55200))",fontsize=16,color="black",shape="box"];10269 -> 10285[label="",style="solid", color="black", weight=3];
67.83/34.97	10270[label="primQuotInt (Neg vuz428) (Pos Zero)",fontsize=16,color="black",shape="box"];10270 -> 10286[label="",style="solid", color="black", weight=3];
67.83/34.97	10271[label="primQuotInt (Neg vuz428) (Neg (Succ vuz55200))",fontsize=16,color="black",shape="box"];10271 -> 10287[label="",style="solid", color="black", weight=3];
67.83/34.97	10272[label="primQuotInt (Neg vuz428) (Neg Zero)",fontsize=16,color="black",shape="box"];10272 -> 10288[label="",style="solid", color="black", weight=3];
67.83/34.97	9840 -> 10185[label="",style="dashed", color="red", weight=0];
67.83/34.97	9840[label="absReal1 (Pos vuz3190 * Neg vuz3170) (Pos vuz3190 * Neg vuz3170 >= fromInt (Pos Zero))",fontsize=16,color="magenta"];9840 -> 10192[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	9840 -> 10193[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	9887 -> 9987[label="",style="dashed", color="red", weight=0];
67.83/34.97	9887[label="abs (Pos vuz367) == fromInt (Pos Zero)",fontsize=16,color="magenta"];9887 -> 10013[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	9888[label="vuz366",fontsize=16,color="green",shape="box"];9889 -> 9857[label="",style="dashed", color="red", weight=0];
67.83/34.97	9889[label="abs (Pos vuz505)",fontsize=16,color="magenta"];9889 -> 10209[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	9890 -> 9857[label="",style="dashed", color="red", weight=0];
67.83/34.97	9890[label="abs (Pos vuz367)",fontsize=16,color="magenta"];9890 -> 10210[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	9079[label="vuz366",fontsize=16,color="green",shape="box"];9891 -> 9987[label="",style="dashed", color="red", weight=0];
67.83/34.97	9891[label="abs (Pos vuz371) == fromInt (Pos Zero)",fontsize=16,color="magenta"];9891 -> 10014[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	9892[label="vuz370",fontsize=16,color="green",shape="box"];9893 -> 10042[label="",style="dashed", color="red", weight=0];
67.83/34.97	9893[label="abs (Neg vuz508)",fontsize=16,color="magenta"];9893 -> 10211[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	9894 -> 9857[label="",style="dashed", color="red", weight=0];
67.83/34.97	9894[label="abs (Pos vuz371)",fontsize=16,color="magenta"];9894 -> 10212[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	9081[label="vuz370",fontsize=16,color="green",shape="box"];10072[label="vuz374",fontsize=16,color="green",shape="box"];10073 -> 10042[label="",style="dashed", color="red", weight=0];
67.83/34.97	10073[label="abs (Neg vuz375)",fontsize=16,color="magenta"];10073 -> 10213[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	10074 -> 10042[label="",style="dashed", color="red", weight=0];
67.83/34.97	10074[label="abs (Neg vuz511)",fontsize=16,color="magenta"];10074 -> 10214[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	10075 -> 9987[label="",style="dashed", color="red", weight=0];
67.83/34.97	10075[label="abs (Neg vuz375) == fromInt (Pos Zero)",fontsize=16,color="magenta"];10075 -> 10215[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	9083[label="vuz374",fontsize=16,color="green",shape="box"];10076[label="vuz378",fontsize=16,color="green",shape="box"];10077 -> 10042[label="",style="dashed", color="red", weight=0];
67.83/34.97	10077[label="abs (Neg vuz379)",fontsize=16,color="magenta"];10077 -> 10216[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	10078 -> 9857[label="",style="dashed", color="red", weight=0];
67.83/34.97	10078[label="abs (Pos vuz514)",fontsize=16,color="magenta"];10078 -> 10217[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	10079 -> 9987[label="",style="dashed", color="red", weight=0];
67.83/34.97	10079[label="abs (Neg vuz379) == fromInt (Pos Zero)",fontsize=16,color="magenta"];10079 -> 10218[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	9085[label="vuz378",fontsize=16,color="green",shape="box"];10223[label="absReal1 vuz554 (compare vuz555 (fromInt (Pos Zero)) /= LT)",fontsize=16,color="black",shape="box"];10223 -> 10259[label="",style="solid", color="black", weight=3];
67.83/34.97	10186 -> 9988[label="",style="dashed", color="red", weight=0];
67.83/34.97	10186[label="Pos vuz3190 * Pos vuz3170",fontsize=16,color="magenta"];10186 -> 10219[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	10186 -> 10220[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	10187 -> 9988[label="",style="dashed", color="red", weight=0];
67.83/34.97	10187[label="Pos vuz3190 * Pos vuz3170",fontsize=16,color="magenta"];10187 -> 10221[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	10187 -> 10222[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	10273[label="gcd0Gcd'2 vuz542 (vuz549 `rem` vuz542)",fontsize=16,color="black",shape="box"];10273 -> 10289[label="",style="solid", color="black", weight=3];
67.83/34.97	10274[label="Pos (primDivNatS vuz416 (Succ vuz54900))",fontsize=16,color="green",shape="box"];10274 -> 10290[label="",style="dashed", color="green", weight=3];
67.83/34.97	10275[label="error []",fontsize=16,color="black",shape="triangle"];10275 -> 10291[label="",style="solid", color="black", weight=3];
67.83/34.97	10276[label="Neg (primDivNatS vuz416 (Succ vuz54900))",fontsize=16,color="green",shape="box"];10276 -> 10292[label="",style="dashed", color="green", weight=3];
67.83/34.97	10277 -> 10275[label="",style="dashed", color="red", weight=0];
67.83/34.97	10277[label="error []",fontsize=16,color="magenta"];10188 -> 9988[label="",style="dashed", color="red", weight=0];
67.83/34.97	10188[label="Neg vuz3190 * Pos vuz3170",fontsize=16,color="magenta"];10188 -> 10224[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	10188 -> 10225[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	10189 -> 9988[label="",style="dashed", color="red", weight=0];
67.83/34.97	10189[label="Neg vuz3190 * Pos vuz3170",fontsize=16,color="magenta"];10189 -> 10226[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	10189 -> 10227[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	10190 -> 9988[label="",style="dashed", color="red", weight=0];
67.83/34.97	10190[label="Neg vuz3190 * Neg vuz3170",fontsize=16,color="magenta"];10190 -> 10228[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	10190 -> 10229[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	10191 -> 9988[label="",style="dashed", color="red", weight=0];
67.83/34.97	10191[label="Neg vuz3190 * Neg vuz3170",fontsize=16,color="magenta"];10191 -> 10230[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	10191 -> 10231[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	10283[label="vuz552",fontsize=16,color="green",shape="box"];10284[label="vuz544",fontsize=16,color="green",shape="box"];10285[label="Neg (primDivNatS vuz428 (Succ vuz55200))",fontsize=16,color="green",shape="box"];10285 -> 10295[label="",style="dashed", color="green", weight=3];
67.83/34.97	10286 -> 10275[label="",style="dashed", color="red", weight=0];
67.83/34.97	10286[label="error []",fontsize=16,color="magenta"];10287[label="Pos (primDivNatS vuz428 (Succ vuz55200))",fontsize=16,color="green",shape="box"];10287 -> 10296[label="",style="dashed", color="green", weight=3];
67.83/34.97	10288 -> 10275[label="",style="dashed", color="red", weight=0];
67.83/34.97	10288[label="error []",fontsize=16,color="magenta"];10192 -> 9988[label="",style="dashed", color="red", weight=0];
67.83/34.97	10192[label="Pos vuz3190 * Neg vuz3170",fontsize=16,color="magenta"];10192 -> 10232[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	10192 -> 10233[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	10193 -> 9988[label="",style="dashed", color="red", weight=0];
67.83/34.97	10193[label="Pos vuz3190 * Neg vuz3170",fontsize=16,color="magenta"];10193 -> 10234[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	10193 -> 10235[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	10013 -> 9857[label="",style="dashed", color="red", weight=0];
67.83/34.97	10013[label="abs (Pos vuz367)",fontsize=16,color="magenta"];10013 -> 10236[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	10209[label="vuz505",fontsize=16,color="green",shape="box"];10210[label="vuz367",fontsize=16,color="green",shape="box"];10014 -> 9857[label="",style="dashed", color="red", weight=0];
67.83/34.97	10014[label="abs (Pos vuz371)",fontsize=16,color="magenta"];10014 -> 10237[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	10211[label="vuz508",fontsize=16,color="green",shape="box"];10212[label="vuz371",fontsize=16,color="green",shape="box"];10213[label="vuz375",fontsize=16,color="green",shape="box"];10214[label="vuz511",fontsize=16,color="green",shape="box"];10215 -> 10042[label="",style="dashed", color="red", weight=0];
67.83/34.97	10215[label="abs (Neg vuz375)",fontsize=16,color="magenta"];10215 -> 10257[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	10216[label="vuz379",fontsize=16,color="green",shape="box"];10217[label="vuz514",fontsize=16,color="green",shape="box"];10218 -> 10042[label="",style="dashed", color="red", weight=0];
67.83/34.97	10218[label="abs (Neg vuz379)",fontsize=16,color="magenta"];10218 -> 10258[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	10259[label="absReal1 vuz554 (not (compare vuz555 (fromInt (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];10259 -> 10278[label="",style="solid", color="black", weight=3];
67.83/34.97	10219[label="Pos vuz3170",fontsize=16,color="green",shape="box"];10220[label="Pos vuz3190",fontsize=16,color="green",shape="box"];10221[label="Pos vuz3170",fontsize=16,color="green",shape="box"];10222[label="Pos vuz3190",fontsize=16,color="green",shape="box"];10289 -> 10297[label="",style="dashed", color="red", weight=0];
67.83/34.97	10289[label="gcd0Gcd'1 (vuz549 `rem` vuz542 == fromInt (Pos Zero)) vuz542 (vuz549 `rem` vuz542)",fontsize=16,color="magenta"];10289 -> 10298[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	10290[label="primDivNatS vuz416 (Succ vuz54900)",fontsize=16,color="burlywood",shape="triangle"];11111[label="vuz416/Succ vuz4160",fontsize=10,color="white",style="solid",shape="box"];10290 -> 11111[label="",style="solid", color="burlywood", weight=9];
67.83/34.97	11111 -> 10299[label="",style="solid", color="burlywood", weight=3];
67.83/34.97	11112[label="vuz416/Zero",fontsize=10,color="white",style="solid",shape="box"];10290 -> 11112[label="",style="solid", color="burlywood", weight=9];
67.83/34.97	11112 -> 10300[label="",style="solid", color="burlywood", weight=3];
67.83/34.97	10291[label="error []",fontsize=16,color="red",shape="box"];10292 -> 10290[label="",style="dashed", color="red", weight=0];
67.83/34.97	10292[label="primDivNatS vuz416 (Succ vuz54900)",fontsize=16,color="magenta"];10292 -> 10301[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	10224[label="Pos vuz3170",fontsize=16,color="green",shape="box"];10225[label="Neg vuz3190",fontsize=16,color="green",shape="box"];10226[label="Pos vuz3170",fontsize=16,color="green",shape="box"];10227[label="Neg vuz3190",fontsize=16,color="green",shape="box"];10228[label="Neg vuz3170",fontsize=16,color="green",shape="box"];10229[label="Neg vuz3190",fontsize=16,color="green",shape="box"];10230[label="Neg vuz3170",fontsize=16,color="green",shape="box"];10231[label="Neg vuz3190",fontsize=16,color="green",shape="box"];10295 -> 10290[label="",style="dashed", color="red", weight=0];
67.83/34.97	10295[label="primDivNatS vuz428 (Succ vuz55200)",fontsize=16,color="magenta"];10295 -> 10302[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	10295 -> 10303[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	10296 -> 10290[label="",style="dashed", color="red", weight=0];
67.83/34.97	10296[label="primDivNatS vuz428 (Succ vuz55200)",fontsize=16,color="magenta"];10296 -> 10304[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	10296 -> 10305[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	10232[label="Neg vuz3170",fontsize=16,color="green",shape="box"];10233[label="Pos vuz3190",fontsize=16,color="green",shape="box"];10234[label="Neg vuz3170",fontsize=16,color="green",shape="box"];10235[label="Pos vuz3190",fontsize=16,color="green",shape="box"];10236[label="vuz367",fontsize=16,color="green",shape="box"];10237[label="vuz371",fontsize=16,color="green",shape="box"];10257[label="vuz375",fontsize=16,color="green",shape="box"];10258[label="vuz379",fontsize=16,color="green",shape="box"];10278[label="absReal1 vuz554 (not (primCmpInt vuz555 (fromInt (Pos Zero)) == LT))",fontsize=16,color="burlywood",shape="box"];11113[label="vuz555/Pos vuz5550",fontsize=10,color="white",style="solid",shape="box"];10278 -> 11113[label="",style="solid", color="burlywood", weight=9];
67.83/34.97	11113 -> 10293[label="",style="solid", color="burlywood", weight=3];
67.83/34.97	11114[label="vuz555/Neg vuz5550",fontsize=10,color="white",style="solid",shape="box"];10278 -> 11114[label="",style="solid", color="burlywood", weight=9];
67.83/34.97	11114 -> 10294[label="",style="solid", color="burlywood", weight=3];
67.83/34.97	10298 -> 9987[label="",style="dashed", color="red", weight=0];
67.83/34.97	10298[label="vuz549 `rem` vuz542 == fromInt (Pos Zero)",fontsize=16,color="magenta"];10298 -> 10306[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	10297[label="gcd0Gcd'1 vuz556 vuz542 (vuz549 `rem` vuz542)",fontsize=16,color="burlywood",shape="triangle"];11115[label="vuz556/False",fontsize=10,color="white",style="solid",shape="box"];10297 -> 11115[label="",style="solid", color="burlywood", weight=9];
67.83/34.97	11115 -> 10307[label="",style="solid", color="burlywood", weight=3];
67.83/34.97	11116[label="vuz556/True",fontsize=10,color="white",style="solid",shape="box"];10297 -> 11116[label="",style="solid", color="burlywood", weight=9];
67.83/34.97	11116 -> 10308[label="",style="solid", color="burlywood", weight=3];
67.83/34.97	10299[label="primDivNatS (Succ vuz4160) (Succ vuz54900)",fontsize=16,color="black",shape="box"];10299 -> 10313[label="",style="solid", color="black", weight=3];
67.83/34.97	10300[label="primDivNatS Zero (Succ vuz54900)",fontsize=16,color="black",shape="box"];10300 -> 10314[label="",style="solid", color="black", weight=3];
67.83/34.97	10301[label="vuz54900",fontsize=16,color="green",shape="box"];10302[label="vuz428",fontsize=16,color="green",shape="box"];10303[label="vuz55200",fontsize=16,color="green",shape="box"];10304[label="vuz428",fontsize=16,color="green",shape="box"];10305[label="vuz55200",fontsize=16,color="green",shape="box"];10293[label="absReal1 vuz554 (not (primCmpInt (Pos vuz5550) (fromInt (Pos Zero)) == LT))",fontsize=16,color="burlywood",shape="box"];11117[label="vuz5550/Succ vuz55500",fontsize=10,color="white",style="solid",shape="box"];10293 -> 11117[label="",style="solid", color="burlywood", weight=9];
67.83/34.97	11117 -> 10309[label="",style="solid", color="burlywood", weight=3];
67.83/34.97	11118[label="vuz5550/Zero",fontsize=10,color="white",style="solid",shape="box"];10293 -> 11118[label="",style="solid", color="burlywood", weight=9];
67.83/34.97	11118 -> 10310[label="",style="solid", color="burlywood", weight=3];
67.83/34.97	10294[label="absReal1 vuz554 (not (primCmpInt (Neg vuz5550) (fromInt (Pos Zero)) == LT))",fontsize=16,color="burlywood",shape="box"];11119[label="vuz5550/Succ vuz55500",fontsize=10,color="white",style="solid",shape="box"];10294 -> 11119[label="",style="solid", color="burlywood", weight=9];
67.83/34.97	11119 -> 10311[label="",style="solid", color="burlywood", weight=3];
67.83/34.97	11120[label="vuz5550/Zero",fontsize=10,color="white",style="solid",shape="box"];10294 -> 11120[label="",style="solid", color="burlywood", weight=9];
67.83/34.97	11120 -> 10312[label="",style="solid", color="burlywood", weight=3];
67.83/34.97	10306[label="vuz549 `rem` vuz542",fontsize=16,color="black",shape="triangle"];10306 -> 10315[label="",style="solid", color="black", weight=3];
67.83/34.97	10307[label="gcd0Gcd'1 False vuz542 (vuz549 `rem` vuz542)",fontsize=16,color="black",shape="box"];10307 -> 10316[label="",style="solid", color="black", weight=3];
67.83/34.97	10308[label="gcd0Gcd'1 True vuz542 (vuz549 `rem` vuz542)",fontsize=16,color="black",shape="box"];10308 -> 10317[label="",style="solid", color="black", weight=3];
67.83/34.97	10313[label="primDivNatS0 vuz4160 vuz54900 (primGEqNatS vuz4160 vuz54900)",fontsize=16,color="burlywood",shape="box"];11121[label="vuz4160/Succ vuz41600",fontsize=10,color="white",style="solid",shape="box"];10313 -> 11121[label="",style="solid", color="burlywood", weight=9];
67.83/34.97	11121 -> 10322[label="",style="solid", color="burlywood", weight=3];
67.83/34.97	11122[label="vuz4160/Zero",fontsize=10,color="white",style="solid",shape="box"];10313 -> 11122[label="",style="solid", color="burlywood", weight=9];
67.83/34.97	11122 -> 10323[label="",style="solid", color="burlywood", weight=3];
67.83/34.97	10314[label="Zero",fontsize=16,color="green",shape="box"];10309[label="absReal1 vuz554 (not (primCmpInt (Pos (Succ vuz55500)) (fromInt (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];10309 -> 10318[label="",style="solid", color="black", weight=3];
67.83/34.97	10310[label="absReal1 vuz554 (not (primCmpInt (Pos Zero) (fromInt (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];10310 -> 10319[label="",style="solid", color="black", weight=3];
67.83/34.97	10311[label="absReal1 vuz554 (not (primCmpInt (Neg (Succ vuz55500)) (fromInt (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];10311 -> 10320[label="",style="solid", color="black", weight=3];
67.83/34.97	10312[label="absReal1 vuz554 (not (primCmpInt (Neg Zero) (fromInt (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];10312 -> 10321[label="",style="solid", color="black", weight=3];
67.83/34.97	10315[label="primRemInt vuz549 vuz542",fontsize=16,color="burlywood",shape="box"];11123[label="vuz549/Pos vuz5490",fontsize=10,color="white",style="solid",shape="box"];10315 -> 11123[label="",style="solid", color="burlywood", weight=9];
67.83/34.97	11123 -> 10324[label="",style="solid", color="burlywood", weight=3];
67.83/34.97	11124[label="vuz549/Neg vuz5490",fontsize=10,color="white",style="solid",shape="box"];10315 -> 11124[label="",style="solid", color="burlywood", weight=9];
67.83/34.97	11124 -> 10325[label="",style="solid", color="burlywood", weight=3];
67.83/34.97	10316 -> 10326[label="",style="dashed", color="red", weight=0];
67.83/34.97	10316[label="gcd0Gcd'0 vuz542 (vuz549 `rem` vuz542)",fontsize=16,color="magenta"];10316 -> 10327[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	10317[label="vuz542",fontsize=16,color="green",shape="box"];10322[label="primDivNatS0 (Succ vuz41600) vuz54900 (primGEqNatS (Succ vuz41600) vuz54900)",fontsize=16,color="burlywood",shape="box"];11125[label="vuz54900/Succ vuz549000",fontsize=10,color="white",style="solid",shape="box"];10322 -> 11125[label="",style="solid", color="burlywood", weight=9];
67.83/34.97	11125 -> 10328[label="",style="solid", color="burlywood", weight=3];
67.83/34.97	11126[label="vuz54900/Zero",fontsize=10,color="white",style="solid",shape="box"];10322 -> 11126[label="",style="solid", color="burlywood", weight=9];
67.83/34.97	11126 -> 10329[label="",style="solid", color="burlywood", weight=3];
67.83/34.97	10323[label="primDivNatS0 Zero vuz54900 (primGEqNatS Zero vuz54900)",fontsize=16,color="burlywood",shape="box"];11127[label="vuz54900/Succ vuz549000",fontsize=10,color="white",style="solid",shape="box"];10323 -> 11127[label="",style="solid", color="burlywood", weight=9];
67.83/34.97	11127 -> 10330[label="",style="solid", color="burlywood", weight=3];
67.83/34.97	11128[label="vuz54900/Zero",fontsize=10,color="white",style="solid",shape="box"];10323 -> 11128[label="",style="solid", color="burlywood", weight=9];
67.83/34.97	11128 -> 10331[label="",style="solid", color="burlywood", weight=3];
67.83/34.97	10318[label="absReal1 vuz554 (not (primCmpInt (Pos (Succ vuz55500)) (Pos Zero) == LT))",fontsize=16,color="black",shape="box"];10318 -> 10332[label="",style="solid", color="black", weight=3];
67.83/34.97	10319[label="absReal1 vuz554 (not (primCmpInt (Pos Zero) (Pos Zero) == LT))",fontsize=16,color="black",shape="box"];10319 -> 10333[label="",style="solid", color="black", weight=3];
67.83/34.97	10320[label="absReal1 vuz554 (not (primCmpInt (Neg (Succ vuz55500)) (Pos Zero) == LT))",fontsize=16,color="black",shape="box"];10320 -> 10334[label="",style="solid", color="black", weight=3];
67.83/34.97	10321[label="absReal1 vuz554 (not (primCmpInt (Neg Zero) (Pos Zero) == LT))",fontsize=16,color="black",shape="box"];10321 -> 10335[label="",style="solid", color="black", weight=3];
67.83/34.97	10324[label="primRemInt (Pos vuz5490) vuz542",fontsize=16,color="burlywood",shape="box"];11129[label="vuz542/Pos vuz5420",fontsize=10,color="white",style="solid",shape="box"];10324 -> 11129[label="",style="solid", color="burlywood", weight=9];
67.83/34.97	11129 -> 10336[label="",style="solid", color="burlywood", weight=3];
67.83/34.97	11130[label="vuz542/Neg vuz5420",fontsize=10,color="white",style="solid",shape="box"];10324 -> 11130[label="",style="solid", color="burlywood", weight=9];
67.83/34.97	11130 -> 10337[label="",style="solid", color="burlywood", weight=3];
67.83/34.97	10325[label="primRemInt (Neg vuz5490) vuz542",fontsize=16,color="burlywood",shape="box"];11131[label="vuz542/Pos vuz5420",fontsize=10,color="white",style="solid",shape="box"];10325 -> 11131[label="",style="solid", color="burlywood", weight=9];
67.83/34.97	11131 -> 10338[label="",style="solid", color="burlywood", weight=3];
67.83/34.97	11132[label="vuz542/Neg vuz5420",fontsize=10,color="white",style="solid",shape="box"];10325 -> 11132[label="",style="solid", color="burlywood", weight=9];
67.83/34.97	11132 -> 10339[label="",style="solid", color="burlywood", weight=3];
67.83/34.97	10327 -> 10306[label="",style="dashed", color="red", weight=0];
67.83/34.97	10327[label="vuz549 `rem` vuz542",fontsize=16,color="magenta"];10326[label="gcd0Gcd'0 vuz542 vuz557",fontsize=16,color="black",shape="triangle"];10326 -> 10340[label="",style="solid", color="black", weight=3];
67.83/34.97	10328[label="primDivNatS0 (Succ vuz41600) (Succ vuz549000) (primGEqNatS (Succ vuz41600) (Succ vuz549000))",fontsize=16,color="black",shape="box"];10328 -> 10341[label="",style="solid", color="black", weight=3];
67.83/34.97	10329[label="primDivNatS0 (Succ vuz41600) Zero (primGEqNatS (Succ vuz41600) Zero)",fontsize=16,color="black",shape="box"];10329 -> 10342[label="",style="solid", color="black", weight=3];
67.83/34.97	10330[label="primDivNatS0 Zero (Succ vuz549000) (primGEqNatS Zero (Succ vuz549000))",fontsize=16,color="black",shape="box"];10330 -> 10343[label="",style="solid", color="black", weight=3];
67.83/34.97	10331[label="primDivNatS0 Zero Zero (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];10331 -> 10344[label="",style="solid", color="black", weight=3];
67.83/34.97	10332[label="absReal1 vuz554 (not (primCmpNat (Succ vuz55500) Zero == LT))",fontsize=16,color="black",shape="box"];10332 -> 10345[label="",style="solid", color="black", weight=3];
67.83/34.97	10333[label="absReal1 vuz554 (not (EQ == LT))",fontsize=16,color="black",shape="triangle"];10333 -> 10346[label="",style="solid", color="black", weight=3];
67.83/34.97	10334[label="absReal1 vuz554 (not (LT == LT))",fontsize=16,color="black",shape="box"];10334 -> 10347[label="",style="solid", color="black", weight=3];
67.83/34.97	10335 -> 10333[label="",style="dashed", color="red", weight=0];
67.83/34.97	10335[label="absReal1 vuz554 (not (EQ == LT))",fontsize=16,color="magenta"];10336[label="primRemInt (Pos vuz5490) (Pos vuz5420)",fontsize=16,color="burlywood",shape="box"];11133[label="vuz5420/Succ vuz54200",fontsize=10,color="white",style="solid",shape="box"];10336 -> 11133[label="",style="solid", color="burlywood", weight=9];
67.83/34.97	11133 -> 10348[label="",style="solid", color="burlywood", weight=3];
67.83/34.97	11134[label="vuz5420/Zero",fontsize=10,color="white",style="solid",shape="box"];10336 -> 11134[label="",style="solid", color="burlywood", weight=9];
67.83/34.97	11134 -> 10349[label="",style="solid", color="burlywood", weight=3];
67.83/34.97	10337[label="primRemInt (Pos vuz5490) (Neg vuz5420)",fontsize=16,color="burlywood",shape="box"];11135[label="vuz5420/Succ vuz54200",fontsize=10,color="white",style="solid",shape="box"];10337 -> 11135[label="",style="solid", color="burlywood", weight=9];
67.83/34.97	11135 -> 10350[label="",style="solid", color="burlywood", weight=3];
67.83/34.97	11136[label="vuz5420/Zero",fontsize=10,color="white",style="solid",shape="box"];10337 -> 11136[label="",style="solid", color="burlywood", weight=9];
67.83/34.97	11136 -> 10351[label="",style="solid", color="burlywood", weight=3];
67.83/34.97	10338[label="primRemInt (Neg vuz5490) (Pos vuz5420)",fontsize=16,color="burlywood",shape="box"];11137[label="vuz5420/Succ vuz54200",fontsize=10,color="white",style="solid",shape="box"];10338 -> 11137[label="",style="solid", color="burlywood", weight=9];
67.83/34.97	11137 -> 10352[label="",style="solid", color="burlywood", weight=3];
67.83/34.97	11138[label="vuz5420/Zero",fontsize=10,color="white",style="solid",shape="box"];10338 -> 11138[label="",style="solid", color="burlywood", weight=9];
67.83/34.97	11138 -> 10353[label="",style="solid", color="burlywood", weight=3];
67.83/34.97	10339[label="primRemInt (Neg vuz5490) (Neg vuz5420)",fontsize=16,color="burlywood",shape="box"];11139[label="vuz5420/Succ vuz54200",fontsize=10,color="white",style="solid",shape="box"];10339 -> 11139[label="",style="solid", color="burlywood", weight=9];
67.83/34.97	11139 -> 10354[label="",style="solid", color="burlywood", weight=3];
67.83/34.97	11140[label="vuz5420/Zero",fontsize=10,color="white",style="solid",shape="box"];10339 -> 11140[label="",style="solid", color="burlywood", weight=9];
67.83/34.97	11140 -> 10355[label="",style="solid", color="burlywood", weight=3];
67.83/34.97	10340 -> 10252[label="",style="dashed", color="red", weight=0];
67.83/34.97	10340[label="gcd0Gcd' vuz557 (vuz542 `rem` vuz557)",fontsize=16,color="magenta"];10340 -> 10356[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	10340 -> 10357[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	10341 -> 10629[label="",style="dashed", color="red", weight=0];
67.83/34.97	10341[label="primDivNatS0 (Succ vuz41600) (Succ vuz549000) (primGEqNatS vuz41600 vuz549000)",fontsize=16,color="magenta"];10341 -> 10630[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	10341 -> 10631[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	10341 -> 10632[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	10341 -> 10633[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	10342[label="primDivNatS0 (Succ vuz41600) Zero True",fontsize=16,color="black",shape="box"];10342 -> 10360[label="",style="solid", color="black", weight=3];
67.83/34.97	10343[label="primDivNatS0 Zero (Succ vuz549000) False",fontsize=16,color="black",shape="box"];10343 -> 10361[label="",style="solid", color="black", weight=3];
67.83/34.97	10344[label="primDivNatS0 Zero Zero True",fontsize=16,color="black",shape="box"];10344 -> 10362[label="",style="solid", color="black", weight=3];
67.83/34.97	10345[label="absReal1 vuz554 (not (GT == LT))",fontsize=16,color="black",shape="box"];10345 -> 10363[label="",style="solid", color="black", weight=3];
67.83/34.97	10346[label="absReal1 vuz554 (not False)",fontsize=16,color="black",shape="triangle"];10346 -> 10364[label="",style="solid", color="black", weight=3];
67.83/34.97	10347[label="absReal1 vuz554 (not True)",fontsize=16,color="black",shape="box"];10347 -> 10365[label="",style="solid", color="black", weight=3];
67.83/34.97	10348[label="primRemInt (Pos vuz5490) (Pos (Succ vuz54200))",fontsize=16,color="black",shape="box"];10348 -> 10366[label="",style="solid", color="black", weight=3];
67.83/34.97	10349[label="primRemInt (Pos vuz5490) (Pos Zero)",fontsize=16,color="black",shape="box"];10349 -> 10367[label="",style="solid", color="black", weight=3];
67.83/34.97	10350[label="primRemInt (Pos vuz5490) (Neg (Succ vuz54200))",fontsize=16,color="black",shape="box"];10350 -> 10368[label="",style="solid", color="black", weight=3];
67.83/34.97	10351[label="primRemInt (Pos vuz5490) (Neg Zero)",fontsize=16,color="black",shape="box"];10351 -> 10369[label="",style="solid", color="black", weight=3];
67.83/34.97	10352[label="primRemInt (Neg vuz5490) (Pos (Succ vuz54200))",fontsize=16,color="black",shape="box"];10352 -> 10370[label="",style="solid", color="black", weight=3];
67.83/34.97	10353[label="primRemInt (Neg vuz5490) (Pos Zero)",fontsize=16,color="black",shape="box"];10353 -> 10371[label="",style="solid", color="black", weight=3];
67.83/34.97	10354[label="primRemInt (Neg vuz5490) (Neg (Succ vuz54200))",fontsize=16,color="black",shape="box"];10354 -> 10372[label="",style="solid", color="black", weight=3];
67.83/34.97	10355[label="primRemInt (Neg vuz5490) (Neg Zero)",fontsize=16,color="black",shape="box"];10355 -> 10373[label="",style="solid", color="black", weight=3];
67.83/34.97	10356[label="vuz542",fontsize=16,color="green",shape="box"];10357[label="vuz557",fontsize=16,color="green",shape="box"];10630[label="vuz41600",fontsize=16,color="green",shape="box"];10631[label="vuz41600",fontsize=16,color="green",shape="box"];10632[label="vuz549000",fontsize=16,color="green",shape="box"];10633[label="vuz549000",fontsize=16,color="green",shape="box"];10629[label="primDivNatS0 (Succ vuz574) (Succ vuz575) (primGEqNatS vuz576 vuz577)",fontsize=16,color="burlywood",shape="triangle"];11141[label="vuz576/Succ vuz5760",fontsize=10,color="white",style="solid",shape="box"];10629 -> 11141[label="",style="solid", color="burlywood", weight=9];
67.83/34.97	11141 -> 10662[label="",style="solid", color="burlywood", weight=3];
67.83/34.97	11142[label="vuz576/Zero",fontsize=10,color="white",style="solid",shape="box"];10629 -> 11142[label="",style="solid", color="burlywood", weight=9];
67.83/34.97	11142 -> 10663[label="",style="solid", color="burlywood", weight=3];
67.83/34.97	10360[label="Succ (primDivNatS (primMinusNatS (Succ vuz41600) Zero) (Succ Zero))",fontsize=16,color="green",shape="box"];10360 -> 10378[label="",style="dashed", color="green", weight=3];
67.83/34.97	10361[label="Zero",fontsize=16,color="green",shape="box"];10362[label="Succ (primDivNatS (primMinusNatS Zero Zero) (Succ Zero))",fontsize=16,color="green",shape="box"];10362 -> 10379[label="",style="dashed", color="green", weight=3];
67.83/34.97	10363 -> 10346[label="",style="dashed", color="red", weight=0];
67.83/34.97	10363[label="absReal1 vuz554 (not False)",fontsize=16,color="magenta"];10364[label="absReal1 vuz554 True",fontsize=16,color="black",shape="box"];10364 -> 10380[label="",style="solid", color="black", weight=3];
67.83/34.97	10365[label="absReal1 vuz554 False",fontsize=16,color="black",shape="box"];10365 -> 10381[label="",style="solid", color="black", weight=3];
67.83/34.97	10366[label="Pos (primModNatS vuz5490 (Succ vuz54200))",fontsize=16,color="green",shape="box"];10366 -> 10382[label="",style="dashed", color="green", weight=3];
67.83/34.97	10367 -> 10275[label="",style="dashed", color="red", weight=0];
67.83/34.97	10367[label="error []",fontsize=16,color="magenta"];10368[label="Pos (primModNatS vuz5490 (Succ vuz54200))",fontsize=16,color="green",shape="box"];10368 -> 10383[label="",style="dashed", color="green", weight=3];
67.83/34.97	10369 -> 10275[label="",style="dashed", color="red", weight=0];
67.83/34.97	10369[label="error []",fontsize=16,color="magenta"];10370[label="Neg (primModNatS vuz5490 (Succ vuz54200))",fontsize=16,color="green",shape="box"];10370 -> 10384[label="",style="dashed", color="green", weight=3];
67.83/34.97	10371 -> 10275[label="",style="dashed", color="red", weight=0];
67.83/34.97	10371[label="error []",fontsize=16,color="magenta"];10372[label="Neg (primModNatS vuz5490 (Succ vuz54200))",fontsize=16,color="green",shape="box"];10372 -> 10385[label="",style="dashed", color="green", weight=3];
67.83/34.97	10373 -> 10275[label="",style="dashed", color="red", weight=0];
67.83/34.97	10373[label="error []",fontsize=16,color="magenta"];10662[label="primDivNatS0 (Succ vuz574) (Succ vuz575) (primGEqNatS (Succ vuz5760) vuz577)",fontsize=16,color="burlywood",shape="box"];11143[label="vuz577/Succ vuz5770",fontsize=10,color="white",style="solid",shape="box"];10662 -> 11143[label="",style="solid", color="burlywood", weight=9];
67.83/34.97	11143 -> 10670[label="",style="solid", color="burlywood", weight=3];
67.83/34.97	11144[label="vuz577/Zero",fontsize=10,color="white",style="solid",shape="box"];10662 -> 11144[label="",style="solid", color="burlywood", weight=9];
67.83/34.97	11144 -> 10671[label="",style="solid", color="burlywood", weight=3];
67.83/34.97	10663[label="primDivNatS0 (Succ vuz574) (Succ vuz575) (primGEqNatS Zero vuz577)",fontsize=16,color="burlywood",shape="box"];11145[label="vuz577/Succ vuz5770",fontsize=10,color="white",style="solid",shape="box"];10663 -> 11145[label="",style="solid", color="burlywood", weight=9];
67.83/34.97	11145 -> 10672[label="",style="solid", color="burlywood", weight=3];
67.83/34.97	11146[label="vuz577/Zero",fontsize=10,color="white",style="solid",shape="box"];10663 -> 11146[label="",style="solid", color="burlywood", weight=9];
67.83/34.97	11146 -> 10673[label="",style="solid", color="burlywood", weight=3];
67.83/34.97	10378 -> 10290[label="",style="dashed", color="red", weight=0];
67.83/34.97	10378[label="primDivNatS (primMinusNatS (Succ vuz41600) Zero) (Succ Zero)",fontsize=16,color="magenta"];10378 -> 10390[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	10378 -> 10391[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	10379 -> 10290[label="",style="dashed", color="red", weight=0];
67.83/34.97	10379[label="primDivNatS (primMinusNatS Zero Zero) (Succ Zero)",fontsize=16,color="magenta"];10379 -> 10392[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	10379 -> 10393[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	10380[label="vuz554",fontsize=16,color="green",shape="box"];10381[label="absReal0 vuz554 otherwise",fontsize=16,color="black",shape="box"];10381 -> 10394[label="",style="solid", color="black", weight=3];
67.83/34.97	10382[label="primModNatS vuz5490 (Succ vuz54200)",fontsize=16,color="burlywood",shape="triangle"];11147[label="vuz5490/Succ vuz54900",fontsize=10,color="white",style="solid",shape="box"];10382 -> 11147[label="",style="solid", color="burlywood", weight=9];
67.83/34.97	11147 -> 10395[label="",style="solid", color="burlywood", weight=3];
67.83/34.97	11148[label="vuz5490/Zero",fontsize=10,color="white",style="solid",shape="box"];10382 -> 11148[label="",style="solid", color="burlywood", weight=9];
67.83/34.97	11148 -> 10396[label="",style="solid", color="burlywood", weight=3];
67.83/34.97	10383 -> 10382[label="",style="dashed", color="red", weight=0];
67.83/34.97	10383[label="primModNatS vuz5490 (Succ vuz54200)",fontsize=16,color="magenta"];10383 -> 10397[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	10384 -> 10382[label="",style="dashed", color="red", weight=0];
67.83/34.97	10384[label="primModNatS vuz5490 (Succ vuz54200)",fontsize=16,color="magenta"];10384 -> 10398[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	10385 -> 10382[label="",style="dashed", color="red", weight=0];
67.83/34.97	10385[label="primModNatS vuz5490 (Succ vuz54200)",fontsize=16,color="magenta"];10385 -> 10399[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	10385 -> 10400[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	10670[label="primDivNatS0 (Succ vuz574) (Succ vuz575) (primGEqNatS (Succ vuz5760) (Succ vuz5770))",fontsize=16,color="black",shape="box"];10670 -> 10682[label="",style="solid", color="black", weight=3];
67.83/34.97	10671[label="primDivNatS0 (Succ vuz574) (Succ vuz575) (primGEqNatS (Succ vuz5760) Zero)",fontsize=16,color="black",shape="box"];10671 -> 10683[label="",style="solid", color="black", weight=3];
67.83/34.97	10672[label="primDivNatS0 (Succ vuz574) (Succ vuz575) (primGEqNatS Zero (Succ vuz5770))",fontsize=16,color="black",shape="box"];10672 -> 10684[label="",style="solid", color="black", weight=3];
67.83/34.97	10673[label="primDivNatS0 (Succ vuz574) (Succ vuz575) (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];10673 -> 10685[label="",style="solid", color="black", weight=3];
67.83/34.97	10390[label="primMinusNatS (Succ vuz41600) Zero",fontsize=16,color="black",shape="triangle"];10390 -> 10406[label="",style="solid", color="black", weight=3];
67.83/34.97	10391[label="Zero",fontsize=16,color="green",shape="box"];10392[label="primMinusNatS Zero Zero",fontsize=16,color="black",shape="triangle"];10392 -> 10407[label="",style="solid", color="black", weight=3];
67.83/34.97	10393[label="Zero",fontsize=16,color="green",shape="box"];10394[label="absReal0 vuz554 True",fontsize=16,color="black",shape="box"];10394 -> 10408[label="",style="solid", color="black", weight=3];
67.83/34.97	10395[label="primModNatS (Succ vuz54900) (Succ vuz54200)",fontsize=16,color="black",shape="box"];10395 -> 10409[label="",style="solid", color="black", weight=3];
67.83/34.97	10396[label="primModNatS Zero (Succ vuz54200)",fontsize=16,color="black",shape="box"];10396 -> 10410[label="",style="solid", color="black", weight=3];
67.83/34.97	10397[label="vuz54200",fontsize=16,color="green",shape="box"];10398[label="vuz5490",fontsize=16,color="green",shape="box"];10399[label="vuz5490",fontsize=16,color="green",shape="box"];10400[label="vuz54200",fontsize=16,color="green",shape="box"];10682 -> 10629[label="",style="dashed", color="red", weight=0];
67.83/34.97	10682[label="primDivNatS0 (Succ vuz574) (Succ vuz575) (primGEqNatS vuz5760 vuz5770)",fontsize=16,color="magenta"];10682 -> 10692[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	10682 -> 10693[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	10683[label="primDivNatS0 (Succ vuz574) (Succ vuz575) True",fontsize=16,color="black",shape="triangle"];10683 -> 10694[label="",style="solid", color="black", weight=3];
67.83/34.97	10684[label="primDivNatS0 (Succ vuz574) (Succ vuz575) False",fontsize=16,color="black",shape="box"];10684 -> 10695[label="",style="solid", color="black", weight=3];
67.83/34.97	10685 -> 10683[label="",style="dashed", color="red", weight=0];
67.83/34.97	10685[label="primDivNatS0 (Succ vuz574) (Succ vuz575) True",fontsize=16,color="magenta"];10406[label="Succ vuz41600",fontsize=16,color="green",shape="box"];10407[label="Zero",fontsize=16,color="green",shape="box"];10408 -> 7115[label="",style="dashed", color="red", weight=0];
67.83/34.97	10408[label="`negate` vuz554",fontsize=16,color="magenta"];10408 -> 10417[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	10409[label="primModNatS0 vuz54900 vuz54200 (primGEqNatS vuz54900 vuz54200)",fontsize=16,color="burlywood",shape="box"];11149[label="vuz54900/Succ vuz549000",fontsize=10,color="white",style="solid",shape="box"];10409 -> 11149[label="",style="solid", color="burlywood", weight=9];
67.83/34.97	11149 -> 10418[label="",style="solid", color="burlywood", weight=3];
67.83/34.97	11150[label="vuz54900/Zero",fontsize=10,color="white",style="solid",shape="box"];10409 -> 11150[label="",style="solid", color="burlywood", weight=9];
67.83/34.97	11150 -> 10419[label="",style="solid", color="burlywood", weight=3];
67.83/34.97	10410[label="Zero",fontsize=16,color="green",shape="box"];10692[label="vuz5760",fontsize=16,color="green",shape="box"];10693[label="vuz5770",fontsize=16,color="green",shape="box"];10694[label="Succ (primDivNatS (primMinusNatS (Succ vuz574) (Succ vuz575)) (Succ (Succ vuz575)))",fontsize=16,color="green",shape="box"];10694 -> 10700[label="",style="dashed", color="green", weight=3];
67.83/34.97	10695[label="Zero",fontsize=16,color="green",shape="box"];10417[label="vuz554",fontsize=16,color="green",shape="box"];10418[label="primModNatS0 (Succ vuz549000) vuz54200 (primGEqNatS (Succ vuz549000) vuz54200)",fontsize=16,color="burlywood",shape="box"];11151[label="vuz54200/Succ vuz542000",fontsize=10,color="white",style="solid",shape="box"];10418 -> 11151[label="",style="solid", color="burlywood", weight=9];
67.83/34.97	11151 -> 10428[label="",style="solid", color="burlywood", weight=3];
67.83/34.97	11152[label="vuz54200/Zero",fontsize=10,color="white",style="solid",shape="box"];10418 -> 11152[label="",style="solid", color="burlywood", weight=9];
67.83/34.97	11152 -> 10429[label="",style="solid", color="burlywood", weight=3];
67.83/34.97	10419[label="primModNatS0 Zero vuz54200 (primGEqNatS Zero vuz54200)",fontsize=16,color="burlywood",shape="box"];11153[label="vuz54200/Succ vuz542000",fontsize=10,color="white",style="solid",shape="box"];10419 -> 11153[label="",style="solid", color="burlywood", weight=9];
67.83/34.97	11153 -> 10430[label="",style="solid", color="burlywood", weight=3];
67.83/34.97	11154[label="vuz54200/Zero",fontsize=10,color="white",style="solid",shape="box"];10419 -> 11154[label="",style="solid", color="burlywood", weight=9];
67.83/34.97	11154 -> 10431[label="",style="solid", color="burlywood", weight=3];
67.83/34.97	10700 -> 10290[label="",style="dashed", color="red", weight=0];
67.83/34.97	10700[label="primDivNatS (primMinusNatS (Succ vuz574) (Succ vuz575)) (Succ (Succ vuz575))",fontsize=16,color="magenta"];10700 -> 10704[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	10700 -> 10705[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	10428[label="primModNatS0 (Succ vuz549000) (Succ vuz542000) (primGEqNatS (Succ vuz549000) (Succ vuz542000))",fontsize=16,color="black",shape="box"];10428 -> 10439[label="",style="solid", color="black", weight=3];
67.83/34.97	10429[label="primModNatS0 (Succ vuz549000) Zero (primGEqNatS (Succ vuz549000) Zero)",fontsize=16,color="black",shape="box"];10429 -> 10440[label="",style="solid", color="black", weight=3];
67.83/34.97	10430[label="primModNatS0 Zero (Succ vuz542000) (primGEqNatS Zero (Succ vuz542000))",fontsize=16,color="black",shape="box"];10430 -> 10441[label="",style="solid", color="black", weight=3];
67.83/34.97	10431[label="primModNatS0 Zero Zero (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];10431 -> 10442[label="",style="solid", color="black", weight=3];
67.83/34.97	10704[label="primMinusNatS (Succ vuz574) (Succ vuz575)",fontsize=16,color="black",shape="box"];10704 -> 10709[label="",style="solid", color="black", weight=3];
67.83/34.97	10705[label="Succ vuz575",fontsize=16,color="green",shape="box"];10439 -> 10769[label="",style="dashed", color="red", weight=0];
67.83/34.97	10439[label="primModNatS0 (Succ vuz549000) (Succ vuz542000) (primGEqNatS vuz549000 vuz542000)",fontsize=16,color="magenta"];10439 -> 10770[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	10439 -> 10771[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	10439 -> 10772[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	10439 -> 10773[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	10440[label="primModNatS0 (Succ vuz549000) Zero True",fontsize=16,color="black",shape="box"];10440 -> 10452[label="",style="solid", color="black", weight=3];
67.83/34.97	10441[label="primModNatS0 Zero (Succ vuz542000) False",fontsize=16,color="black",shape="box"];10441 -> 10453[label="",style="solid", color="black", weight=3];
67.83/34.97	10442[label="primModNatS0 Zero Zero True",fontsize=16,color="black",shape="box"];10442 -> 10454[label="",style="solid", color="black", weight=3];
67.83/34.97	10709[label="primMinusNatS vuz574 vuz575",fontsize=16,color="burlywood",shape="triangle"];11155[label="vuz574/Succ vuz5740",fontsize=10,color="white",style="solid",shape="box"];10709 -> 11155[label="",style="solid", color="burlywood", weight=9];
67.83/34.97	11155 -> 10712[label="",style="solid", color="burlywood", weight=3];
67.83/34.97	11156[label="vuz574/Zero",fontsize=10,color="white",style="solid",shape="box"];10709 -> 11156[label="",style="solid", color="burlywood", weight=9];
67.83/34.97	11156 -> 10713[label="",style="solid", color="burlywood", weight=3];
67.83/34.97	10770[label="vuz549000",fontsize=16,color="green",shape="box"];10771[label="vuz542000",fontsize=16,color="green",shape="box"];10772[label="vuz549000",fontsize=16,color="green",shape="box"];10773[label="vuz542000",fontsize=16,color="green",shape="box"];10769[label="primModNatS0 (Succ vuz594) (Succ vuz595) (primGEqNatS vuz596 vuz597)",fontsize=16,color="burlywood",shape="triangle"];11157[label="vuz596/Succ vuz5960",fontsize=10,color="white",style="solid",shape="box"];10769 -> 11157[label="",style="solid", color="burlywood", weight=9];
67.83/34.97	11157 -> 10802[label="",style="solid", color="burlywood", weight=3];
67.83/34.97	11158[label="vuz596/Zero",fontsize=10,color="white",style="solid",shape="box"];10769 -> 11158[label="",style="solid", color="burlywood", weight=9];
67.83/34.97	11158 -> 10803[label="",style="solid", color="burlywood", weight=3];
67.83/34.97	10452 -> 10382[label="",style="dashed", color="red", weight=0];
67.83/34.97	10452[label="primModNatS (primMinusNatS (Succ vuz549000) Zero) (Succ Zero)",fontsize=16,color="magenta"];10452 -> 10467[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	10452 -> 10468[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	10453[label="Succ Zero",fontsize=16,color="green",shape="box"];10454 -> 10382[label="",style="dashed", color="red", weight=0];
67.83/34.97	10454[label="primModNatS (primMinusNatS Zero Zero) (Succ Zero)",fontsize=16,color="magenta"];10454 -> 10469[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	10454 -> 10470[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	10712[label="primMinusNatS (Succ vuz5740) vuz575",fontsize=16,color="burlywood",shape="box"];11159[label="vuz575/Succ vuz5750",fontsize=10,color="white",style="solid",shape="box"];10712 -> 11159[label="",style="solid", color="burlywood", weight=9];
67.83/34.97	11159 -> 10745[label="",style="solid", color="burlywood", weight=3];
67.83/34.97	11160[label="vuz575/Zero",fontsize=10,color="white",style="solid",shape="box"];10712 -> 11160[label="",style="solid", color="burlywood", weight=9];
67.83/34.97	11160 -> 10746[label="",style="solid", color="burlywood", weight=3];
67.83/34.97	10713[label="primMinusNatS Zero vuz575",fontsize=16,color="burlywood",shape="box"];11161[label="vuz575/Succ vuz5750",fontsize=10,color="white",style="solid",shape="box"];10713 -> 11161[label="",style="solid", color="burlywood", weight=9];
67.83/34.97	11161 -> 10747[label="",style="solid", color="burlywood", weight=3];
67.83/34.97	11162[label="vuz575/Zero",fontsize=10,color="white",style="solid",shape="box"];10713 -> 11162[label="",style="solid", color="burlywood", weight=9];
67.83/34.97	11162 -> 10748[label="",style="solid", color="burlywood", weight=3];
67.83/34.97	10802[label="primModNatS0 (Succ vuz594) (Succ vuz595) (primGEqNatS (Succ vuz5960) vuz597)",fontsize=16,color="burlywood",shape="box"];11163[label="vuz597/Succ vuz5970",fontsize=10,color="white",style="solid",shape="box"];10802 -> 11163[label="",style="solid", color="burlywood", weight=9];
67.83/34.97	11163 -> 10804[label="",style="solid", color="burlywood", weight=3];
67.83/34.97	11164[label="vuz597/Zero",fontsize=10,color="white",style="solid",shape="box"];10802 -> 11164[label="",style="solid", color="burlywood", weight=9];
67.83/34.97	11164 -> 10805[label="",style="solid", color="burlywood", weight=3];
67.83/34.97	10803[label="primModNatS0 (Succ vuz594) (Succ vuz595) (primGEqNatS Zero vuz597)",fontsize=16,color="burlywood",shape="box"];11165[label="vuz597/Succ vuz5970",fontsize=10,color="white",style="solid",shape="box"];10803 -> 11165[label="",style="solid", color="burlywood", weight=9];
67.83/34.97	11165 -> 10806[label="",style="solid", color="burlywood", weight=3];
67.83/34.97	11166[label="vuz597/Zero",fontsize=10,color="white",style="solid",shape="box"];10803 -> 11166[label="",style="solid", color="burlywood", weight=9];
67.83/34.97	11166 -> 10807[label="",style="solid", color="burlywood", weight=3];
67.83/34.97	10467 -> 10390[label="",style="dashed", color="red", weight=0];
67.83/34.97	10467[label="primMinusNatS (Succ vuz549000) Zero",fontsize=16,color="magenta"];10467 -> 10482[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	10468[label="Zero",fontsize=16,color="green",shape="box"];10469 -> 10392[label="",style="dashed", color="red", weight=0];
67.83/34.97	10469[label="primMinusNatS Zero Zero",fontsize=16,color="magenta"];10470[label="Zero",fontsize=16,color="green",shape="box"];10745[label="primMinusNatS (Succ vuz5740) (Succ vuz5750)",fontsize=16,color="black",shape="box"];10745 -> 10755[label="",style="solid", color="black", weight=3];
67.83/34.97	10746[label="primMinusNatS (Succ vuz5740) Zero",fontsize=16,color="black",shape="box"];10746 -> 10756[label="",style="solid", color="black", weight=3];
67.83/34.97	10747[label="primMinusNatS Zero (Succ vuz5750)",fontsize=16,color="black",shape="box"];10747 -> 10757[label="",style="solid", color="black", weight=3];
67.83/34.97	10748[label="primMinusNatS Zero Zero",fontsize=16,color="black",shape="box"];10748 -> 10758[label="",style="solid", color="black", weight=3];
67.83/34.97	10804[label="primModNatS0 (Succ vuz594) (Succ vuz595) (primGEqNatS (Succ vuz5960) (Succ vuz5970))",fontsize=16,color="black",shape="box"];10804 -> 10808[label="",style="solid", color="black", weight=3];
67.83/34.97	10805[label="primModNatS0 (Succ vuz594) (Succ vuz595) (primGEqNatS (Succ vuz5960) Zero)",fontsize=16,color="black",shape="box"];10805 -> 10809[label="",style="solid", color="black", weight=3];
67.83/34.97	10806[label="primModNatS0 (Succ vuz594) (Succ vuz595) (primGEqNatS Zero (Succ vuz5970))",fontsize=16,color="black",shape="box"];10806 -> 10810[label="",style="solid", color="black", weight=3];
67.83/34.97	10807[label="primModNatS0 (Succ vuz594) (Succ vuz595) (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];10807 -> 10811[label="",style="solid", color="black", weight=3];
67.83/34.97	10482[label="vuz549000",fontsize=16,color="green",shape="box"];10755 -> 10709[label="",style="dashed", color="red", weight=0];
67.83/34.97	10755[label="primMinusNatS vuz5740 vuz5750",fontsize=16,color="magenta"];10755 -> 10765[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	10755 -> 10766[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	10756[label="Succ vuz5740",fontsize=16,color="green",shape="box"];10757[label="Zero",fontsize=16,color="green",shape="box"];10758[label="Zero",fontsize=16,color="green",shape="box"];10808 -> 10769[label="",style="dashed", color="red", weight=0];
67.83/34.97	10808[label="primModNatS0 (Succ vuz594) (Succ vuz595) (primGEqNatS vuz5960 vuz5970)",fontsize=16,color="magenta"];10808 -> 10812[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	10808 -> 10813[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	10809[label="primModNatS0 (Succ vuz594) (Succ vuz595) True",fontsize=16,color="black",shape="triangle"];10809 -> 10814[label="",style="solid", color="black", weight=3];
67.83/34.97	10810[label="primModNatS0 (Succ vuz594) (Succ vuz595) False",fontsize=16,color="black",shape="box"];10810 -> 10815[label="",style="solid", color="black", weight=3];
67.83/34.97	10811 -> 10809[label="",style="dashed", color="red", weight=0];
67.83/34.97	10811[label="primModNatS0 (Succ vuz594) (Succ vuz595) True",fontsize=16,color="magenta"];10765[label="vuz5740",fontsize=16,color="green",shape="box"];10766[label="vuz5750",fontsize=16,color="green",shape="box"];10812[label="vuz5970",fontsize=16,color="green",shape="box"];10813[label="vuz5960",fontsize=16,color="green",shape="box"];10814 -> 10382[label="",style="dashed", color="red", weight=0];
67.83/34.97	10814[label="primModNatS (primMinusNatS (Succ vuz594) (Succ vuz595)) (Succ (Succ vuz595))",fontsize=16,color="magenta"];10814 -> 10816[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	10814 -> 10817[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	10815[label="Succ (Succ vuz594)",fontsize=16,color="green",shape="box"];10816 -> 10709[label="",style="dashed", color="red", weight=0];
67.83/34.97	10816[label="primMinusNatS (Succ vuz594) (Succ vuz595)",fontsize=16,color="magenta"];10816 -> 10818[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	10816 -> 10819[label="",style="dashed", color="magenta", weight=3];
67.83/34.97	10817[label="Succ vuz595",fontsize=16,color="green",shape="box"];10818[label="Succ vuz594",fontsize=16,color="green",shape="box"];10819[label="Succ vuz595",fontsize=16,color="green",shape="box"];}
67.83/34.97	
67.83/34.97	----------------------------------------
67.83/34.97	
67.83/34.97	(489)
67.83/34.97	TRUE
67.83/34.99	EOF